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A recursive method for discretely monitored geometric Asian option prices

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초록

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.

Abstract

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.

참고문헌 (13)

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  3. N. Cai, "Pricing Asian options under a hyper-exponential jump diffusion model", Oper. Res, 60(1), pp.64~77 (2012)
  4. A. Cerny, "An improved convolution algorithm for discretely sampled Asian options", Quant. Finance, 11(3), pp.381~389 (2011)
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  7. G. Fusai, "Pricing discretely monitored Asian options under Levy pro-cesses", J. Bank. Financ, 32(10), pp.2076~2088 (2008)
  8. S. L. Heston, "A closed-form solution for options with stochastic volatility with applica-tions to bonds and currency options", Rev. Financ. Stud, 6(2), pp.327~343 (1993)
  9. W. Kang, "Large deviations for affine diffusion processes on Rm +× Rn", Stochastic Process. Appl, 124(6), pp.2188~2227 (2014)
  10. J. Kim, "Valuation of power options under Heston’s stochastic volatility model", J. Econom. Dynam. Control, 36(11), pp.1796~1813 (2012)
  11. B. Kim, "Pricing of geometric Asian options under Heston’s stochastic volatility model", Quant. Financ, 14, pp.1795~1809 (2014)
  12. N. Tahani, "Exotic geometric average options pricing under stochastic volatility", Appl. Math. Finance, 20(3), pp.229~245 (2013)
  13. Y. Umezawa, "Pricing path-dependent options with discrete monitoring under time-changed Levy processes", Appl. Math. Finance, 22(2), pp.133~161 (2015)

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