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A new method of option pricing based on Black-Scholes model. (Chinese. English summary) Zbl 1249.62014

Summary: Actual financial markets are incompleted and distributions of yield rate are fat-tailed, so based on the classical Black-Scholes model and using the downward convex property of functions, the option pricing formula \(H(a)=E[(X-a)^2]\) is generalized to \(H_k(a)=E[(X-a)^{2k}]\). With the GARCH model of the DJSH rate and by using the method of stochastic simulations, the effects of the two pricing formulas are compared. The results show that the new formula of option pricing effectively increases the price and reduces the risk.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
91B84 Economic time series analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
91G70 Statistical methods; risk measures
91B30 Risk theory, insurance (MSC2010)
91B25 Asset pricing models (MSC2010)
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