Relevant bibliographies by topics / Options (Finance) – Prices – Mathematical models

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Options (Finance) – Prices – Mathematical models'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 January 2023

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Journal articles on the topic "Options (Finance) – Prices – Mathematical models"

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Abraham, Rebecca, and Hani El-Chaarani. "A Mathematical Formulation of the Valuation of Ether and Ether Derivatives as a Function of Investor Sentiment and Price Jumps." Journal of Risk and Financial Management 15, no. 12 (December 8, 2022): 591. http://dx.doi.org/10.3390/jrfm15120591.

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The purpose of this study was to create quantitative models to value ether, ether futures, and ether options based upon the ability of cryptocurrencies to transform existing intermediary-verified payments to non-intermediary-based currency transfers, the ability of ether as a late mover to displace bitcoin as the first mover, and the valuation of ether in the context of investor irrationality models. The risk-averse investor’s utility function is a combination of expectations of the performance of ether, expectations of cryptocurrencies’ transformative power, and expectations of ether superseding bitcoin. The moderate risk-taker’s utility function is an alt-Weibull distribution, along with a gamma distribution. Risk-takers have a utility function in the form of a Bessel function. Ether price functions consist of a Levy jump process. Ether futures are valued as the combination of current spot prices along with term prices. The value of spot prices is the product of a spot premium and a lognormal distribution of spot prices. The value of term prices is equal to the product of a term premium, and the Levy jump process of price fluctuations during the delivery period. For ether options, a less risky ether option portfolio offsets ether’s risk by a fixed-income trading strategy.
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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.

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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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Kumar Jaiswal, Jitendra, and Raja Das. "Artificial Neural Network Algorithms based Nonlinear Data Analysis for Forecasting in the Finance Sector." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 169. http://dx.doi.org/10.14419/ijet.v7i4.10.20829.

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The involvement of big populace in the quantitative trading has been increased remarkably since the wired and wireless systems have become quite ubiquitous in the fields of finance and economics. Statistical, mathematical and technical analysis in parallel with machine learning and artificial intelligence are frequently being applied to perceive prices moving pattern and forecasting. However stock price do not follow any deterministic regulatory function, factor or circumstances rather than many considerations such as economy and finance, political environments, demand and supply, buying and selling tendency, trading and investment, etc. Historical data assist remarkably for prices forecasting as an important option for mathematicians and researchers. In this paper, we have followed backpropagation and radial basis function neural network for predicting future prices by modifying these techniques as per requirements. We have also performed a comparative analysis of the two ANN techniques for existing and our modified models.
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Eissa, Mahmoud A., and M. Elsayed. "Improve Stock Price Model-Based Stochastic Pantograph Differential Equation." Symmetry 14, no. 7 (July 1, 2022): 1358. http://dx.doi.org/10.3390/sym14071358.

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Although the concept of symmetry is widely used in many fields, it is almost not discussed in finance. This concept appears to be relevant in relation, for example, to mathematical models that can predict stock prices to contribute to the decision-making process. This work considers the stock price of European options with a new class of the non-constant delay model. The stochastic pantograph differential equation (SPDE) with a variable delay is provided in order to overcome the weaknesses of using stochastic models with constant delay. The proposed model is constructed to improve the evaluation process and prediction accuracy for stock prices. The feasibility of the proposed model is introduced under relatively weak conditions imposed on its volatility function. Furthermore, the sensitivity of time lag is discussed. The robust stochastic theta Milstein (STM) method is combined with the Monte Carlo simulation to compute asset prices within the proposed model. In addition, we prove that the numerical solution can preserve the non-negativity of the solution of the model. Numerical experiments using real financial data indicate that there is an increasing possibility of prediction accuracy for the proposed model with a variable delay compared to non-linear models with constant delay and the classical Black and Scholes model.
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Fernández, Lexuri, Peter Hieber, and Matthias Scherer. "Double-barrier first-passage times of jump-diffusion processes." mcma 19, no. 2 (July 1, 2013): 107–41. http://dx.doi.org/10.1515/mcma-2013-0005.

