Options Pricing in Jump Diffusion Markets during Financial Crisis

El-Khatib, Youssef; Hajji, Mohamed; Al-Refai, Mohammed

doi:10.12785/amis/070623

Cited by 9 publications

(5 citation statements)

References 19 publications

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“…The market has an European call option with underlying risky asset S. The return on asset without risk is denoted by r. For the sake of the simplicity, we use the denotation P for the risk-neutral probability. As in [5] we assume that the underlying ‡ For recent papers on modeling with jump, we refer to [2] for jump-diffusion model, to [4] for price sensitivities calculation using Malliaivn calculus and to [3] where a jump diffusion model during crisis is studied.…”

Section: Options Pricing and Price Sensitivities In Crisis Timementioning

confidence: 99%

Computation of second order price sensitivities in depressed markets

El-Khatib,

Hatemi-J

2017

Preprint

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Risk management in financial derivative markets requires inevitably the calculation of the different price sensitivities. The literature contains an abundant amount of research works that have studied the computation of these important values. Most of these works consider the well-known Black and Scholes model where the volatility is assumed to be constant. Moreover, to our best knowledge, they compute only the first order price sensitivities. Some works that attempt to extend to markets affected by financial crisis appeared recently. However, none of these papers deal with the calculation of the price sensitivities of second order. Providing second derivatives for the underlying price sensitivities is an important issue in financial risk management because the investor can determine whether or not each source of risk is increasing at an increasing rate. In this paper, we work on the computation of second order prices sensitivities for a market under crisis. The underlying second order price sensitivities are derived explicitly. The obtained formulas are expected to improve on the accuracy of the hedging strategies during a financial crunch.

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Section: Options Pricing and Price Sensitivities In Crisis Timementioning

confidence: 99%

Computation of second order price sensitivities in depressed markets

El-Khatib,

Hatemi-J

2017

Preprint

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“…So, according to (20), by using two given initial values 1|0 and Σ 1|0 , the values of can be calculated. Therefore, we obtain the estimated values of ln̂2 and̂( ).…”

Section: Parameter Estimation Of Dev Modelmentioning

confidence: 99%

“…In addition, Lillo and Mantenga in [18] show that ex-postfinancial markets of crisis have characteristics of a power-law relaxation decay. By using results of [19], El-Khatib et al in [20] study European option pricing model with postcrash relaxation times in 2007. In [7], Zhu and Galbraith present an evidence that stock returns can be fitted by Student's -distribution during postcrash relaxation times, which is consistent with the results in [17,18].…”

Section: Introductionmentioning

confidence: 99%

Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

Fan

Xiang

Chen

2016

Discrete Dynamics in Nature and Society

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Market crashes often appear in daily trading activities and such instantaneous occurring events would affect the stock prices greatly. In an unstable market, the volatility of financial assets changes sharply, which leads to the fact that classical option pricing models with constant volatility coefficient, even stochastic volatility term, are not accurate. To overcome this problem, in this paper we put forward a dynamic elasticity of variance (DEV) model by extending the classical constant elasticity of variance (CEV) model. Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. In addition, Kalman filtering method is employed to estimate the volatility term of our model. Our main finding is that the prices of European call option under our model are more accurate than those calculated by Black-Scholes model and CEV model in financial crashes.

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“…In the last Section concluding remarks are provided. ‡ We can find recent works using numerical techniques for pricing and hedging financial derivatives in jump markets see for instance [5] and [6].…”

Section: Introductionmentioning

confidence: 99%

Price sensitivities for a general stochastic volatility model

El-Khatib,

Hatemi-J

2017

Preprint

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We deal with the calculation of price sensitivities for stochastic volatility models. General forms for the dynamics of the underlying asset price and its volatility are considered. We make use of the chaotic (or Malliavin) calculus to compute the price sensitivities. The obtained results are applied to several recent stochastic volatility models as well as the existing ones that are commonly used by practitioners. Each price sensitivity is a source of financial risk. The suggested formulas are expected to improve on the hedging of the underlying risk.

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Options Pricing in Jump Diffusion Markets during Financial Crisis

Cited by 9 publications

References 19 publications

Computation of second order price sensitivities in depressed markets

Computation of second order price sensitivities in depressed markets

Efficient Option Pricing in Crisis Based on Dynamic Elasticity of Variance Model

Price sensitivities for a general stochastic volatility model

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