Journal articles: 'Valuation equation'

1

Callen, Jeffrey L., and Mindy Morel. "A Lintnerian Linear Accounting Valuation Model." Journal of Accounting, Auditing & Finance 15, no. 3 (July 2000): 301–14. http://dx.doi.org/10.1177/0148558x0001500307.

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This paper develops and tests a linear valuation accounting model based on Lintner's (1956) dividend model. Two test methodologies are employed on a firm-level time-series basis. First, abstracting from the nonlinear relationships among the parameters, the information dynamic and valuation equation are estimated by linear OLS and linear SUR. The estimated equations are evaluated by reference to the sign and value predictions of the model. Second, recognizing the underlying nonlinear relationships among the parameters, the Lintnerian system of equations is estimated by nonlinear OLS and nonlinear SUR. All parameters are estimated endogenously at the firm level, including each firm's cost of capital. The resulting parameter estimates are evaluated for statistical and, in the case of costs of capital, for economic significance. Results of the first (linear) methodology by and large confirm the validity of the Lintner model. The signs and values of the estimated coefficients are consistent with the predictions of the Lintner model except that the (mean) estimated book value coefficient in the price equation exceeds its theoretical upper bound. The results of the second (nonlinear) methodology are somewhat more problematic. Although the Lintner model yields statistically significant firm-level costs of capital, these estimates are not economically significant for the sample period.

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2

Matsutani, Shigeki. "p-adic difference-difference Lotka-Volterra equation and ultra-discrete limit." International Journal of Mathematics and Mathematical Sciences 27, no. 4 (2001): 251–60. http://dx.doi.org/10.1155/s0161171201010808.

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We study the difference-difference Lotka-Volterra equations inp-adic number space and itsp-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of thep-adic valuation space. Since ultra-discrete limit can be regarded as a classical limit of a quantum object, it implies that a correspondence between classical and quantum objects might be associated with valuation theory.

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3

Matenda, Frank Ranganai, Justin Chirima, and Mabutho Sibanda. "Valuation of Corporate Debt and Equity in Uncertain Markets." International Journal of Economics and Financial Issues 13, no. 1 (January 14, 2023): 7–12. http://dx.doi.org/10.32479/ijefi.13706.

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In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertainty, and fuzziness are three basic types of indeterminacy. A multiplicity of differential equations have been designed to depict various processes powered by different kinds of indeterminacy. Among others, these differential equations include uncertain differential equations, stochastic differential equations, and fuzzy differential equations. In this study, we propose that the value of a firm can be described by an uncertain differential equation powered by a geometric canonical Liu process. Uncertain differential equations describe processes driven by uncertainty. Implementing the uncertain Liu option pricing theory, we develop and analyse a framework for valuing debt and equity for a levered firm in uncertain markets. Numerical calculations are demonstrated.

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4

Schwaiger, Jens. "Connections Between the Completion of Normed Spaces Over Non-Archimedean Fields and the Stability of the Cauchy Equation." Annales Mathematicae Silesianae 34, no. 1 (July 1, 2020): 151–63. http://dx.doi.org/10.2478/amsil-2020-0002.

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AbstractIn [12] a close connection between stability results for the Cauchy equation and the completion of a normed space over the rationals endowed with the usual absolute value has been investigated. Here similar results are presented when the valuation of the rationals is a p-adic valuation. Moreover a result by Zygfryd Kominek ([5]) on the stability of the Pexider equation is formulated and proved in the context of Banach spaces over the field of p-adic numbers.

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5

Shokrollahi, Foad. "Equity Warrants Pricing Formula for Uncertain Financial Market." Mathematical and Computational Applications 27, no. 2 (February 22, 2022): 18. http://dx.doi.org/10.3390/mca27020018.

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In this paper, inside the system of uncertainty theory, the valuation of equity warrants is explored. Different from the strategies of probability theory, the valuation problem of equity warrants is unraveled by utilizing the strategy of uncertain calculus. Based on the suspicion that the firm price follows an uncertain differential equation, a valuation formula of equity warrants is proposed for an uncertain stock model.

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6

Schall, Lawrence D. "Valuation of an Equity Interest." Review of Pacific Basin Financial Markets and Policies 18, no. 04 (December 2015): 1550021. http://dx.doi.org/10.1142/s0219091515500216.

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The equity cash flow approach to valuing an equity interest is intuitive, rigorous, and practical, and is easily implemented using historical and forecasted statements of cash flows. This method is compared with popular alternatives. The equity cash flow equation for valuing equity is derived taking into account employee compensation expense in the form of equity participation (stock options and stock grants). This is of particular interest in light of the importance of options and grants as a form of compensation.

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7

Lindgren, Jussi. "Efficient Markets and Contingent Claims Valuation: An Information Theoretic Approach." Entropy 22, no. 11 (November 12, 2020): 1283. http://dx.doi.org/10.3390/e22111283.

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This research article shows how the pricing of derivative securities can be seen from the context of stochastic optimal control theory and information theory. The financial market is seen as an information processing system, which optimizes an information functional. An optimization problem is constructed, for which the linearized Hamilton–Jacobi–Bellman equation is the Black–Scholes pricing equation for financial derivatives. The model suggests that one can define a reasonable Hamiltonian for the financial market, which results in an optimal transport equation for the market drift. It is shown that in such a framework, which supports Black–Scholes pricing, the market drift obeys a backwards Burgers equation and that the market reaches a thermodynamical equilibrium, which minimizes the free energy and maximizes entropy.

