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Error estimates for option prices in jump-diffusion models
위인숙 대한수학회 2002 대한수학회보 Vol.39 No.4
We consider a jump-diffusion model generated by a L'{e}vy processfor an asset price. We present an error estimate for the optionprices between the jump-diffusion model and the Black-Scholesmodel when the former converges weakly to the latter.
Approximations of option prices for a jump-diffusion model
위인숙 대한수학회 2006 대한수학회지 Vol.43 No.2
We consider a geometric L\'{e}vy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the L\'{e}vy process.
Residual empirical process for diffusion processes
이상열,위인숙 대한수학회 2008 대한수학회지 Vol.45 No.3
In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge. In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.
Comparison of stochastic volatility models: Empirical study on KOSPI 200 index options
문경숙,Jung-Yon Seon,위인숙,Choongseok Yoon 대한수학회 2009 대한수학회보 Vol.46 No.2
We examine a unified approach of calculating the closed form solutions of option price under stochastic volatility models using stochastic calculus and the Fourier inversion formula. In particular, we review and derive the option pricing formulas under Heston and correlated Stein-Stein models using a systematic and comprehensive approach which were derived individually earlier. We compare the empirical performances of the two stochastic volatility models and the Black-Scholes model in pricing KOSPI 200 index options.
A recursive method for discretely monitored geometric Asian option prices
김바라,Jeongsim Kim,김제림,위인숙 대한수학회 2016 대한수학회보 Vol.53 No.3
We aim to compute discretely monitored geometric Asian option prices under the Heston model. This method involves explicit formula for multivariate generalized Fourier transform of volatility process and their integrals over different time intervals using a recursive method. As numerical results, we illustrate efficiency and accuracy of our method. In addition, we simulate scenarios which show evidently practical importance of our work.