Option Valuation using Fast Integral Transforms

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  • 高速積分変換に基づくオプション価格評価法
  • コウソク セキブン ヘンカン ニ モトズク オプション カカク ヒョウカホウ

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Abstract

This paper surveys recent developments in numerical methods for option pricing, focusing on the approaches based on fast integral transforms. Under the Black-Scholes framework, the pricing of discrete path dependent options and Bermudan options can be reduced to evaluation of a series of convolutions of the Gaussian distribution and a known function. These convolutions can be computed efficiently using the double-exponential integration formula and fast integral transforms. The resulting algorithms have computational complexity of O (N) at each time step, where N is the number of sample points at each step, and the error decreases exponentially with N. Thus these algorithms can be shown to be faster and more accurate than any other existing algorithms. Extensions of this approach to a wider variety of options including weather derivatives and options under jump-diffusion models are also discussed.

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