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8

Adamowicz, Krzysztof. "The unresolved problem of determining the forest interest rate." Folia Forestalia Polonica 60, no. 2 (June 1, 2018): 122–30. http://dx.doi.org/10.2478/ffp-2018-0012.

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Abstract Valuation of forests and their components is a significant problem, both for science and practice. At present, in many countries, the market of forest property is limited. As a result, no conclusions may be inferred on the forest value based on the information on forest purchase and sale transactions. In this situation, we apply static methods of forest valuation. The problem of forest statics has been discussed for years (e.g., Brukas et al. 2001; Chang 1983, 2001; Dieter 2001; Hartman 1976; Manley and Bare 2001; Mohring 2001; Zhang 2001; Viitala 2016). Static methods of forest valuation are well known. In the construction of the proposed mathematical formula (Eq. 6), the Faustmann theory was applied, concerning the economic equilibrium in forestry. Numerous modifications of his equation for economic equilibrium were used to develop, for example, an income method for forest valuation based on discounting the final value or prolongation of initial value. The forest interest rate is a key element in these equations. At present, there are no procedures for the establishment of this interest rate, which would be generally accepted by the scientific community. Therefore, the article presents and discusses selected concepts for determining the forest interest rate.

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9

Sawal, A. S., S. N. I. Ibrahim, and T. R. N. Roslan. "Pricing equity warrants with jumps, stochastic volatility, and stochastic interest rates." Mathematical Modeling and Computing 9, no. 4 (2022): 882–91. http://dx.doi.org/10.23939/mmc2022.04.882.

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A warrant is a derivative that gives the right, but not the obligation, to buy or sell a security at a certain price before the expiration. The warrant valuation method was inspired by option valuation because of the certain similarities between these two derivatives. The warrant price formula under the Black–Scholes is available in the literature. However, the Black–Scholes formula is known to have a number of flaws; hence, this study aims to develop a pricing formula for warrants by incorporating jumps, stochastic volatility, and stochastic interest rates into the Black–Scholes model. The closed-form pricing formula is presented in this study, where the derivation involves stochastic differential equations (SDE), which include the Cauchy problem and heat equation.

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10

EKSTRÖM, ERIK, and JOHAN TYSK. "DUPIRE'S EQUATION FOR BUBBLES." International Journal of Theoretical and Applied Finance 15, no. 06 (September 2012): 1250041. http://dx.doi.org/10.1142/s0219024912500410.

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We study Dupire's equation for local volatility models with bubbles, i.e. for models in which the discounted underlying asset follows a strict local martingale. If option prices are given by risk-neutral valuation, then the discounted option price process is a true martingale, and we show that the Dupire equation for call options contains extra terms compared to the usual equation. However, the Dupire equation for put options takes the usual form. Moreover, uniqueness of solutions to the Dupire equation is lost in general, and we show how to single out the option price among all possible solutions. The Dupire equation for models in which the discounted derivative price process is merely a local martingale is also studied.

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11

MALLIER, R., and J. GOARD. "INTEGRAL EQUATION FORMULATION FOR SHOUT OPTIONS." ANZIAM Journal 60, no. 1 (July 2018): 65–85. http://dx.doi.org/10.1017/s1446181118000160.

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We use an integral equation formulation approach to value shout options, which are exotic options giving an investor the ability to “shout” and lock in profits while retaining the right to benefit from potentially favourable movements in the underlying asset price. Mathematically, the valuation is a free boundary problem involving an optimal exercise boundary which marks the region between shouting and not shouting. We also find the behaviour of the optimal exercise boundary for one- and two-shout options close to expiry.

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12

Irmak, Nurettin. "PRODUCT OF FACTORIALS IN THE SEQUENCE {gn}." Journal of Mathematical Sciences: Advances and Applications 69, no. 1 (November 20, 2021): 37–42. http://dx.doi.org/10.18642/jmsaa_7100122231.

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13

Ghosh, Saibal. "Leverage, managerial monitoring and firm valuation: A simultaneous equation approach." Research in Economics 61, no. 2 (June 2007): 84–98. http://dx.doi.org/10.1016/j.rie.2007.03.001.

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14

Dehghan, Mehdi, and Somayeh Pourghanbar. "Solution of the Black-Scholes Equation for Pricing of Barrier Option." Zeitschrift für Naturforschung A 66, no. 5 (May 1, 2011): 289–96. http://dx.doi.org/10.1515/zna-2011-0504.

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In this paper two different methods are presented to approximate the solution of the Black-Scholes equation for valuation of barrier option. These techniques can be applied directly for all types of differential equations, homogeneous or inhomogeneous. The use of these methods provides the solution of the problem in a closed form while the mesh point techniques provide the approximation at mesh points only. Also, the two schemes need less computational work in comparison with the traditional methods. These techniques can be employed for problems with initial condition. In this paper we use the variational iteration and homotopy perturbation methods for solving the Black-Scholes equation with terminal condition. Numerical results are compared with theoretical solutions in order to confirm the validity of the presented procedures.

