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1
Loerx, Andre, and Ekkehard W. Sachs. "Model Calibration in Option Pricing." Sultan Qaboos University Journal for Science [SQUJS] 16 (April 1, 2012): 84. http://dx.doi.org/10.24200/squjs.vol17iss1pp84-102.
Testo completoAbstract (sommario):
We consider calibration problems for models of pricing derivatives which occur in mathematical finance. We discuss various approaches such as using stochastic differential equations or partial differential equations for the modeling process. We discuss the development in the past literature and give an outlook into modern approaches of modelling. Furthermore, we address important numerical issues in the valuation of options and likewise the calibration of these models. This leads to interesting problems in optimization, where, e.g., the use of adjoint equations or the choice of the parametrization for the model parameters play an important role.
2
HUEHNE, FLORIAN. "DEFAULTABLE LÉVY LIBOR RATES AND CREDIT DERIVATIVES." International Journal of Theoretical and Applied Finance 10, no. 03 (May 2007): 407–35. http://dx.doi.org/10.1142/s0219024907004172.
Testo completoAbstract (sommario):
We introduce the intensity-based defaultable Lévy Libor model, which generalizes the default-free Lévy Libor model introduced by Eberlein and Özkan in [The defaultable Lévy term structure: Ratings and restructuring, Mathematical Finance13(2) (2003) 277–300], and the intensity-based defaultable model presented by Bielecki and Rutkowski in [Credit Risk: Modeling, Valuation and Hedging, Springer Finance (Springer-Verlag, 2002)] by embedding it in the defaultable HJM framework introduced by Eberlein and Özkan in [The defaultable Lévy term structure: Ratings and restructuring, Mathematical Finance13(2) (2003) 277–300]. We also derive some additional results for defaultable HJM models such as the dynamics of credit spreads. We then go on and model the default-free Libor rates and credit spreads as the primal variable and derive the dynamics of the defaultable Libor rates under the defaultable forward measure. Finally, we derive an explicit formula for options on credit default swaps, using an idea introduced by Raible in [Lévy Processes in finance: Theory, numerics and empirical facts, PhD thesis, University of Freiburg i. Brsg. (2000)].
3
Giribone, Pier Giuseppe, and Roberto Revetria. "Certificate pricing using Discrete Event Simulations and System Dynamics theory." Risk Management Magazine 16, no. 2 (August 18, 2021): 75–93. http://dx.doi.org/10.47473/2020rmm0092.
Testo completoAbstract (sommario):
The study proposes an innovative application of Discrete Event Simulations (DES) and System Dynamics (SD) theory to the pricing of a certain kind of certificates very popular among private investors and, more generally, in the context of wealth management. The paper shows how numerical simulation software mainly used in traditional engineering, such as industrial and mechanical engineering, can be successfully adapted to the risk analysis of structured financial products. The article can be divided into three macro-sections: in the first part a synthetic overview of the most widespread option pricing models in the quantitative finance branch is given to the readers together with the fundamental technical-instrumental background of the implemented DES and SD simulator. After dealing with some of the most popular models adopted for Equity and Equity index options, which are the most common underlying assets for the certificates structuring, we move, in the second part, to describe how the mathematical models can be integrated into a general simulation environment able to provide both DES and SD extensively used in the engineering field. The core stochastic differential equation (SDE) will therefore be translated, together with all its input parameters, into a visual block model which allows an immediate quantitative analysis of how market parameters and the other model variables can change over time. The possibility for the structurer to observe how the variables evolve day-by-day gives a strong sensitivity to evaluate how the price and the associated risk measures can be directly affected. The third part of the study compares the results obtained from the simulator designed by the authors with the more traditional pricing approaches, which consist in programming Matlab® codes for the numerical integration of the core stochastic dynamics through a Euler-Maruyama scheme. The comparison includes a price check using the Bloomberg® DLIB pricing module and a check directly against the valuation provided by the counterparty. In this section, real market cases will therefore be examined with a complete quantitative analysis of two of the most widespread categories of certificates in wealth management: Multi-asset Barrier Reverse Convertible with Issuer Callability and Multi-asset Express Certificate with conditional memory fixed coupon.
4
LORENZO, MERCURI. "PRICING ASIAN OPTIONS IN AFFINE GARCH MODELS." International Journal of Theoretical and Applied Finance 14, no. 02 (March 2011): 313–33. http://dx.doi.org/10.1142/s0219024911006371.
Testo completoAbstract (sommario):
We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case.
5
CHU, CHI CHIU, and YUE KUEN KWOK. "VALUATION OF GUARANTEED ANNUITY OPTIONS IN AFFINE TERM STRUCTURE MODELS." International Journal of Theoretical and Applied Finance 10, no. 02 (March 2007): 363–87. http://dx.doi.org/10.1142/s0219024907004160.
Testo completoAbstract (sommario):
We propose three analytic approximation methods for numerical valuation of the guaranteed annuity options in deferred annuity pension policies. The approximation methods include the stochastic duration approach, Edgeworth expansion, and analytic approximation in affine diffusions. The payoff structure in the annuity policies is similar to a quanto call option written on a coupon-bearing bond. To circumvent the limitations of the one-factor interest rate model, we model the interest rate dynamics by a two-factor affine interest rate term structure model. The numerical accuracy and the computational efficiency of these approximation methods are analyzed. We also investigate the value sensitivity of the guaranteed annuity option with respect to different parameters in the pricing model.
6
Dassios, Angelos, and Shanle Wu. "Double-Barrier Parisian Options." Journal of Applied Probability 48, no. 01 (March 2011): 1–20. http://dx.doi.org/10.1017/s0021900200007592.
Testo completoAbstract (sommario):
In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.
7
Dassios, Angelos, and Shanle Wu. "Double-Barrier Parisian Options." Journal of Applied Probability 48, no. 1 (March 2011): 1–20. http://dx.doi.org/10.1239/jap/1300198132.
Testo completoAbstract (sommario):
In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.
