OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2014, v.21 no.4, pp.295-305

https://doi.org/10.7468/jksmeb.2014.21.4.295

Kim, Ju Hong (Department of Mathematics, Sungshin Women's University)

Kim, Ju Hong. (2014). OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES. 한국수학교육학회지시리즈B:순수및응용수학, 21(4), 295-305, https://doi.org/10.7468/jksmeb.2014.21.4.295

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Abstract

Yan & Hanson [8] and Makate & Sattayatham [6] extended Bates' model to the stochastic volatility model with jumps in both the stock price and the variance processes. As the solution processes of finding the characteristic function, they sought such a function f satisfying <TEX>$$f({\ell},{\nu},t;k,T)=exp\;(g({\tau})+{\nu}h({\tau})+ix{\ell})$$</TEX>. We add the term of order <TEX>${\nu}^{1/2}$</TEX> to the exponent in the above equation and seek the explicit solution of f.

keywords: stochastic-volatility, jump-diffusion, risk-neutral option pricing, characteristic function

참고문헌

D. Bates. (1996). Jump and Stochastic Volatility: Exchange Rate Processes Implict in Deutche Mark in Options. Review of Financial Studies, 9, 69-107. 10.1093/rfs/9.1.69.

R. Cont & P. Tankov. Financial Modeling with Jump Processes.

B. Eraker, M. Johannes & N. Polson. (2003). The impact of jumps in volatility and returns. The Journal of Finance, 58, 1269-1300. 10.1111/1540-6261.00566.

F.B. Hanson. Applied Stochastic Process and Control for Jump Diffusions: Modeling, Analysis and Computation.

S. Heston. (1993). A Closed-Form Solution For Option with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Study, 6, 337-343.

N. Makate & P. Sattayatham. (2011). Stochastic Volatility Jump-Diffusion Model for Option Pricing. J. Math. Finance, 3, 90-97.

I. Karatzas & S.E. Shreve. Brownian Motion and Stochastic Calculus.

G. Yan & F.B. Hanson. (2006). Option Pricing for a Stochastic-Volatility Jump-Diffusion Model with Log-Uniform Jump-Amplitudes (1-7). Proc. Amer. Control Conference.

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논문 상세

Vol.21 No.4

OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES

OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학