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15

Maulana, Kinan Bahuweda, and Ari Prasetyo. "Pengaruh Metode Penilaian Persediaan dan Gross Profit Margin Terhadap Nilai Pasar (Studi Pada Perusahaan Dagang Yang Terdaftar Di Daftar Efek Syariah Periode 2009-2014)." Jurnal Ekonomi Syariah Teori dan Terapan 2, no. 8 (December 17, 2015): 627. http://dx.doi.org/10.20473/vol2iss20158pp627-641.

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This research attempt to know the influence of inventory valuation methods and gross profit margin againts market value of trading company that listed on Daftar Efek Syariah from 2009 through 2014. The independent variable was inventory valuation methods and gross profit margin, the dependent variable was market value. The analysis techniques used is multiple linear regression with variable dummy and the equation is FIFO method Ymv = 10,694 - 0,385 (0) + 0,127 (GPM)= 10,694 + 0,127 (GPM) and Average method Ymv = 10,694 - 0,385 (1) + 0,127 (GPM) = 10,309 + 0,127 (GPM).Based on the results of t-test, the inventory valuation methods has not a significant influence. Similarly, the gross profit margin partially has not significant influence to market value. The result of simultaneous test showed that inventory valuation methods, gross profit margin has significant effect to against market value of trading company.

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16

Salvador, Beatriz, Cornelis W. Oosterlee, and Remco van der Meer. "European and American Options Valuation by Unsupervised Learning with Artificial Neural Networks." Proceedings 54, no. 1 (August 19, 2020): 14. http://dx.doi.org/10.3390/proceedings2020054014.

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Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). In this work, the classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option, we solve the linear complementarity problem formulation.

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17

Le, Nhat-Tan, and Minh-Man Ngo. "Valuation of non-recourse stock loan using an integral equation approach." Journal of Integral Equations and Applications 32, no. 2 (June 2020): 181–92. http://dx.doi.org/10.1216/jie.2020.32.181.

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18

SADEK, MOHAMMAD. "Counting models of genus one curves." Mathematical Proceedings of the Cambridge Philosophical Society 150, no. 3 (January 12, 2011): 399–417. http://dx.doi.org/10.1017/s0305004110000666.

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AbstractLet C be a soluble smooth genus one curve over a Henselian discrete valuation field. There is a unique minimal Weierstrass equation defining C up to isomorphism. In this paper we consider genus one equations of degree n defining C, namely a (generalised) binary quartic when n = 2, a ternary cubic when n = 3 and a pair of quaternary quadrics when n = 4. In general, minimal genus one equations of degree n are not unique up to isomorphism. We explain how the number of these equations varies according to the Kodaira symbol of the Jacobian of C. Then we count these equations up to isomorphism over a number field of class number 1.

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19

Dierkes, Stefan, and Imke de Maeyer. "Valuation with mixed financing strategies." Business Research 13, no. 3 (October 15, 2020): 1317–41. http://dx.doi.org/10.1007/s40685-020-00126-w.

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AbstractIn corporate valuation, it is common to assume either passive or active debt management. However, it is questionable whether these pure financing policies reflect the real financing policies of firms with a sufficient degree of accuracy. This shortcoming has led to the development of mixed financing strategies as combinations of pure financing strategies. Whereas hybrid financing is directly linked to the two-phase model, it is unclear how to apply discontinuous financing in such a setting. In this study, according to the two versions of hybrid financing, we analyze the implementation of discontinuous financing in a two-phase model. Thereby, we present a simpler and more intuitive derivation of the valuation equation for discontinuous financing to increase its acceptance and its use for corporate valuation practice. Moreover, we compare the different mixed financing strategies with each other theoretically, and we conduct simulations to elucidate the impact on market values and the sensitivities of input parameters. The study concludes that the presented mixed financing strategies can help in the attempt to reflect the real financing behavior of firms more accurately and, therefore, constitute a valuable alternative to pure financing strategies for valuation.

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20

Azar, Samih Antoine. "LOSS AVERSION IS CONSISTENT WITH STOCK MARKET BEHAVIOR." International Journal of Accounting & Finance Review 5, no. 4 (November 25, 2020): 60–73. http://dx.doi.org/10.46281/ijafr.v5i4.893.

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The purpose of this paper is to verify that discrete statistical distributions of the US stock market are consistent with loss aversion. Loss aversion has the following tenets: an S-shaped valuation function, characterized by diminishing sensitivity, a loss aversion coefficient higher than +1, probability weighting, and reference-dependence. Diminishing sensitivity implies that the exponent of the valuation function is between 0 and +1. It is expected that this exponent be higher for losses. Probability weighting replaces objective with subjective probabilities. Loss aversion is indicated by a coefficient higher than +1 for the valuation of losses. There are three parameters: the two exponents of the valuation function, and the loss aversion coefficient. There is one non-linear equation: the certainty equivalence relation. The procedure is to fix two parameters and find the third parameter by solving the non-linear certainty equivalence equation, using the EXCEL spreadsheet. The program is repeated for more than one case about the fixed parameters, and by enriching the analysis with probability weighting. The calibrations executed point strongly to the conclusion that loss aversion is consistent with six discrete distributions of the first two moments of returns of the US stock markets. The calibration process provides for reasonable estimates of the key parameters of loss aversion. These estimates suggest a more pronounced diminishing sensitivity, and a higher than expected coefficient of loss aversion, especially when probability weighting is imposed.

