OPTION PRICING UNDER STOCHASTIC VOLATILITY MODEL WITH JUMPS IN BOTH THE STOCK PRICE AND THE VARIANCE PROCESSES
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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.
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 (8)
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- R. Cont, "Financial Modeling with Jump Processes" (2004), CRC Press
- B. Eraker, "The impact of jumps in volatility and returns", The Journal of Finance, 58, pp.1269~1300 (2003)
- F.B. Hanson, "Applied Stochastic Process and Control for Jump Di®usions: Modeling, Analysis and Computation" (2007), Society for Industrial and Applied Mathematics
- S. Heston, "A Closed-Form Solution For Option with Stochastic Volatility with Appli-cations to Bond and Currency Options", Review of Financial Study, 6, pp.337~343 (1993)
- N. Makate, "Stochastic Volatility Jump-Di®usion Model for Option Pricing", J. Math. Finance, 3, pp.90~97 (2011)
- I. Karatzas, "Brownian Motion and Stochastic Calculus" (1991), Springer-Verlag
- G. Yan, "Option Pricing for a Stochastic-Volatility Jump-Diffusion Model with Log-Uniform Jump-Amplitudes", Proc. Amer. Control Conference, pp.1~7 (2006)