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ISSN : 1226-0657

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Vol.21 No.4
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OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Kim,, J. H. (2014). OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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

Reference

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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.

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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.

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

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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.

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

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

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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.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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