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21

Ruan, Xinfeng, Wenli Zhu, Shuang Li, and Jiexiang Huang. "Option Pricing under Risk-Minimization Criterion in an Incomplete Market with the Finite Difference Method." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/165727.

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We study option pricing with risk-minimization criterion in an incomplete market where the dynamics of the risky underlying asset is governed by a jump diffusion equation with stochastic volatility. We obtain the Radon-Nikodym derivative for the minimal martingale measure and a partial integro-differential equation (PIDE) of European option. The finite difference method is employed to compute the European option valuation of PIDE.

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22

Holland, Larry C. "A Flexible Valuation Model Incorporating Declining Growth Rates." Accounting and Finance Research 7, no. 1 (November 27, 2017): 116. http://dx.doi.org/10.5430/afr.v7n1p116.

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A new model is developed in this paper which demonstrates a flexible method for modeling a cash flow stream with a declining growth rate that asymptotically approaches a mature long-term growth rate. This model can be applied when the initial growth rate in cash flows is temporarily larger than the required rate of return. A simple closed form equation of the valuation model is presented along with an example to illustrate the valuation of future cash flows with a declining growth rate. A comparison is made with the valuation from multi-stage models that have constant growth segments, the H-Model, and the Ohlson-Juettner Model. This highlights the difference in valuation that results from using this new model. An example is also included to illustrate how to match a decline curve to a specific forecast of future cash flows. This new declining growth model provides a flexible and practical approach for valuing equities.

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23

Paseka, Alex, and Aerambamoorthy Thavaneswaran. "Bond valuation for generalized Langevin processes with integrated Lévy noise." Journal of Risk Finance 18, no. 5 (November 20, 2017): 541–63. http://dx.doi.org/10.1108/jrf-09-2016-0125.

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Purpose Recently, Stein et al. (2016) studied theoretical properties and parameter estimation of continuous time processes derived as solutions of a generalized Langevin equation (GLE). In this paper, the authors extend the model to a wider class of memory kernels and then propose a bond and bond option valuation model based on the extension of the generalized Langevin process of Stein et al. (2016). Design/methodology/approach Bond and bond option pricing based on the proposed interest rate models presents new difficulties as the standard partial differential equation method of stochastic calculus for bond pricing cannot be used directly. The authors obtain bond and bond option prices by finding the closed form expression of the conditional characteristic function of the integrated short rate process driven by a general Lévy noise. Findings The authors obtain zero-coupon default-free bond and bond option prices for short rate models driven by a variety of Lévy processes, which include Vasicek model and the short rate model obtained by solving a second-order Langevin stochastic differential equation (SDE) as special cases. Originality/value Bond and bond option pricing plays an important role in capital markets and risk management. In this paper, the authors derive closed form expressions for bond and bond option prices for a wider class of interest rate models including second-order SDE models. Closed form expressions may be especially instrumental in facilitating parameter estimation in these models.

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24

Salvador, Beatriz, Cornelis W. Oosterlee, and Remco van der Meer. "Financial Option Valuation by Unsupervised Learning with Artificial Neural Networks." Mathematics 9, no. 1 (December 28, 2020): 46. http://dx.doi.org/10.3390/math9010046.

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Artificial neural networks (ANNs) have recently also been applied to solve partial differential equations (PDEs). The classical problem of pricing European and American financial options, based on the corresponding PDE formulations, is studied here. Instead of using numerical techniques based on finite element or difference methods, we address the problem using ANNs in the context of unsupervised learning. As a result, the ANN learns the option values for all possible underlying stock values at future time points, based on the minimization of a suitable loss function. For the European option, we solve the linear Black–Scholes equation, whereas for the American option we solve the linear complementarity problem formulation. Two-asset exotic option values are also computed, since ANNs enable the accurate valuation of high-dimensional options. The resulting errors of the ANN approach are assessed by comparing to the analytic option values or to numerical reference solutions (for American options, computed by finite elements). In the short note, previously published, a brief introduction to this work was given, where some ideas to price vanilla options by ANNs were presented, and only European options were addressed. In the current work, the methodology is introduced in much more detail.

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25

Trojovský, Pavel. "On Diophantine Equations Related to Order of Appearance in Fibonacci Sequence." Mathematics 7, no. 11 (November 7, 2019): 1073. http://dx.doi.org/10.3390/math7111073.

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Let F n be the nth Fibonacci number. Order of appearance z ( n ) of a natural number n is defined as smallest natural number k, such that n divides F k . In 1930, Lehmer proved that all solutions of equation z ( n ) = n ± 1 are prime numbers. In this paper, we solve equation z ( n ) = n + ℓ for | ℓ | ∈ { 1 , … , 9 } . Our method is based on the p-adic valuation of Fibonacci numbers.

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Zhang, Shuhua, and Zhuo Yang. "The Valuation of Carbon Bonds Linked with Carbon Price." Computational Methods in Applied Mathematics 16, no. 2 (April 1, 2016): 345–59. http://dx.doi.org/10.1515/cmam-2016-0001.