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Abstract. Required in a wide range of applications in, e.g., finance, engineering, and physics, first-passage time problems have attracted considerable interest over the past decades. Since analytical solutions often do not exist, one strand of research focuses on fast and accurate numerical techniques. In this paper, we present an efficient and unbiased Monte-Carlo simulation to obtain double-barrier first-passage time probabilities of a jump-diffusion process with arbitrary jump size distribution; extending single-barrier results by [Journal of Derivatives 10 (2002), 43–54]. In mathematical finance, the double-barrier first-passage time is required to price exotic derivatives, for example corridor bonus certificates, (step) double barrier options, or digital first-touch options, that depend on whether or not the underlying asset price exceeds certain threshold levels. Furthermore, it is relevant in structural credit risk models if one considers two exit events, e.g., default and early repayment.
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Aghabeygi, Mona, Kamel Louhichi, and Sergio Gomez y Paloma. "Impacts of fertilizer subsidy reform options in Iran: an assessment using a Regional Crop Programming model." Bio-based and Applied Economics 11, no. 1 (July 20, 2022): 55–73. http://dx.doi.org/10.36253/bae-10981.

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The aim of this paper is to assess the potential impacts of different fertilizer subsidy reform options on the performance of the Iranian crops production sector. This is achieved using a Regional Crop Programming (RCP) model, based on Positive Mathematical Programming, which includes in total 14 crop activities and encompasses 31 administrative regions. The RCP model is a collection of micro-economic models, working with exogenous prices, each representing the optimal crop allocation at the regional level. The model is calibrated against observed data on crop acreage, yield responses to nitrogen application, and exogenous supply elasticities. Simulation results show that a total removal of nitrogen fertilizer subsidies would affect the competitiveness of crops with the highest nitrogen application rates and lead to a slight reduction of national agricultural income, at approximately 1%. This effect, which is more pronounced at the regional level, is driven by area reallocation rather than land productivity. The reallocation of nitrogen fertilizer subsidy to only strategic crops boost their production and income but increase disparity among regions and affects negatively welfare compared to the current universal fertilizer program. The transfer efficiency analysis shows that both target and universal simulated options are inefficient with an efficiency score below one.
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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.

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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.
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Nguyen, Ngoc Quynh Anh, and Thi Ngoc Trang Nguyen. "Risk measures computation by Fourier inversion." Journal of Risk Finance 18, no. 1 (January 16, 2017): 76–87. http://dx.doi.org/10.1108/jrf-03-2016-0034.

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Purpose The purpose of this paper is to present the method for efficient computation of risk measures using Fourier transform technique. Another objective is to demonstrate that this technique enables an efficient computation of risk measures beyond value-at-risk and expected shortfall. Finally, this paper highlights the importance of validating assumptions behind the risk model and describes its application in the affine model framework. Design/methodology/approach The method proposed is based on Fourier transform methods for computing risk measures. The authors obtain the loss distribution by fitting a cubic spline through the points where Fourier inversion of the characteristic function is applied. From the loss distribution, the authors calculate value-at-risk and expected shortfall. As for the calculation of the entropic value-at-risk, it involves the moment generating function which is closely related to the characteristic function. The expectile risk measure is calculated based on call and put option prices which are available in a semi-closed form by Fourier inversion of the characteristic function. We also consider mean loss, standard deviation and semivariance which are calculated in a similar manner. Findings The study offers practical insights into the efficient computation of risk measures as well as validation of the risk models. It also provides a detailed description of algorithms to compute each of the risk measures considered. While the main focus of the paper is on portfolio-level risk metrics, all algorithms are also applicable to single instruments. Practical implications The algorithms presented in this paper require little computational effort which makes them very suitable for real-world applications. In addition, the mathematical setup adopted in this paper provides a natural framework for risk model validation which makes the approach presented in this paper particularly appealing in practice. Originality/value This is the first study to consider the computation of entropic value-at-risk, semivariance as well as expectile risk measure using Fourier transform method.
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Madan, Dilip B., and King Wang. "Risk Neutral Jump Arrival Rates Implied in Option Prices and Their Models." Applied Mathematical Finance 28, no. 3 (May 4, 2021): 201–35. http://dx.doi.org/10.1080/1350486x.2021.2007145.