8
Kamińska, Barbara. "Options in Corporate Finance Management." Przedsiebiorczosc i Zarzadzanie 15, no. 1 (January 1, 2014): 69–81. http://dx.doi.org/10.2478/eam-2014-0005.
Testo completoAbstract (sommario):
Abstract Although there are many opinions critical of options, especially after the 2008 scandal, they are becoming increasingly popular in Poland again. Therefore, issues connected with options are not only the subject of interest in academic circles again but also arouse interest of economic entities, allowing enterprises to assess a variety of action strategies. Those instruments enable planning safeguards to protect against various negative future scenarios. Hence, it comes as no surprise that there has been an increase in the number and variety of enterprises that have accepted options as a way to plan for their future. The article provides a brief presentation of options. It also describes one of their pricing methods. Light of the foregoing has been hypothesized that 'valuation of options using mathematical calculators using the binomial model is an effective tool for supporting management positions in futures instruments’.
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Ciurlia, Pierangelo, and Andrea Gheno. "Pricing and Applications of Digital Installment Options." Journal of Applied Mathematics 2012 (2012): 1–21. http://dx.doi.org/10.1155/2012/584705.
Testo completoAbstract (sommario):
For its theoretical interest and strong impact on financial markets, option valuation is considered one of the cornerstones of contemporary mathematical finance. This paper specifically studies the valuation of exotic options with digital payoff and flexible payment plan. By means of the Incomplete Fourier Transform, the pricing problem is solved in order to find integral representations of the upfront price for European call and put options. Several applications in the areas of corporate finance, insurance, and real options are discussed. Finally, a new type of digital derivative named supercash option is introduced and some payment schemes are also presented.
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ZEGHAL, AMINA BOUZGUENDA, and MOHAMED MNIF. "OPTIMAL MULTIPLE STOPPING AND VALUATION OF SWING OPTIONS IN LÉVY MODELS." International Journal of Theoretical and Applied Finance 09, no. 08 (December 2006): 1267–97. http://dx.doi.org/10.1142/s0219024906004037.
Testo completoAbstract (sommario):
In this paper, we extend the results of Carmona and Touzi [6] for an optimal multiple stopping problem to a market where the price process is allowed to jump. We also generalize the problem of valuation swing options to the context of a Lévy market. We prove the existence of multiple exercise policies under an additional condition on Snell envelops. This condition emerges naturally in the case of Lévy processes. Then, we give a constructive solution for perpetual put swing options when the price process has no negative jumps. We use the Monte Carlo approximation method based on Malliavin calculus in order to solve the finite horizon case. Numerical results are given in the last two sections. We illustrate the theoretical results of the perpetual case and give the numerical solution for the finite horizon case.
11
Wu, Ting-Pin, and Son-Nan Chen. "Analytical Valuation of Barrier Interest Rate Options Under Market Models." Journal of Derivatives 17, no. 1 (August 31, 2009): 21–37. http://dx.doi.org/10.3905/jod.2009.17.1.021.
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Wang, Xingchun. "Valuation of Asian options with default risk under GARCH models." International Review of Economics & Finance 70 (November 2020): 27–40. http://dx.doi.org/10.1016/j.iref.2020.06.019.
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Dorion, Christian. "Option Valuation with Macro-Finance Variables." Journal of Financial and Quantitative Analysis 51, no. 4 (August 2016): 1359–89. http://dx.doi.org/10.1017/s0022109016000442.
Testo completoAbstract (sommario):
I propose a model in which the price of an option is partly determined by macro-finance variables. In an application using an index of current business conditions, the new model outperforms existing benchmarks in fitting underlying asset returns and in pricing options. The model performs particularly well when business conditions are deteriorating. Using the recent financial crisis as an out-of-sample experiment, the new model has option-pricing errors that are 18% below those of a nested 2-component volatility benchmark. Results are robust to using alternative business conditions proxies and comparing to different benchmark models.
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Eales, James, and Robert J. Hauser. "Analyzing biases in valuation models of options on futures." Journal of Futures Markets 10, no. 3 (June 1990): 211–28. http://dx.doi.org/10.1002/fut.3990100302.
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Bollen, Nicolas P. B., and Emma Rasiel. "The performance of alternative valuation models in the OTC currency options market." Journal of International Money and Finance 22, no. 1 (February 2003): 33–64. http://dx.doi.org/10.1016/s0261-5606(02)00073-6.
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Cao, Hongkai, Alexandru Badescu, Zhenyu Cui, and Sarath Kumar Jayaraman. "Valuation of VIX and target volatility options with affine GARCH models." Journal of Futures Markets 40, no. 12 (September 2020): 1880–917. http://dx.doi.org/10.1002/fut.22157.
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ERIKSSON, BJORN, and MARTIJN PISTORIUS. "METHOD OF MOMENTS APPROACH TO PRICING DOUBLE BARRIER CONTRACTS IN POLYNOMIAL JUMP-DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 14, no. 07 (November 2011): 1139–58. http://dx.doi.org/10.1142/s0219024911006644.
Testo completoAbstract (sommario):
We present a method of moments approach to pricing double barrier contracts when the underlying is modelled by a polynomial jump-diffusion. By general principles the price is linked to certain infinite dimensional linear programming problems. Subsequently approximating these by finite dimensional linear programming problems, upper and lower bounds for the prices of such options are found. We derive theoretical convergence results for this algorithm, and provide numerical illustrations by applying the method to the valuation of several double barrier-type contracts (double barrier knock-out call, American corridor and double-no-touch options) under a number of different models, also allowing for a deterministic short rate.
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Vimpari, Jussi, and Seppo Junnila. "Valuing retail lease options through time." Journal of Property Investment & Finance 35, no. 4 (July 3, 2017): 369–81. http://dx.doi.org/10.1108/jpif-05-2016-0036.
