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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 satisfying f(`, ν, t; k, T ) = exp (g(τ) + νh(τ) + ix`) . We add the term of order ν to the exponent in the above equation and seek the explicit solution of f .

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