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SKIADOPOULOS, GEORGE. "VOLATILITY SMILE CONSISTENT OPTION MODELS: A SURVEY." International Journal of Theoretical and Applied Finance 04, no. 03 (June 2001): 403–37. http://dx.doi.org/10.1142/s021902490100105x.

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The developing literature on "smile consistent" no-arbitrage models has emerged from the need to price and hedge exotic options consistently with the prices of standard European options. This survey paper describes the steps through which this literature has evolved by providing a taxonomy of the various models. It highlights the main ideas behind the different models, and it outlines their advantages and limitations. Practical issues in implementing the models are also discussed.
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Dissertations / Theses on the topic "Options (Finance) – Prices – Mathematical models"

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Glover, Elistan Nicholas. "Analytic pricing of American put options." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1002804.

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American options are the most commonly traded financial derivatives in the market. Pricing these options fairly, so as to avoid arbitrage, is of paramount importance. Closed form solutions for American put options cannot be utilised in practice and so numerical techniques are employed. This thesis looks at the work done by other researchers to find an analytic solution to the American put option pricing problem and suggests a practical method, that uses Monte Carlo simulation, to approximate the American put option price. The theory behind option pricing is first discussed using a discrete model. Once the concepts of arbitrage-free pricing and hedging have been dealt with, this model is extended to a continuous-time setting. Martingale theory is introduced to put the option pricing theory in a more formal framework. The construction of a hedging portfolio is discussed in detail and it is shown how financial derivatives are priced according to a unique riskneutral probability measure. Black-Scholes model is discussed and utilised to find closed form solutions to European style options. American options are discussed in detail and it is shown that under certain conditions, American style options can be solved according to closed form solutions. Various numerical techniques are presented to approximate the true American put option price. Chief among these methods is the Richardson extrapolation on a sequence of Bermudan options method that was developed by Geske and Johnson. This model is extended to a Repeated-Richardson extrapolation technique. Finally, a Monte Carlo simulation is used to approximate Bermudan put options. These values are then extrapolated to approximate the price of an American put option. The use of extrapolation techniques was hampered by the presence of non-uniform convergence of the Bermudan put option sequence. When convergence was uniform, the approximations were accurate up to a few cents difference.
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Lee, Mou Chin. "An empirical test of variance gamma options pricing model on Hang Seng index options." HKBU Institutional Repository, 2000. http://repository.hkbu.edu.hk/etd_ra/263.

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Song, Na, and 宋娜. "Mathematical models and numerical algorithms for option pricing and optimal trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50662168.

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Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis. The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem. Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively.
published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Zhao, Jing Ya. "Numerical methods for pricing Bermudan barrier options." Thesis, University of Macau, 2012. http://umaclib3.umac.mo/record=b2592939.

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Dharmawan, Komang School of Mathematics UNSW. "Superreplication method for multi-asset barrier options." Awarded by:University of New South Wales. School of Mathematics, 2005. http://handle.unsw.edu.au/1959.4/30169.

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The aim of this thesis is to study multi-asset barrier options, where the volatilities of the stocks are assumed to define a matrix-valued bounded stochastic process. The bounds on volatilities may represent, for instance, the extreme values of the volatilities of traded options. As the volatilities are not known exactly, the value of the option can not be determined. Nevertheless, it is possible to calculate extreme values. We show that these values correspond to the best and the worst case scenarios of the future volatilities for short positions and long positions in the portfolio of the options. Our main tool is the equivalence of the option pricing and a certain stochastic control problem and the resulting concept of superhedging. This concept has been well known for some time but never applied to barrier options. First, we prove the dynamic programming principle (DPP) for the control problem. Next, using rather standard arguments we derive the Hamilton-Jacobi-Bellman equation for the value function. We show that the value function is a unique viscosity solution of the Hamilton-Jacobi-Bellman equation. Then we define the super price and superhedging strategy for the barrier options and show equivalence with the control problem studied above. The superprice price can be found by solving the nonlinear Hamilton-Jacobi-Equation studied above. It is called sometimes the Black-Scholes-Barenblatt (BSB) equation. This is the Hamilton-Jacobi-Bellman equation of the exit control problem. The sup term in the BSB equation is determined dynamically: it is either the upper bound or the lower bound of the volatility matrix, according to the convexity or concavity of the value function with respect to the stock prices. By utilizing a probabilistic approach, we show that the value function of the exit control problem is continuous. Then, we also obtain bounds for the first derivative of the value function with respect to the space variable. This derivative has an important financial interpretation. Namely, it allows us to define the superhedging strategy. We include an example: pricing and hedging of a single-asset barrier option and its numerical solution using the finite difference method.
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Mimouni, Karim. "Three essays on volatility specification in option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103274.