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AbstractThe carbon bonds issued by countries or enterprises can solve the problem of funds in low carbon economy growth. Now most of carbon bonds pay fixed interest rates, and a few pay floating rates. The diversity of carbon bonds can attract more investors to participate green energy projects. The London Accord project group proposed the index linked carbon bonds in the World Band Government Borrowers' Forum in May 2009, and pointed out that the interest paid regularly may be linked to carbon price, governments' carbon emission targets, in-country fossil fuel prices or tariff feed-in prices. In this paper, the interests are considered to be linked with carbon prices in the condition of stochastic risk-free interest rate, and a partial differential equation is established for carbon bond interests. Also, a fitted finite volume method is employed to solve the resulting partial differential equation numerically, and on the basis of the valuation for zero-coupon bonds, the price of carbon bonds is obtained. Finally, some data are utilized for the calibration of the parameters in the established pricing models, and some numerical examples are presented and the effects of parameters on solutions are also demonstrated, which can provide references for the issuers of carbon bonds.

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27

Whitehead, John C. "Measuring Use Value from Recreation Participation." Journal of Agricultural and Applied Economics 24, no. 2 (December 1992): 113–19. http://dx.doi.org/10.1017/s0081305200018434.

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AbstractRecreation demand studies have traditionally utilized a two-step valuation method, estimating conditional recreation participation probabilities and then intensity of use decisions. These two steps of analysis are combined to estimate the use value of natural resource recreation sites. The purpose of this paper is to provide a method by which use value can be estimated solely from the participation decision. The one-step resource valuation method allows estimation of use values from coefficients of the logistic regression recreation participation equation. The benefits of the method are the reduced data and effort required to value natural resource areas.

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Gantino, Rilla, and Erwin Erwin. "PENGARUH BIAYA KUALITAS TERHADAP PENJUALAN PADA PT. GUARDIAN PHARMATAMA." Journal of Applied Finance & Accounting 2, no. 2 (June 30, 2010): 138–67. http://dx.doi.org/10.21512/jafa.v2i2.159.

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This is an empirical research to determine the influence of the independent variable quality cost to the dependent variable sales. A T-test on prevention cost, valuation cost, internal failure cost, and external failure cost showed significant influence on sales. An F-test on prevention cost, valuation cost, internal failure cost and external failure cost also showed significant influence on sales. Regression analysis was done using the multiple linear regression equation Y = -240710057,3 + 496,753 X1 + 411,237 X2 + 38,384 X3 + 21,283 X4. Regression analysis showed positive that prevention cost, valuation cost, internal failure cost, and external failure cost had a positive influence on sales, which indicates that increasing costs of quality leads to increase in sales. A coefficient determination test (Kd) showed that 95% of quality cost contributes to sales; the remaining 5% is influenced by factors other than cost of quality.

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Chawla, M. M., and D. J. Evans. "Numerical volatility in option valuation from Black–Scholes equation by finite differences." International Journal of Computer Mathematics 81, no. 8 (August 2004): 1039–41. http://dx.doi.org/10.1080/03057920412331272234.

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Roch, Alexandre F. "Viscosity Solutions and American Option Pricing in a Stochastic Volatility Model of the Ornstein-Uhlenbeck Type." Journal of Probability and Statistics 2010 (2010): 1–18. http://dx.doi.org/10.1155/2010/863585.

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We study the valuation of American-type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condition.

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Luo, Xiankang, and Jie Xing. "Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility." Mathematical Problems in Engineering 2021 (July 13, 2021): 1–20. http://dx.doi.org/10.1155/2021/9969937.

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This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

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Gómez-Valle, Lourdes, Miguel Angel López-Marcos, and Julia Martínez-Rodríguez. "Two New Strategies for Pricing Freight Options by Means of a Valuation PDE and by Functional Bounds." Mathematics 8, no. 4 (April 17, 2020): 620. http://dx.doi.org/10.3390/math8040620.

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Freight derivative prices have been modeled assuming that the spot freight follows a particular stochastic process in order to manage them, like freight futures, forwards and options. However, an explicit formula for pricing freight options is not known, not even for simple spot freight processes. This is partly due to the fact that there is no valuation equation for pricing freight options. In this paper, we deal with this problem from two independent points of view. On the one hand, we provide a novel theoretical framework for pricing these Asian-style options. In this way, we build a partial differential equation whose solution is the freight option price obtained from stochastic delay differential equations. On the other hand, we prove lower and upper bounds for those freight options which enables us to estimate the option price. In this work, we consider that the spot freight rate follows a general stochastic diffusion process without restrictions in the drift and volatility functions. Finally, using recent data from the Baltic Exchange, we compare the described bounds with the freight option prices.

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Jeon, Junkee, and Geonwoo Kim. "Analytic Valuation Formula for American Strangle Option in the Mean-Reversion Environment." Mathematics 10, no. 15 (July 29, 2022): 2688. http://dx.doi.org/10.3390/math10152688.

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This paper investigates the American strangle option in a mean-reversion environment. When the underlying asset follows a mean-reverting lognormal process, an analytic pricing formula for an American strangle option is explicitly provided. To present the pricing formula, we consider the partial differential equation (PDE) for American strangle options with two optimal stopping boundaries and use Mellin transform techniques to derive the integral equation representation formula arising from the PDE. A Monte Carlo simulation is used as a benchmark to validate the formula’s accuracy and efficiency. In addition, the numerical examples are provided to demonstrate the effects of the mean-reversion on option prices and the characteristics of options with respect to several significant parameters.