Testo completoAbstract (sommario):
Purpose Retail properties are a perfect example of a property class where revenues determine the rent for the property owners. Estimating the value of new retail developments is challenging, as the initial revenues can have a significant variance from the long-term revenue levels. Owners and tenants try to manage this problem by introducing different kind of options, such as overage rent and extension rights, to the lease contracts. The purpose of this paper is to value these options through time for different types of retailers, using real-life data with a method that can be easily applied in practice. Design/methodology/approach This paper builds upon the existing papers on real option studies but has a strong practical focus, which has been identified as a challenge in the field. The paper presents simple mathematical equations for valuing overage rent and extension options. The equations capture the value related to uncertainty (volatility) that is missed by standard valuation practices. Findings The results indicate that overage and extension options can represent a significant proportion of retail lease contract’s value and their value is heavily time-dependent. The option values differ greatly between tenants, as the volatilities can have a large spread across tenants. The paper suggests that the applicability of option pricing theory and calculus should not be considered as an insurmountable barrier any more, rather a greater challenge for the practical adaptability of the method can be the availability of real-life data that is a common problem in real option analysis. Practical implications The value of extension and overage options varies greatly between tenants. In general, the property owner can try balance the positive effects from the overage rents to the negative effects of tenant extensions. However, this study tries to highlight that, as usual, using the “law of averages” can result into poor valuation in this context as well. Even the data used in this study provide valuable findings for the property owner as an analytical deduction can be made that certain types of tenants have higher volatilities and this should be acknowledged when valuing options within lease contracts. Originality/value Previous literature in this topic often takes the input data for the option valuation as granted rather than trying to identify the real-life data available for the calculation. This is a common problem in real options valuation and it seems to be one of the reasons why option valuation has not been used widely in practice. This study has used real-life data to assess the problem and more importantly assessed the data across different types of tenants. The volatility spread between different types of tenants has not been discussed previously, even though it has a significant importance when using option pricing in practice.
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Miller, Tom W. "Terminal values for firms with growth opportunities: explaining valuation and IPO price behavior." Studies in Economics and Finance 35, no. 2 (June 4, 2018): 244–72. http://dx.doi.org/10.1108/sef-03-2016-0078.
Testo completoAbstract (sommario):
PurposeThe purpose of this paper is to use fundamental models incorporating structural relationships within the firm in a terminal value model for the second stage of a two-stage valuation model utilized to estimate the value of a company.Design/methodology/approachThe innovation is that growth options are identified within the structural relationships and a model capturing the value of the optionality is incorporated in the second stage of the two-stage valuation model.FindingsSignificant outcomes are that terminal value is shown to be a large portion of a company’s total value and the price behavior for initial public offerings produced by the model is consistent with the result of empirical studies.Originality/valueThis paper explicitly incorporates growth options in the second stage of a two-stage valuation model for the firm.
20
BENTH, FRED ESPEN, and RODWELL KUFAKUNESU. "PRICING OF EXOTIC ENERGY DERIVATIVES BASED ON ARITHMETIC SPOT MODELS." International Journal of Theoretical and Applied Finance 12, no. 04 (June 2009): 491–506. http://dx.doi.org/10.1142/s0219024909005324.
Testo completoAbstract (sommario):
Based on a non-Gaussian Ornstein–Uhlenbeck model for energy spot, we derive prices for Asian and spread options using Fourier techniques. The option prices are expressed in terms of the Fourier transform of the payoff function and the characteristic functions of the driving noises, being independent increment processes. In many relevant situations, these functions are explicitly available, and fast Fourier transform can be used for efficient numerical valuation. The arithmetic nature of our model implies that only a one-dimensional Fourier transform is required in the computation of the price, contrary to geometric models where transformation along both underlying variables is necessary.
21
Wang, Xingchun. "Analytical valuation of Asian options with counterparty risk under stochastic volatility models." Journal of Futures Markets 40, no. 3 (October 14, 2019): 410–29. http://dx.doi.org/10.1002/fut.22064.
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Tajani, Francesco, Pierluigi Morano, and Klimis Ntalianis. "Automated valuation models for real estate portfolios." Journal of Property Investment & Finance 36, no. 4 (July 2, 2018): 324–47. http://dx.doi.org/10.1108/jpif-10-2017-0067.
Testo completoAbstract (sommario):
Purpose As regards the assessment of the market values of properties that compose real estate portfolios, the purpose of this paper is to propose and test an automated valuation model. In particular, the method defined allows for providing for objective, reliable and “quick” valuations of the assets in the phases of periodic reviews of the property values. Design/methodology/approach Aiming at both predictive and interpretative purposes, the method, based on multi-objective genetic algorithms to search those model expressions that simultaneously maximize the accuracy of the data and the parsimony of the mathematical functions, is applied to a sample data of office properties characterized by medium and large size, located in the city of Milan (Italy) and sold in the period between 2004 and 2015. Findings The model obtained could be an integration of the canonical methodologies (market approach, income approach, cost approach) implemented in the assessment of the market values of properties, so as to provide an additional tool to verify the results. In particular, the inclusion of economic variables in the model is consistent with the need to reiterate the valuations, contextualizing them to the locational characteristics and to the current property cycle phase in the specific area. Practical implications The model can be applied by all the operators involved in the periodic reviews of the values of property portfolios: from real estate funds’ insiders, in order to monitor the values obtained through the canonical approaches, to the public institutions, such as the revenue agencies, in order to ensure the fair payment of the taxes through the updating values of the properties according to the actual and current market trends. Originality/value The method proposed can be a valid support for all public and private entities that hold significant property assets and that, for various reasons (periodic reviews of the balance sheets, sales, enhancement, investment, etc.), require cyclical updated values of the properties. The automated valuation model developed can be used for the assessment of “comparison” values with the estimates values obtained by other assessment techniques, in order to ensure a further monitoring tool of the results from the subjects involved.
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CARMONA, RENÉ, and SERGEY NADTOCHIY. "TANGENT MODELS AS A MATHEMATICAL FRAMEWORK FOR DYNAMIC CALIBRATION." International Journal of Theoretical and Applied Finance 14, no. 01 (February 2011): 107–35. http://dx.doi.org/10.1142/s0219024911006280.
