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

다국어 초록 (Multilingual 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 satisfying𝑓(𝓁, 𝒗, 𝒕; 𝒌, 𝑻) = exp(𝒈(τ) + 𝒗𝒉(τ) + 𝒾𝓍𝓁) .
We add the term of order 𝑣1/2 to the exponent in the above equation and seek the explicit solution of f.

참고문헌 (Reference)

1 B. Eraker, "The impact of jumps in volatility and returns" 58 : 1269-1300, 2003

2 N. Makate, "Stochastic Volatility Jump-Di®usion Model for Option Pricing" 3 : 90-97, 2011

3 G. Yan, "Option Pricing for a Stochastic-Volatility Jump-Diffusion Model with Log-Uniform Jump-Amplitudes" 1-7, 2006

4 D. Bates, "Jump and Stochastic Volatility: Exchange Rate Processes Implict in Deutche Mark in Options" 9 : 69-107, 1996

5 R. Cont, "Financial Modeling with Jump Processes" CRC Press 2004

6 I. Karatzas, "Brownian Motion and Stochastic Calculus" Springer-Verlag 1991

7 F.B. Hanson, "Applied Stochastic Process and Control for Jump Di®usions: Modeling, Analysis and Computation" Society for Industrial and Applied Mathematics 2007

8 S. Heston, "A Closed-Form Solution For Option with Stochastic Volatility with Appli-cations to Bond and Currency Options" 6 : 337-343, 1993