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LEVIN, ALEXANDER. "ONE- AND MULTI-FACTOR VALUATION OF MORTGAGES: COMPUTATIONAL PROBLEMS AND SHORTCUTS." International Journal of Theoretical and Applied Finance 02, no. 04 (October 1999): 441–69. http://dx.doi.org/10.1142/s0219024999000224.

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A new valuation method is proposed that can be mathematically viewed as a numerical shortcut to approximately solve the partial differential equation written for Expected Instantaneous Return. The method derives OAS as "static spread plus cost of convexity" and is based on some simplified parametric assumption about the static spread's time behavior. The modeling and numerical procedure details are disclaimed with proven accuracy and time efficiency in option-adjusted valuation. The method is especially effective for multi-scenario pricing, portfolio pricing, risk management and reporting, and for quantifying the impact of "non-traded" factors on reward and risk of holding mortgages. A systematic methodology for comprehensive multi-factor analysis is covered.

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Damanik, Mario, and Khaerul Amru. "Carbon Stocks Potential and Economic Value Valuation of Carbon Stocks in Ebony Stands." Jurnal Pengelolaan Sumberdaya Alam dan Lingkungan (Journal of Natural Resources and Environmental Management) 12, no. 4 (December 30, 2022): 696–705. http://dx.doi.org/10.29244/jpsl.12.4.696-705.

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One of the important activities to achieve the implementation of REDD+ activities is the measurement and reporting of carbon stocks (Masripatin et.al. 2010). Information on the potential for carbon stocks in a plant stand or forest area can provide an overview for related parties of the potential carbon stocks and the added value that will be obtained if it maintains and develops a certain plant species to support the reduction of greenhouse gas emissions. This study aims to determine the potential of biomass, carbon stocks, and economic valuation of the carbon stocks potential of several Ebony stands contained in the Kawanua Arboretum BP2LHK Manado. The types of Ebony stands that were the object of this study were Dyospiros celebica, Dyospiros rumphii, and Dyospiros ebenum. Determination of biomass potential and carbon stocks using the allometric equation. The economic valuations of each potential carbon stocks of Ebony stands are obtained based on the selling value of carbon set by the World Bank Group. Based on the results of the study, it is known that the carbon stocks potential of each Ebony stand, namely Diospyros rumphii, is 74.246 tons/ha, followed by the potential carbon storage in the Diospyros celebica stand of 67.768 tons/ha and Diospyros ebenum of 64.977 tons / ha, while the economic valuation value of the highest carbon storage potential is found in the Diospyros rumphii stand of USD 148.492 followed by Diospyros celebica is USD 135.536 and Diospyros ebenum is USD 129.954

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MASTINSEK, MIKLAVZ. "ON ROBUSTNESS OF THE BLACK–SCHOLES PARTIAL DIFFERENTIAL EQUATION MODEL." International Journal of Theoretical and Applied Finance 19, no. 02 (March 2016): 1650013. http://dx.doi.org/10.1142/s0219024916500138.

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When the discretely adjusted option hedges are constructed by the continuous-time Black–Scholes delta, then the hedging errors appear. The first objective of the paper is to consider a discrete-time adjusted delta, such that the hedging error can be reduced. Consequently, a partial differential equation for option valuation associated with the problem is derived and solved. The second objective is to compare the obtained results with the results given by the Black–Scholes formula. The obtained option values may be higher than those given by the Black–Scholes formula, however, unless the option is near expiry, the difference is relatively small.

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Cunningham, William A., Amanda Kesek, and Samantha M. Mowrer. "Distinct Orbitofrontal Regions Encode Stimulus and Choice Valuation." Journal of Cognitive Neuroscience 21, no. 10 (October 2009): 1956–66. http://dx.doi.org/10.1162/jocn.2008.21148.

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The weak axiom of revealed preferences suggests that the value of an object can be understood through the simple examination of choices. Although this axiom has driven economic theory, the assumption of equation between value and choice is often violated. fMRI was used to decouple the processes associated with evaluating stimuli from evaluating one's actions. Whereas activity in left posterior areas of the orbitofrontal cortex (OFC) was associated with processing the objective value of stimuli, activity in medial anterior areas of the OFC was associated with accepting high value gambles and rejecting low value gambles; that is, making correct decisions. These data demonstrate that distinct areas of the OFC provide dissociated representations for use in adaptive decision-making and suggest an important processing distinction between the concepts of good/bad and right/wrong.

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LAPEYRE, BERNARD, and MAROUAN IBEN TAARIT. "A FORWARD EQUATION FOR COMPUTING DERIVATIVES EXPOSURE." International Journal of Theoretical and Applied Finance 22, no. 03 (May 2019): 1950015. http://dx.doi.org/10.1142/s0219024919500158.

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We derive a forward equation for computing the expected exposure of financial derivatives. Under general assumptions about the underlying diffusion process, we give an explicit decomposition of the exposure into an intrinsic value which can be directly deduced from the term structure of the forward mark-to-market, and a time value which expresses the variability of the future mark-to-market. Our approach is inspired by Dupire’s equation for local volatility and leads to an ordinary differential equation qualifying the evolution of the expected exposure with respect to the observation dates. We show how this approach can be linked with local times theory in dimension one and to the co-area formula in a higher dimension. As for numerical considerations, we show how this approach leads to an efficient numerical method in the case of one or two risk factors. The accuracy and time-efficiency of this forward representation in small dimension are of special interest in benchmarking XVA valuation adjustments at trade level.