Testo completoAbstract (sommario):
Motivated by the desire to integrate repeated calibration procedures into a single dynamic market model, we introduce the notion of a "tangent model" in an abstract set up, and we show that this new mathematical paradigm accommodates all the recent attempts to study consistency and absence of arbitrage in market models. For the sake of illustration, we concentrate on the case when market quotes provide the prices of European call options for a specific set of strikes and maturities. While reviewing our recent results on dynamic local volatility and tangent Lévy models, we present a theory of tangent models unifying these two approaches and construct a new class of tangent Lévy models, which allows the underlying to have both continuous and pure jump components.
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Core, John E., Wayne R. Guay, and S. P. Kothari. "The Economic Dilution of Employee Stock Options: Diluted EPS for Valuation and Financial Reporting." Accounting Review 77, no. 3 (July 1, 2002): 627–52. http://dx.doi.org/10.2308/accr.2002.77.3.627.
Testo completoAbstract (sommario):
In this paper, we derive a measure of diluted EPS that incorporates the economic implications of the dilutive effects of employee stock options. We show that the existing FASB treasury-stock method of accounting for the dilutive effects of outstanding options systematically understates the options' dilutive effect, and thus overstates reported EPS. Using firm-wide data on 731 employee stock option plans, our proposed measure suggests that economic dilution from options is, on average, 100 percent greater than dilution in reported diluted EPS using the FASB treasury-stock method. We examine the implications of our analysis for stock price valuation, the price-earnings relation, and the return-earnings relation. We demonstrate analytically that when firms have options outstanding, empirical applications of equity valuation models that use reported per-share earnings as an input (e.g., Ohlson 1995) yield upwardly biased estimates of the market value of common stock. We predict that when the difference between our measure of economic dilution from options and the FASB treasury-stock method dilution from options is greater, the observed return-earnings and price-earnings coefficients will be smaller, and we provide some (albeit weak) empirical support for this prediction.
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Wang, Xingchun. "Valuation of options on the maximum of two prices with default risk under GARCH models." North American Journal of Economics and Finance 57 (July 2021): 101422. http://dx.doi.org/10.1016/j.najef.2021.101422.
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Massironi, Carlo. "Philip Fisher’s sense of numbers." Qualitative Research in Financial Markets 6, no. 3 (November 10, 2014): 302–31. http://dx.doi.org/10.1108/qrfm-01-2013-0004.
Testo completoAbstract (sommario):
Purpose – This paper aims to propose an account of the use of numbers and mathematical formulae and, more generally, of the quantitative aspects in the qualitative equity valuation model of the American investor Philip A. Fisher who is considered to be one of the fathers of the qualitative equity valuation models. Design/methodology/approach – A Conceptual analysis was conducted (Glasersfeld, 1992) of the four volumes published by Fisher between 1954 and 1980 (1958, 1960, 1975, 1980) in relation to his equity valuation process. On the basis of this analysis, a modelization of this author’s perspective on quantitative instruments was built. Findings – A modelization to use quantitative data in a qualitative equity valuation model that is sufficiently detailed and useful for an asset manager is proposed. Originality/value – What is propose is a qualitative analysis of quantitative elements in the thought of a qualitative author on the subject of equity valuation. It is believed that this paper could be of interest to all those who use or are involved in the development of qualitative models of equity valuation or business valuation. This work is also an example of how conceptual analysis – generally employed in the field of mathematics education research – can be used to build descriptive models of decision-making processes of individual investors, models designed to enable the reproduction/approximation of the conceptual operations of the investor.
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French, Nick, and Laura Gabrielli. "Pricing to market." Journal of Property Investment & Finance 36, no. 4 (July 2, 2018): 391–96. http://dx.doi.org/10.1108/jpif-05-2018-0033.
Testo completoAbstract (sommario):
Purpose Since the global financial economic crisis hit the world markets in 2007/2008, the role of property valuation has been under greater and greater scrutiny. The process of valuation and its quality assurance has been addressed by the higher prominence of the International Valuation Standards Council (IVSC). This is a significant initiative worldwide. However, there has been little written on the appropriate use of valuation approaches and methods in market valuations. There is now a hierarchy of valuation definitions. In order, there are valuation approaches, valuation methods and, as a subset of the methods, techniques or models. The purpose of this paper is to look at the importance of identifying the appropriate approach to be adopted in market valuations and the methods, techniques and models that should be applied to determine market value. Design/methodology/approach This practice briefing is an overview of the valuation approaches, methods and models available to the valuer and comments on the appropriateness of valuation each in assessing market value. Findings This paper reviews the IVSC-recognised approaches and prompts the valuer to be careful with the semantics involved so that they are better placed to provide an unambiguous service to their clients. Practical implications The role of the valuer in practice is to identify the appropriate approach for the valuation of the subject property, choose the right method and then apply the correct mathematical model for the valuation task in hand. Originality/value This provides guidance on how valuations can be presented to the client in accordance with the International Valuation Standards.
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CUTHBERTSON, CHARLES, GRIGORIOS PAVLIOTIS, AVRAAM RAFAILIDIS, and PETTER WIBERG. "ASYMPTOTIC ANALYSIS FOR FOREIGN EXCHANGE DERIVATIVES WITH STOCHASTIC VOLATILITY." International Journal of Theoretical and Applied Finance 13, no. 07 (November 2010): 1131–47. http://dx.doi.org/10.1142/s0219024910006145.
Testo completoAbstract (sommario):
We consider models for the valuation of derivative securities that depend on foreign exchange rates. We derive partial differential equations for option prices in an arbitrage-free market with stochastic volatility. By use of standard techniques, and under the assumption of fast mean reversion for the volatility, these equations can be solved asymptotically. The analysis goes further to consider specific examples for a number of options, and to a considerable degree of complexity.
