| Numerical methods on the Heston Option Pricing Model |
| کد مقاله : 1048-FEMATH5-FULL (R1) |
| نویسندگان: |
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فرشته گل دوست *1، جعفر بی آزار2 1گیلان .رشت . خیاباننامجو. دانشکده علوم ریاضی دانشگاه گیلان 2دانشکده ریاضی دانشگاه گیلان |
| چکیده مقاله: |
| Abstract Real-world problems in natural phenomena are modeled as partial, integral and integro differential or stochastic equations. Since finding the solution of these equations is complicated, in recent years a lot of attention has been devoted by researchers to find the analytical and numerical solution of these equations. In financial topics, Heston (1993), one of the most popular stochastic volatility option pricing models, this model is based on the stock price and variance dynamics,( Heston formula in real abstract) Modeling derivative products in mathematical finance usually start with a system of stochastic differential equations that correspond to state variables like stock, interest rate and volatility. In this paper, PDE form of the Heston model that has derived from stochastic model was applied with the Legendre wavelets method. The Heston SDE model has changed to a partial differential equation with a basic lemma in stochastic differential equation which called Ito lemma that includes derivatives and integration in stochastic calculus, By considering the properties and using structure of wavelets for given problem leads to reduce the time. Keywords: partial and stochastic differential equation, Heston model, Legendre wavelet method. |
| کلیدواژه ها: |
| Keywords: partial and stochastic differential equation, Heston model, Legendre wavelet method. |
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