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Reisinger, Christoph, and Rasmus Wissmann. "Numerical valuation of derivatives in high-dimensional settings via partial differential equation expansions." Journal of Computational Finance 18, no. 4 (June 2015): 95–127. http://dx.doi.org/10.21314/jcf.2015.302.

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Zagheni, Emilio, and Francesco C. Billari. "A cost valuation model based on a stochastic representation of the IPAT equation." Population and Environment 29, no. 2 (November 2007): 68–82. http://dx.doi.org/10.1007/s11111-008-0061-1.

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Kaiser, Zoltán. "On stability of the Cauchy equation in normed spaces over fields with valuation." Publicationes Mathematicae Debrecen 64, no. 1-2 (January 1, 2004): 189–200. http://dx.doi.org/10.5486/pmd.2004.2937.

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Trifonov, Nikolai Yu. "Development of the Risk Accumulation Method for Calculating the Capitalization Rate." Economics of Contemporary Russia, no. 1 (March 29, 2021): 7–14. http://dx.doi.org/10.33293/1609-1442-2021-1(92)-7-14.

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Risk build-up method is the most used for calculating the capitalization rates. With the help of the literature analysis, the origin of this method is considered. The method was based on the relationship between risk and profitability of a stock in exchange trading, proven statistically. Later, when formulating the build-up method, this idea was transferred without any justification to the valuation of enterprises that do not list their securities on stock exchange. In other words, the formulas traditionally used in the application of the build-up method are empirical in nature and not precise.It is more accurate to write them down by analogy with Irwin Fisher's equation of returns. Based on the principle of dependence, one of the main ones for the valuation procedure, the essence of which is that the value of the valuation subject depends on its economic location, a set of four independent risks is given for use in the build-up method in general case: risk-free rate, country risk premium, branch risk premium, and subject risk adjustment. It is noted that the numerical value of these parameters used in the method fundamentally depends on the monetary unit used in the calculation (the valuation currency). Recommendations are given on finding a risk-free rate for various currencies, on calculating country risk premium, branch risk premium, and subject risk adjustment. The article is intended for academics, lecturers, and practitioners in such areas as corporate finance, business microeconomics, valuation, and investment analysis.

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DasGupta, Ranjan, and Rashmi Singh. "Antecedents of Firm’s Risk-play – A Structural Equation Modeling Approach in an Emerging Market Context." Australasian Business, Accounting & Finance Journal 15, no. 2 (2021): 56–82. http://dx.doi.org/10.14453/aabfj.v15i2.5.

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Firm-risk and managerial risk-taking though distinct are used interchangeably in empirical literature. Here, we identify these two distinctly by examining different proxies for them. We use income stream uncertainty and accounting beta to proxy firm-risk, and market risk and capital intensity ratio represent managerial risk-taking. Once defined, our objective is to find the antecedents of both these by using the most advanced structural equation modelling (SEM) approach from created constructs of performance, psychological, corporate governance, shareholding patterns, fundamental valuation and firm’s characteristics drivers. We formulate seven hypotheses based on empirical literature representing these constructs. We use data of 269 Indian firms for 18 (1999-2017) years to run SEM and then analyse our results individually and combinedly. SEM is used here to test the unidimensionality of the seven constructs (consisting of 19 drivers) and to analyze these drivers (i.e. antecedents) influence on firm-risk and managerial risk-taking i.e. firm’s risk-play. Results prove that present firm-performance, corporate governance drivers, promoters’ shareholding and firm’s characteristics are driving firm’s risk-play. However, fundamental valuation drivers have no role to play in influencing income stream uncertainty, systematic operating risks and managerial risk-attitudes. Psychological drivers and foreign shareholdings act only as a catalyst of firm-risk.

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Dasgupta, Ranjan, and Rashmi Singh. "Antecedents of Firm’s Risk-play – A Structural Equation Modeling Approach in an Emerging Market Context." Australasian Business, Accounting and Finance Journal 15, no. 3 (2021): 67–94. http://dx.doi.org/10.14453/aabfj.v15i3.5.

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Firm-risk and managerial risk-taking though distinct are used interchangeably in empirical literature. Here, we identify these two distinctly by examining different proxies for them. We use income stream uncertainty and accounting beta to proxy firm-risk, and market risk and capital intensity ratio represent managerial risk-taking. Once defined, our objective is to find the antecedents of both these by using the most advanced structural equation modelling (SEM) approach from created constructs of performance, psychological, corporate governance, shareholding patterns, fundamental valuation and firm’s characteristics drivers. We formulate seven hypotheses based on empirical literature representing these constructs. We use data of 269 Indian firms for 18 (1999-2017) years to run SEM and then analyse our results individually and combinedly. SEM is used here to test the unidimensionality of the seven constructs (consisting of 19 drivers) and to analyze these drivers (i.e. antecedents) influence on firm-risk and managerial risk-taking i.e. firm’s risk-play. Results prove that present firm-performance, corporate governance drivers, promoters’ shareholding and firm’s characteristics are driving firm’s risk-play. However, fundamental valuation drivers have no role to play in influencing income stream uncertainty, systematic operating risks and managerial risk-attitudes. Psychological drivers and foreign shareholdings act only as a catalyst of firm-risk.