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SIDENIUS, JAKOB, VLADIMIR PITERBARG, and LEIF ANDERSEN. "A NEW FRAMEWORK FOR DYNAMIC CREDIT PORTFOLIO LOSS MODELLING." International Journal of Theoretical and Applied Finance 11, no. 02 (March 2008): 163–97. http://dx.doi.org/10.1142/s0219024908004762.
Testo completoAbstract (sommario):
We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two-layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This background process can be explicitly calibrated to the full grid of marginal loss distributions as implied by initial CDO tranche values indexed on maturity, as well as to the prices of suitable options. We give sufficient conditions for consistent dynamics. The second layer models the loss process itself as a Markov process conditioned on the path taken by the background process. The choice of loss process is non-unique. We present a number of choices, and discuss their advantages and disadvantages. Several concrete model examples are given, and valuation in the new framework is described in detail. Among the specific securities for which algorithms are presented are CDO tranche options and leveraged super-senior tranches.
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Cakici, Nusret, Sris Chatterjee, and Avner Wolf. "Empirical tests of valuation models for options on t-note and t-bond futures." Journal of Futures Markets 13, no. 1 (February 1993): 1–13. http://dx.doi.org/10.1002/fut.3990130102.
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d’Amato, Maurizio. "Supporting property valuation with automatic reconciliation." Journal of European Real Estate Research 11, no. 1 (May 8, 2018): 125–38. http://dx.doi.org/10.1108/jerer-01-2017-0005.
Testo completoAbstract (sommario):
Purpose Valuation is a professional activity based on international and local standards. In the valuation process more than one method can be modified. In this case, a final reconciliation of different opinions of value may be required. It is a matter of fact that the final result of these different valuation methods may vary. Therefore, in the final part of the valuation process, the valuer is required to assign a weight to the different methodologies to reach an appropriate opinion of value. This process is essentially based on valuer’s expertise. This paper aims to propose an automatic procedure of calculating the weights to assist the valuer in the valuation process. Design/methodology/approach The work provides methodologies to assign the weights through simple mathematical procedures that can be used to support subjective judgement in the valuation process. The models proposed can be applied to other phases of reconciliation inside the valuation process and are based on the collection of previous property data in the same market segment. Findings Two different methodologies are proposed to support valuers in the valuation process and in particular in the phase of the choice of the weights for final reconciliation purposes. Research limitations/implications The implication is the development of an information system to support the appraiser in providing these weights. The models proposed are only two but represent a future, much larger field of research. Practical implications The models may help in determining more consistent valuation reports. Social implications Consistent valuation reports for the determination of mortgage lending value may contribute to the stability of the social and economic system, especially after the 2008 non-agency mortgage crisis. Originality/value These are original models proposed in literature for such kind of problems.
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Manola, Ana, and Branko Urosevic. "Option-based valuation of mortgage-backed securities." Ekonomski anali 55, no. 186 (2010): 42–66. http://dx.doi.org/10.2298/eka1086042m.
Testo completoAbstract (sommario):
Pure econometric approaches to pricing mortgage-backed securities (MBSs) - principal pricing vehicles used by financial practitioners - fail to capture their true risks. This point was powerfully driven home by the global financial crisis. Since prior to the crisis default rates of MBSs were quite modest, econometric pricing models systematically underestimated the possibility of default. As a result, MBSs were severely overvalued. It is widely believed that the global crisis was largely triggered by incorrect valuation of mortgage-backed securities. In the aftermath, it is important to revisit the foundations for pricing MBSs and to pay much closer attention to default risk. This paper introduces a comprehensive model for valuation of fixed-rate pass-through mortgagebacked securities in a simple option-based framework. In the model, we use bivariate binomial tree approach to simultaneously model prepayment and default options. Our simulation results demonstrate that the proposed model has sufficient flexibility to capture the two principal risks.
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Lindström, Erik. "Implications of Parameter Uncertainty on Option Prices." Advances in Decision Sciences 2010 (May 5, 2010): 1–15. http://dx.doi.org/10.1155/2010/598103.
Testo completoAbstract (sommario):
Financial markets are complex processes where investors interact to set prices. We present a framework for option valuation under imperfect information, taking risk neutral parameter uncertainty into account. The framework is a direct generalization of the existing valuation methodology. Many investors base their decisions on mathematical models that have been calibrated to market prices. We argue that the calibration process introduces a source of uncertainty that needs to be taken into account. The models and parameters used may differ to such extent that one investor may find an option underpriced; whereas another investor may find the very same option overpriced. This problem is not taken into account by any of the standard models. The paper is concluded by presenting simulations and an empirical study on FX options, where we demonstrate improved predictive performance (in sample and out of sample) using this framework.
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Behera, Prashanta kumar, and Dr Ramraj T. Nadar. "Dynamic Approach for Index Option Pricing Using Different Models." Journal of Global Economy 13, no. 2 (June 26, 2017): 105–20. http://dx.doi.org/10.1956/jge.v13i2.460.
Testo completoAbstract (sommario):
Option pricing is one of the exigent and elementary problems of computational finance. Our aims to determine the nifty index option price through different valuation technique. In this paper, we illustrate the techniques for pricing of options and extracting information from option prices. We also describe various ways in which this information has been used in a number of applications. When dealing with options, we inevitably encounter the Black-Scholes-Merton option pricing formula, which has revolutionized the way in which options are priced in modern time. Black and Scholes (1973) and Merton (1973) on pricing European style options assumes that stock price follows a geometric Brownian motion, which implies that the terminal stock price has a lognormal distribution. Through hedging arguments, BSM shows that the terminal stock price distribution needed for pricing option can be stated without reference to the preference parameter and to the growth rate of the stock. This is now known as the risk-neutral approach to option pricing. The terminal stock price distribution, for the purpose of pricing options, is now known as the state-price density or the risk-neutral density in contrast to the actual stock price distribution, which is sometimes referred to as the physical, objective, or historical distribution.
