East Asian mathematical journal

  • 제35권1호
  • /
  • Pages.59-66
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  • 2019
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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IMEX METHODS FOR PRICING FIXED STRIKE ASIAN OPTIONS WITH JUMP-DIFFUSION MODELS

  • Lee, Sunju (Department of Mathematics, Chungnam National University) ;
  • Lee, Younhee (Department of Mathematics, Chungnam National University)
  • 투고 : 2018.11.22
  • 심사 : 2018.12.19
  • 발행 : 2019.01.31
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초록

In this paper we study implicit-explicit (IMEX) methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian option is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order convergence rate.

키워드

E1BGBB_2019_v35n1_59_f0001.png 이미지

FIGURE 1. The discrete l2-errors for the European fixed strike arithmetic Asian put option under the Merton model by using the LF method, the CN method, and the BDF2 method.

TABLE 1. The prices of the European xed strike arithmetic Asian put option at S = 100 under the Merton model. These prices are obtained by using the LF method, the CN method, and the BDF2 method with the parameters in (15). N is the number of time steps, M is the number of spatial steps, and L is the number of arithmetic average steps.

E1BGBB_2019_v35n1_59_t0001.png 이미지

참고문헌

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