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Lo, C. F., H. M. Tang, K. C. Ku, and C. H. Hui. "Valuing Time-Dependent CEV Barrier Options." Journal of Applied Mathematics and Decision Sciences 2009 (August 6, 2009): 1–17. http://dx.doi.org/10.1155/2009/359623.

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We have derived the analytical kernels of the pricing formulae of the CEV knockout options with time-dependent parameters for a parametric class of moving barriers. By a series of similarity transformations and changing variables, we are able to reduce the pricing equation to one which is reducible to the Bessel equation with constant parameters. These results enable us to develop a simple and efficient method for computing accurate estimates of the CEV single-barrier option prices as well as their upper and lower bounds when the model parameters are time-dependent. By means of the multistage approximation scheme, the upper and lower bounds for the exact barrier option prices can be efficiently improved in a systematic manner. It is also natural that this new approach can be easily applied to capture the valuation of other standard CEV options with specified moving knockout barriers. In view of the CEV model being empirically considered to be a better candidate in equity option pricing than the traditional Black-Scholes model, more comparative pricing and precise risk management in equity options can be achieved by incorporating term structures of interest rates, volatility, and dividend into the CEV option valuation model.

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Ataguba, Joseph Obaje. "Spreadsheet Iteration of Reversionary Leasehold Rental Growth Rate Within The Framework of Explicit DCF Appraisals." International Journal of Built Environment and Sustainability 8, no. 1 (December 29, 2020): 29–45. http://dx.doi.org/10.11113/ijbes.v8.n1.576.

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Income growth rates are required to justify decisions and strategies for property investments. Although existing studies addressed this phenomenon in freehold investments, a relative question regarding the determination of rental growth rates of leasehold investment properties valued part-way through rent review periods has not been addressed before now. This study examined the spreadsheet-assisted scenario analysis tools and techniques that are required for the determination of rental growth rates of leasehold investment properties valued part-way through rent review periods. A precursor to the scenario analysis was the development of a hybrid leasehold DCF valuation model arising from the equation of the formula for reversionary leasehold equivalent yield valuation to the formula for reversionary leasehold growth explicit DCF valuation model; thereby culminating into the identification of four unknown variables comprising the all risks yield and the implied growth rates of leasehold cash inflows and cash outflows which were subsequently derived using the solver tool of Excel®. From a total of eleven scenarios generated, the 9th successive scenario produced optimal results indicating zero slack between iterated and calculated values for the growth rates of leasehold cash inflows and cash outflows respectively. With recourse to the hybrid leasehold DCF valuation model, the spreadsheet-assisted scenario was found to produce mathematically valid growth rates that justify the valuation of leasehold investment properties part-way through rent review periods. The value of this research is the analytical tools and rigour it avails investors seeking income returns and growth from reversionary leasehold property as an instance of terminable investments.

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SUZUKI, ATSUO, and KATSUSHIGE SAWAKI. "THE VALUATION OF RUSSIAN OPTIONS FOR DOUBLE EXPONENTIAL JUMP DIFFUSION PROCESSES." Asia-Pacific Journal of Operational Research 27, no. 02 (April 2010): 227–42. http://dx.doi.org/10.1142/s021759591000265x.

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In this paper, we derive closed form solution for Russian option with jumps. First, we discuss the pricing of Russian options when the stock pays dividends continuously. Secondly, we derive the value function of Russian options by solving the ordinary differential equation with some conditions (the value function is continuous and differentiable at the optimal boundary for the buyer). And we investigate properties of optimal boundaries of the buyer. Finally, some numerical results are presented to demonstrate analytical properties of the value function.

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Kwok, Yue-Kuen, Lixin Wu, and Hong Yu. "Pricing Multi-Asset Options with an External Barrier." International Journal of Theoretical and Applied Finance 01, no. 04 (October 1998): 523–41. http://dx.doi.org/10.1142/s021902499800028x.

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An external barrier of an option contract is a stochastic variable which determines whether the option is knocked in or out when the value of the variable is above or below some predetermined level, but itself is not the price of an asset which underlies the option. In this paper, we present analytic formulation for the valuation of European options on one or multiple assets with single external barrier, where the barrier level can be exponential. As the domain of the problem becomes semi-infinite due to the presence of the external barrier, we employ the method of images to find the Green function of the governing differential equation. An efficient and accurate fractional step finite difference scheme is proposed for the numerical valuation of these barrier options.

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BUFFINGTON, JOHN, and ROBERT J. ELLIOTT. "AMERICAN OPTIONS WITH REGIME SWITCHING." International Journal of Theoretical and Applied Finance 05, no. 05 (August 2002): 497–514. http://dx.doi.org/10.1142/s0219024902001523.

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A Black-Scholes market is considered in which the underlying economy, as modeled by the parameters and volatility of the processes, switches between a finite number of states. The switching is modeled by a hidden Markov chain. European options are priced and a Black-Scholes equation obtained. The approximate valuation of American options due to Barone-Adesi and Whaley is extended to this setting.

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Kaiser, Zoltán. "On stability of the monomial functional equation in normed spaces over fields with valuation." Journal of Mathematical Analysis and Applications 322, no. 2 (October 2006): 1188–98. http://dx.doi.org/10.1016/j.jmaa.2005.04.087.

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Journal articles on the topic 'Valuation equation'

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