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Mintah, Kwabena, David Higgins, Judith Callanan, and Ron Wakefield. "Staging option application to residential development: real options approach." International Journal of Housing Markets and Analysis 11, no. 1 (February 5, 2018): 101–16. http://dx.doi.org/10.1108/ijhma-02-2017-0022.
Testo completoAbstract (sommario):
Purpose Real option valuation is capable of accounting for uncertainties in residential development projects but still lacks practical adoption due to limited evidence to support application of the theory in practice. The purpose of this paper is to use option valuation to value staging option embedded in residential projects and compare with results from DCF to determine which of the two methods delivers superior results. Design/methodology/approach The fuzzy payoff method (FPOM), a real options model that uses scenario planning approach to generate a range of figures, from which a single-numerical value is computed for decision-making. Findings The results showed that the use of a range of figures was able to represent uncertainties to a higher degree of accuracy than the static DCF. As a result, the FPOM was able to capture about 3 per cent of the value of the project that was missed by the DCF. The staging option offers an opportunity to abandon unprofitable phases of a project, thereby limiting downside losses. Thus, real option models are practically applicable to cases in property sector. Practical implications Residential property developers must consider flexibility in financial feasibility evaluation of development because of the embedded value in uncertain property projects. It is important to account for optionality in financial evaluation of property projects for value maximisation. Originality/value The FPOM has been used for the first time to evaluate a horizontal phasing of a residential development project.
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Lazzati, Natalia, and Amilcar A. Menichini. "A Dynamic Approach to the Dividend Discount Model." Review of Pacific Basin Financial Markets and Policies 18, no. 03 (September 2015): 1550018. http://dx.doi.org/10.1142/s0219091515500186.
Testo completoAbstract (sommario):
We derive a dynamic model of the firm with endogenous investment and leverage ratio within the framework of the dividend discount model (DDM). Our valuation model incorporates two relevant components, namely, managerial flexibility and long-run growth. We dispense with any utility specification capturing the preferences of shareholders and obtain closed-form solutions for the firm problem. A standard parameterization suggests that the value of the real options and long-run growth opportunities can easily represent more than 8% and 10% of share price, respectively. We also find that these two components of the stock price are both complements and countercyclical. We finally identify industries where valuation models that do not incorporate these features can lead to considerable underpricing of securities.
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TAKAHASHI, AKIHIKO, and KOHTA TAKEHARA. "A HYBRID ASYMPTOTIC EXPANSION SCHEME: AN APPLICATION TO LONG-TERM CURRENCY OPTIONS." International Journal of Theoretical and Applied Finance 13, no. 08 (December 2010): 1179–221. http://dx.doi.org/10.1142/s0219024910006169.
Testo completoAbstract (sommario):
This paper develops a general approximation scheme, henceforth called a hybrid asymptotic expansion scheme for valuation of multi-factor European path-independent derivatives. Specifically, we apply it to pricing long-term currency options under a market model of interest rates and a general diffusion stochastic volatility model with jumps of spot exchange rates. Our scheme is very effective for a type of models in which there exist correlations among all the factors whose dynamics are not necessarily affine nor even Markovian so long as the randomness is generated by Brownian motions. It can also handle models that include jump components under an assumption of their independence of the other random variables when the characteristic functions for the jump parts can be analytically obtained. An asymptotic expansion approach provides a closed-form approximation formula for their values, which can be calculated in a moment and thus can be used for calibration or for an explicit approximation of Greeks of options. Moreover, this scheme develops Fourier transform method with an asymptotic expansion as well as with closed-form characteristic functions obtainable in parts of a model, extending the method proposed by Takehara and Takahashi (2008) to be applicable to a general class of models. It also introduces a characteristic-function-based Monte Carlo simulation method with the asymptotic expansion as a control variable in order to make full use of analytical approximations by the asymptotic expansion and of the closed-form characteristic functions. Finally, a series of numerical examples shows the effectiveness of our scheme.
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LUDKOVSKI, MICHAEL, and QUNYING SHEN. "EUROPEAN OPTION PRICING WITH LIQUIDITY SHOCKS." International Journal of Theoretical and Applied Finance 16, no. 07 (November 2013): 1350043. http://dx.doi.org/10.1142/s021902491350043x.
Testo completoAbstract (sommario):
We study the valuation and hedging problem of European options in a market subject to liquidity shocks. Working within a Markovian regime-switching setting, we model illiquidity as the inability to trade. To isolate the impact of such liquidity constraints, we focus on the case where the market is completely static in the illiquid regime. We then consider derivative pricing using either equivalent martingale measures or exponential indifference mechanisms. Our main results concern the analysis of the semi-linear coupled Hamilton–Jacobi–Bellman (HJB) equation satisfied by the indifference price, as well as its asymptotics when the probability of a liquidity shock is small. A comparative analysis between the model price and the classical Black–Scholes benchmark is given using the concepts of implied and adjusted time to maturity. We then present several numerical studies of the liquidity risk premia obtained in our models leading to practical guidelines on how to adjust for liquidity risk in option valuation and hedging.
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Heidari, Massoud, and Liuren Wu. "A Joint Framework for Consistently Pricing Interest Rates and Interest Rate Derivatives." Journal of Financial and Quantitative Analysis 44, no. 3 (June 2009): 517–50. http://dx.doi.org/10.1017/s0022109009990093.
Testo completoAbstract (sommario):
AbstractDynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options. Most existing option pricing practices take the yield curve as given, thus having little to say about the fair valuation of the underlying interest rates. This paper proposes an m + n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first m factors capture the yield curve variation, whereas the latter n factors capture the interest rate options movements that cannot be effectively identified from the yield curve. We propose a sequential estimation procedure that identifies the m yield curve factors from the LIBOR and swap rates in the first step and the n options factors from interest rate caps in the second step. The three yield curve factors explain over 99% of the variation in the yield curve but account for less than 50% of the implied volatility variation for the caps. Incorporating three additional options factors improves the explained variation in implied volatilities to over 99%.
