Article

Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model

Operations Research (Impact Factor: 1.74). 07/2011; 60(1). DOI: 10.2307/41476338

ABSTRACT

We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only Itô's formula and do not need more advanced results such as those of Bessel processes and Lamperti's representation. As a by-product we also show that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transform can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate, and performs well even in the case of low volatilities. Subject classifications: Finance: asset pricing. Probability: stochastic model applica-tions. Area of review: Financial engineering.

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    • "We set the parameters as follows: S 0 = 100, r = 0.03, T = 1 and K = 90 for the VG process and K = 110 for the CGMY process. In order to compute the price of the Asian option we use the technique pioneered for hyperexponential processes by Cai and Kou [7] (see also [17, Section 4.2]). Since we were unable to find any results in the literature for pricing two-sided one-sided one-sided one-sided [2N + 1/2N ] [N/N ] "

    Full-text · Dataset · Dec 2014
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    • "We set the parameters as follows: S 0 = 100, r = 0.03, T = 1 and K = 90 for the VG process and K = 110 for the CGMY process. In order to compute the price of the Asian option we use the technique pioneered for hyperexponential processes by Cai and Kou [7] (see also [17, Section 4.2]). Since we were unable to find any results in the literature for pricing two-sided one-sided one-sided one-sided [2N + 1/2N ] [N/N ] "

    Full-text · Article · Dec 2014
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    • "For an extensive literature review, we refer to, e.g., Cai and Kou (2012). 3 A symmetry result between the floating-strike case and the fixed-strike case is first obtained in Henderson and Wojakowski (2002). "
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    ABSTRACT: In this paper, we consider a generalized Asian option that includes any type of Asian options studied in the literature as a special case, and propose a unified approximation method for the pricing of such options when the underlying process is a diffusion. It is shown that options on the ratio of averages such as Australian-Asian options and volume-weighted average (VWAP) options can also be priced within this unified approach. Some numerical examples are given to support the usefulness of our unified approximation method for practical use. Our method can be easily extended to the cases of stochastic volatility and stochastic interest-rate economies.
    Full-text · Article · Nov 2014
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