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# Pricing Discrete Double-barrier Option under a Hyper-exponential Jump-diffusion Model

Author: LiuMin
Tutor: ZuoMing
School: Huazhong University of Science and Technology
Course: Operational Research and Cybernetics
Keywords: option pricing discrete double barrier option jump-diffusion model probability density function
CLC: F830.9
Type: Master's thesis
Year: 2011
Quote: 0

### Abstract

 In the financial markets, barrier option can put investors’returns and risk in certain limits, and the price is cheaper than standard options, so they are welcome by the investors. Barrier option study also becomes increasingly hotspots in the option pricing field. Jump-diffusion model is consisting of diffusion model and jump parts. This model can describe asset returns asymmetric leptokurtic feature. The existence of jumping part is also reasonable from the angle of economic significance, financial products’price will change greatly under the influence of various external factors. The jumping part can be considered as the reaction of the assets price to the external news. This paper will price the discrete double barrier options under a hyper-exponential jump diffusion model.In this paper we consider three problems on double barrier option:deriving a formula of double barrier option under a hyper-exponential jump-diffusion model; proposing a fast and accurate numerical algorithm for its valuation and the discrete double barrier option parity formula.Firstly, this paper find out the probability density function of the asset price hit the two barriers on the monitoring dates through the probability method based on the hyper-exponential jump-diffusion model. According to the option value can be expressed as the discount of the final earnings expectations, a multidimensional integral formula of the discrete double barrier option can be derived. Then because high dimensional integrals could not be quickly estimated on a computer, we put forward a fast and accurate numerical algorithm to calculate the value of the discrete monitoring double option. The final result of this method will be that the option value can be obtained by finite sums. Finally we obtain the discrete double barrier option parity formula.

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