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A pricing option approach based on backward stochastic differential equation theory. (English) Zbl 1422.91705

Summary: In option pricing, backward stochastic differential equation (BSDE) has wide application and Black-Scholes model is one of the classic pricing model. However, the model needs many preconditions which causes the implementing environment of model to approach perfection, leading to large deviation in actual application. Therefore, this article study the optimization problem of option pricing model under limited conditions intensively. It means that when random volatility is given, the option pricing formula with random interest rate is proposed and corresponding revision is also provided. Then we adopt call option and put option of S&P 500 index options to perform empirical research. The results indicate the assumption of random volatility is closer to reality. Compared to tradition models, the approach proposed in this article has enough theoretical basis. It is proved to own simple modeling method and higher accuracy which also shows certain reference significance to option pricing.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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