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Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type.
In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit.
The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.
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劉伯文 and Pak-man Lau. "Option pricing: a survey." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1994. http://hub.hku.hk/bib/B31977911.

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Chan, Ka Hou. "European call option pricing under partial information." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691380.

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Oagile, Joel. "Sequential Calibration of Asset Pricing Models to Option Prices." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29840.

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This paper implements four calibration methods on stochastic volatility models. We estimate the latent state and parameters of the models using three non-linear filtering methods, namely the extended Kalman filter (EKF), iterated extended Kalman filter (IEKF) and the unscented Kalman filter (UKF). A simulation study is performed and the non-linear filtering methods are compared to the standard least square method (LSQ). The results show that both methods are capable of tracking the hidden state and time varying parameters with varying success. The non-linear filtering methods are faster and generally perform better on validation. To test the stability of the parameters, we carry out a delta hedging study. This exercise is not only of interest to academics, but also to traders who have to hedge their positions. Our results do not show any significant benefits resulting from performing delta hedging using parameter estimates obtained from non-linear filtering methods as compared to least square parameter estimates.
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蕭德權 and Tak-kuen Siu. "Risk measures in finance and insurance." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31242297.

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Books on the topic "Options (Finance) – Prices – Mathematical models"

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Wilmott, Paul. Option pricing: Mathematical models and computation. Oxford, UK: Oxford Financial Press, 1997.

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Katz, Jeffrey Owen. Advanced option pricing models: An empirical approach to valuing options. New York: McGraw-Hill, 2005.

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Bates, David S. Testing option pricing models. Cambridge, MA: National Bureau of Economic Research, 1995.

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Matthias, Ehrhardt, ed. Nonlinear models in mathematical finance: New research trends in option pricing. New York: Nova Science Publishers, 2008.

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Hughston, L. P., and Matheus R. Grasselli. Finance at Fields. Singapore: World Scientific, 2013.

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Mandler, Martin. Market expectations and option prices: Techniques and applications. Heidelberg: Physica Verlag, 2003.

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Mandler, Martin. Market expectations and option prices: Techniques and applications. New York: Physica-Verlag, 2003.

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Capiński, Marek. The Black-Scholes model. New York: Cambridge University Press, 2013.

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Chriss, Neil. Black-Scholes and beyond: Option pricing models. New York: McGraw-Hill, 1997.

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Chriss, Neil. Black-Scholes and beyond: Option pricing models. Chicago: Irwin, 1997.

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Book chapters on the topic "Options (Finance) – Prices – Mathematical models"

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Hobson, David. "The Skorokhod Embedding Problem and Model-Independent Bounds for Option Prices." In Paris-Princeton Lectures on Mathematical Finance 2010, 267–318. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-14660-2_4.

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Eberlein, Ernst, Kathrin Glau, and Antonis Papapantoleon. "Analyticity of the Wiener–Hopf Factors and Valuation of Exotic Options in Lévy Models." In Advanced Mathematical Methods for Finance, 223–45. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18412-3_8.

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Nardon, Martina, and Paolo Pianca. "Extracting implied dividends from options prices: Some applications to the Italian derivatives market." In Mathematical and Statistical Methods for Actuarial Sciences and Finance, 315–22. Milano: Springer Milan, 2012. http://dx.doi.org/10.1007/978-88-470-2342-0_37.

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Nardon, Martina, and Paolo Pianca. "The Effects of Curvature and Elevation of the Probability Weighting Function on Options Prices." In Mathematical and Statistical Methods for Actuarial Sciences and Finance, 149–52. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05014-0_35.

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Davis, Mark H. A. "3. The classical theory of option pricing." In Mathematical Finance: A Very Short Introduction, 30–60. Oxford University Press, 2019. http://dx.doi.org/10.1093/actrade/9780198787945.003.0003.

