Sima Mashayekhi; Seyed Nourollah Mousavi
Abstract
This study compares the performance of the classic Black-Scholes model and the generalized Liu and Young model in pricing European options and calculating derivatives sensitivities in high volatile illiquid markets. The generalized Liu and Young model is a more accurate option pricing model that incorporates ...
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This study compares the performance of the classic Black-Scholes model and the generalized Liu and Young model in pricing European options and calculating derivatives sensitivities in high volatile illiquid markets. The generalized Liu and Young model is a more accurate option pricing model that incorporates both the efficacy of the number of invested stocks and the abnormal increase of volatility during a financial crisis for hedging pur- poses and the financial risk management. To evaluate the performance of these models, we use numerical methods such as finite difference schemes and Monte-Carlo simulation with antithetic variate variance reduction tech- nique. Our results show that the generalized Liu and Young model outper- forms the classic Black-Scholes model in terms of accuracy, especially in high volatile illiquid markets. Additionally, we find that the finite differ- ence schemes are more efficient and faster than the Monte-Carlo simulation in this model. Based on these findings, we recommend using the general- ized Liu and Young model with finite difference schemes for the European options and Greeks valuing in high volatile illiquid markets.
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.
