The option pricing problem is one of central contents in modern finance. In this paper, European option pricing formula is formulated for Liu’s hybrid stock model with randomness and fuzziness. This formula may be regarded as a generalization of Black-Scholes formula and Qin-Li’s option pricing formula.

This paper mainly discusses the American option’s hedging strategies via binomial model and the basic idea of pricing and hedging American option. Although the essential scheme of hedging is almost the same as European option, small differences may arise when simulating the process for American option holder has more rights, spelling that the option can be exercised at anytime before its maturi...

Along with the well-known “call-put parity” relation, that makes it possible to express the rational price of a put option in terms of the rational price of a call option, we introduce a “call-put duality” relation. This new concept offers a simple explanation of the relationship between the rational price of a put option and a call option, not only for options of the European type, but also fo...

Previous option pricing research typically assumes that the risk-free rate or the short rate is constant during the life of the option. In this study, we incorporate the stochastic nature of the short rate in our option valuation model and derive explicit formulas for European call and put options on a stock when the short rate follows the Merton model. Using our option model as a benchmark, ou...