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Tahani, Nabil, and Xiaofei Li. "Pricing interest rate derivatives under stochastic volatility." Managerial Finance 37, no. 1 (January 31, 2011): 72–91. http://dx.doi.org/10.1108/03074351111092157.
Testo completoAbstract (sommario):
PurposeThe purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.Design/methodology/approachThe paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.FindingsThis paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.Research limitations/implicationsFuture research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.Practical implicationsThe valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.Originality/valueThis paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.
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Epstein, D., and P. Wilmott. "A New Model for Interest Rates." International Journal of Theoretical and Applied Finance 01, no. 02 (April 1998): 195–226. http://dx.doi.org/10.1142/s0219024998000114.
Testo completoAbstract (sommario):
There are many theories and models underlying the valuation of fixed income security portfolios. This work addresses the problem from a new perspective: the objective is to find a lower bound for the value of a portfolio of cash flows. We set up conditions for the evolution of a short-term interest rate and value a liability using its present value. We formulate a first-order nonlinear hyperbolic partial differential equation for the value, V, of the portfolio. We explore the solution of this equation and then hedge our portfolio with market-traded zero-coupon bonds of known value. We include some salient examples — generating the Yield Envelope and valuing caps, floors and bond options.
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GEORGIOPOULOS, NICK. "HIGH UNCERTAINTY FINANCING." International Journal of Theoretical and Applied Finance 20, no. 07 (November 2017): 1750043. http://dx.doi.org/10.1142/s0219024917500431.
Testo completoAbstract (sommario):
In this paper, we study the financing of high uncertainty projects. High uncertainty is defined as the lack of knowledge of whether growth options exist. In this paper, we will describe this uncertainty by a probability distribution which describes the arrival of a growth option at a deterministic time. Once the option arrives, an additional uncertainty exists since it is not certain that it is profitable to exercise it. We value the corporate securities with contingent claims valuation both for a whole equity-financed firm and a debt-equity-financed firm. Unlike traditional capital structure models, we find nonconvex value functions for the firm vis-a-vis the debt coupon under specific parametrizations. High and low leverage can yield similar firm value maximizing policies.
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Tonkes, Elliot, and Dharma Lesmono. "A Longstaff and Schwartz Approach to the Early Election Problem." Advances in Decision Sciences 2012 (October 18, 2012): 1–18. http://dx.doi.org/10.1155/2012/287579.
Testo completoAbstract (sommario):
In many democratic parliamentary systems, election timing is an important decision availed to governments according to sovereign political systems. Prudent governments can take advantage of this constitutional option in order to maximize their expected remaining life in power. The problem of establishing the optimal time to call an election based on observed poll data has been well studied with several solution methods and various degrees of modeling complexity. The derivation of the optimal exercise boundary holds strong similarities with the American option valuation problem from mathematical finance. A seminal technique refined by Longstaff and Schwartz in 2001 provided a method to estimate the exercise boundary of the American options using a Monte Carlo method and a least squares objective. In this paper, we modify the basic technique to establish the optimal exercise boundary for calling a political election. Several innovative adaptations are required to make the method work with the additional complexity in the electoral problem. The transfer of Monte Carlo methods from finance to determine the optimal exercise of real-options appears to be a new approach.
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ANÉ, THIERRY, and VINCENT LACOSTE. "UNDERSTANDING BID-ASK SPREADS OF DERIVATIVES UNDER UNCERTAIN VOLATILITY AND TRANSACTION COSTS." International Journal of Theoretical and Applied Finance 04, no. 03 (June 2001): 467–89. http://dx.doi.org/10.1142/s0219024901001073.
Testo completoAbstract (sommario):
The classical option valuation models assume that the option payoff can be replicated by continuously adjusting a portfolio consisting of the underlying asset and a risk-free bond. This strategy implies a constant volatility for the underlying asset and perfect markets. However, the existence of non-zero transaction costs, the consequence of trading only at discrete points in time and the random nature of volatility prevent any portfolio from being perfectly hedged continuously and hence suppress any hope of completely eliminating all risks associated with derivatives. Building upon the uncertain parameters framework we present a model for pricing and hedging derivatives where the volatility is simply assumed to lie between two bounds and in the presence of transaction costs. It is shown that the non-arbitrageable prices for the derivatives, which arise in this framework, can be derived by a non-linear PDE related to the convexity of the derivatives. We use Monte Carlo simulations to investigate the error in the hedging strategy. We show that the standard arbitrage is exposed to such large risks and transaction costs that it can only establish very wide bounds on equilibrium prices, obviously in contradiction with the very tight bid-ask spreads of derivatives observed on the market. We explain how the market spreads can be compatible with our model through portfolio diversification. This has important implications for price determination in options markets as well as for testing of valuation models.
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Bell, Timothy B., Wayne R. Landsman, Bruce L. Miller, and Shu Yeh. "The Valuation Implications of Employee Stock Option Accounting for Profitable Computer Software Firms." Accounting Review 77, no. 4 (October 1, 2002): 971–96. http://dx.doi.org/10.2308/accr.2002.77.4.971.
Testo completoAbstract (sommario):
We use the Ohlson (1995, 1999) and Feltham and Ohlson (1999) valuation models to investigate the market's perception of the economic effect of employee stock options (ESOs) on firm value for a sample of 85 profitable computer software companies. Our results suggest that the market appears to value these firms' ESO expense not as an expense but as an intangible asset (even after controlling for the endogeneity bias arising from the mechanical relation between ESOs and the underlying stock prices). However, we also find a conflict between: (1) the positive manner in which investors appear to value ESO expense, and (2) the negative relation between current ESO expense and future abnormal earnings. This conflict not only could be an artifact of the restrictiveness of the abnormal earnings forecasting equation we estimate, but it also calls into question whether investors assess correctly the effect of ESOs on profitable software firm value.
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Reis, Pedro Nogueira, and Mário Gomes Augusto. "What Is a Firm’s Life Expectancy? Empirical Evidence in the Context of Portuguese Companies." Journal of Business Valuation and Economic Loss Analysis 10, no. 1 (January 1, 2015): 45–75. http://dx.doi.org/10.1515/jbvela-2014-0003.
