Parisa Karami; Ali Safdari
Abstract
In financial markets , dynamics of underlying assets are often specified via stochasticdifferential equations of jump - diffusion type . In this paper , we suppose that two financialassets evolved by correlated Brownian motion . The value of a contingent claim written on twounderlying assets under jump ...
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In financial markets , dynamics of underlying assets are often specified via stochasticdifferential equations of jump - diffusion type . In this paper , we suppose that two financialassets evolved by correlated Brownian motion . The value of a contingent claim written on twounderlying assets under jump diffusion model is given by two - dimensional parabolic partialintegro - differential equation ( P I D E ) , which is an extension of the Black - Scholes equation witha new integral term . We show how basket option prices in the jump - diffusion models , mainlyon the Merton model , can be approximated using finite difference method . To avoid a denselinear system solution , we compute the integral term by using the Trapezoidal method . Thenumerical results show the efficiency of proposed method .Keywords: basket option pricing, jump-diffusion models, finite difference method.
Moslem Peymany
Abstract
This study emphasizes on the mathematical modeling procedure of stock price behavior and option valuation in order to highlight the role and importance of advanced mathematics and subsequently computer software in financial analysis. To this end, following price process modeling and explaining the procedure ...
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This study emphasizes on the mathematical modeling procedure of stock price behavior and option valuation in order to highlight the role and importance of advanced mathematics and subsequently computer software in financial analysis. To this end, following price process modeling and explaining the procedure of option pricing based on it, the resulting model is solved using advanced numerical methods and is executed by MATLAB software. As derivatives pricing models are based on price behavior of underling assets and are subject to change as a result of variation in the behavior of the asset, studying the price behavior of underlying asset is of significant importance. A number of such models (such as Geometric Brownian Motion and jump-diffusion model) are, therefore, analyzed in this article, and results of their execution based on real data from Tehran Stock Exchange total index are presented by parameter estimation and simulation methods and also by using numerical methods.