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‘The classical theory of option pricing’ explains the theory of arbitrage pricing, which is closely related to the Dutch Book Arguments, but which brings in a new factor: prices in financial markets evolve over time and participants are able to trade at any time, instead of just taking bets and awaiting the result. In addition to the general theory, pricing models and methods have been developed for specific markets—foreign exchange, interest rates, and credit. The binomial and continuous-time mathematical models for stock prices are introduced along with the Black–Scholes formula, the volatility surface, the difference between European and American options, and the Fundamental Theorem of Asset Pricing.
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"Estimation of models for stock prices." In Mathematical Finance, 168–81. Routledge, 2007. http://dx.doi.org/10.4324/9780203964729.ch9.

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"Estimation of models for stock prices." In Mathematical Finance, 177–90. Routledge, 2007. http://dx.doi.org/10.4324/9780203964729-14.

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"Barrier Options in the BK and Verhulst Models." In Generalized Integral Transforms in Mathematical Finance, 289–308. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811231742_0014.

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"Barrier Options in the Time-Dependent CEV and CIR Models." In Generalized Integral Transforms in Mathematical Finance, 251–87. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811231742_0013.

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Özel, Gamze. "Stochastic Processes for the Risk Management." In Handbook of Research on Behavioral Finance and Investment Strategies, 188–200. IGI Global, 2015. http://dx.doi.org/10.4018/978-1-4666-7484-4.ch011.

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The financial markets use stochastic models to represent the seemingly random behavior of assets such as stocks, commodities, relative currency prices such as the price of one currency compared to that of another, such as the price of US Dollar compared to that of the Euro, and interest rates. These models are then used by quantitative analysts to value options on stock prices, bond prices, and on interest rates. This chapter gives an overview of the stochastic models and methods used in financial risk management. Given the random nature of future events on financial markets, the field of stochastic processes obviously plays an important role in quantitative risk management. Random walk, Brownian motion and geometric Brownian motion processes in risk management are explained. Simulations of these processes are provided with some software codes.
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Conference papers on the topic "Options (Finance) – Prices – Mathematical models"

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Kasparinsky, Felix Osvaldovich. "Complex Indicators of the Multitrading System." In 24th Scientific Conference “Scientific Services & Internet – 2022”. Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/abrau-2022-14.

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Abstract:
The article summarizes the experience of 4 years of work on setting up the Metatrder 5 Internet terminal tools for a multitrading system, which was developed to increase the effectiveness of price change forecasts in the Forex market by applying a set of interrelated technical analysis indicators to data of different time scales (timeframes), as well as to optimization of work with a variety of financial instruments, with the simultaneous use of multiple accounts. Possible ways of integrating technical and fundamental analysis tools, advantages and disadvantages of using mathematical models to predict changes in prices of financial instruments are discussed. A unidirectional (monophasic) price change is proposed to be called the term "oscillation". To integrate classical Elliott wave models and harmonic patterns, the concept of a block consisting of 8 oscillations distributed between 2 packages has been introduced. It was found that a series of 4 blocks form modules with a variable structure. Alternative options for the distribution of block oscillations between trend and correction packages are discussed to be consistent with the Dow theory of driving factors and stages of price change. A method of target distribution of 16 technical analysis indicators of various types (oscillators, trend indicators, volume indicators) over 4 sections of the Analytical window: "Price", "Oscillation", "Trend" and "Control" is proposed. The main principle in the formation of complex indicators is the unmasking of trends of oscillating indicators by applying trend indicators to their data. The ways of setting up the technical analysis indicators involved to optimize their use as part of complex trend indicators are described in detail. Recommendations are given for determining a trading group from three adjacent Analytical windows in a 6- window Analytical display to optimally select a trading timeframe in accordance with the operational situation. Examples of using complex indicators for generating trading signals for opening and closing deals are given. The results of preliminary experiments on the use of complex indicators and Fibonacci levels to determine pivot points when building price channels are discussed. Plans have been outlined to create a unified methodology for the formation of various price channels using complex indicators, Fibonacci levels, Elliott waves and harmonic patterns.
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