Testo completoAbstract (sommario):
AbstractIt isa fact that the uncertainty about a firm’s future has to be measured and incorporated into a company’s valuation throughout the explicit analysis period – in the continuing or terminal value within valuation models. One of the concerns that can influence the continuing value of enterprises, which is not explicitly considered in traditional valuation models, is a firm’s average life expectancy. Although the literature has studied the life cycle of a firm, there is still a considerable lack of references on this topic. If we ignore the period during which a company has the ability to produce future cash flows, the valuations can fall into irreversible errors, leading to results markedly different from market values. This paper aims to provide a contribution in this area. Its main objective is to construct a mortality table for non-listed Portuguese enterprises, showing that the use of a terminal value through a mathematical expression of perpetuity of free cash flows is not adequate. We provide the use of an appropriate coefficient to perceive the number of years in which the company will continue to operate until its theoretical extinction. If well addressed regarding valuation models, this issue can be used to reduce or even to eliminate one of the main problems that cause distortions in contemporary enterprise valuation models: the premise of an enterprise’s unlimited existence in time. Besides studying the companies involved in it, from their existence to their demise, our study intends to push knowledge forward by providing a consistent life and mortality expectancy table for each age of the company, presenting models with an explicitly and different survival rate for each year. Moreover, we show that, after reaching a certain age, firms can reinvent their business, acquiring maturity and consequently postponing their mortality through an additional life period.
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Singh, Vipul Kumar. "Pricing competitiveness of jump-diffusion option pricing models: evidence from recent financial upheavals." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 357–78. http://dx.doi.org/10.1108/sef-08-2012-0099.
Testo completoAbstract (sommario):
Purpose – The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future. Design/methodology/approach – Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility. Findings – The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options. Practical implications – The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions. Originality/value – The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.
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Heath, Davidson. "Macroeconomic Factors in Oil Futures Markets." Management Science 65, no. 9 (September 2019): 4407–21. http://dx.doi.org/10.1287/mnsc.2017.3008.
Testo completoAbstract (sommario):
This paper documents new evidence against perfect risk spanning in crude oil futures, and develops an affine futures pricing model that allows for unspanned macroeconomic factors. Compared to previous estimates, the oil spot premium is more volatile and strongly procyclical, which suggests that previous models miss the majority of variation in oil risk premiums. The estimates reveal a dynamic two-way relationship between oil futures and economic activity: productivity shocks are associated with higher oil prices, while oil price shocks affect economic activity by lowering future consumption spending. Unspanned macro factors also affect the valuation of real options. This paper was accepted by Karl Diether, finance.
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Tajani, Francesco, Pierluigi Morano, Francesca Salvo, and Manuela De Ruggiero. "Property valuation: the market approach optimised by a weighted appraisal model." Journal of Property Investment & Finance 38, no. 5 (September 13, 2019): 399–418. http://dx.doi.org/10.1108/jpif-07-2019-0094.
Testo completoAbstract (sommario):
Purpose The purpose of this paper is to develop an innovative model that can be included within the market approach methods for property valuations. The algorithm takes into account the frequent high level of dissimilarity of the comparables selected for the assessment, thus providing for the use of appropriate similarity and reliability coefficients capable of weighing the data of the comparison sample with respect to the different degrees of similarity and reliability. Design/methodology/approach The proposed model borrows the operative logics of the goal programming techniques, in order to identify the solution, the market value of the subject property and the implicit prices of the different influencing factors, since they are more reliable from the mathematical and empirical points of view. Findings The model has been applied to two case studies, relating to samples of residential properties located in the city of Naples (Southern Italy). The results obtained have outlined the high valuation performance of the developed appraisal model, capable of overcoming the applicability limits of classical market approach methods as well as providing solutions that are highly consistent with the expected empirical phenomena. Practical implications The research takes into account the growing need of both professionals and end users (banks, courts, public and private Entities, etc.) for valuation models that are easily repeatable and sufficiently objective. They are required in order to allow for the rapid verification of the elaborations carried out as well as to check the valuer’s appreciation of the contribution of the influencing factors in the market price formation. The outputs of the two applications developed have highlighted the ability of the proposed model to satisfy these market requests. Originality/value The proposed model can be easily implemented through a simple calculation program, with the mathematical structure elaborated allowing to overcome some application limits of the classical market approach methods. Furthermore, the introduction in the algorithm of appropriate similarity and reliability coefficients, capable of suitably weighting the data of the comparison sample, allows to widen the spatial horizon for the identification of the comparables as well as select properties characterized by a high level of dissimilarity. This makes it possible to apply the model in territorial contexts characterized by markets that are not excessively dynamic.
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Chutka, Jan, and Katarina Kramarova. "Usage of P/E earning models as a tool for valuation of shares in condition of global market." SHS Web of Conferences 74 (2020): 01007. http://dx.doi.org/10.1051/shsconf/20207401007.
Testo completoAbstract (sommario):
With the rapid development of computational technology, non-traditional mathematical and statistical methods have also parallely developed to help simplify and accelerate the computation of certain tasks, or even to solve problems that are usually unsolvable. The aim of this paper is to get closer to the P/E earning models and briefly summarize their calculation and usage options. In the first part of our paper we briefly worked out the theoretical basis of these models. Furthermore, we focused on a detailed description of their calculation and use in calculating the value of shares. In the second part of the work we focused on the application of the calculation of the selected P / E model to Apple inc. in the course of 2018 and compared the data obtained with another instrument to identify the intrinsic value of the action. In the last part we focused on the interpretation and summary of the results of the application. We consider the greatest added value of our contribution to be a theoretical comparison of different types of calculation and deeper application of the selected model to real market prices of Apple inc. with the interpretation of the results obtained. We can conclude that the aim we have set is met and we believe that our article will be a valuable addition to the issue in this area.