The Numerical Methods And Application For Option Pricing

In recent years, option pricing becomes one of the hottest issues in thefield of financial research with the development of global economy. In thispaper, we study the numerical methods for option pricing, and improve avariety of models to make them important investment advices for theinvestors.Aiming at the inadequacy of the parameters in CRR model, a new type ofbinomial model (NCRR) with different parameters is derived using theprobability theory, and a generalized binomial model with two extendedparameters is proposed via modifying the generalized binomial model. Thetwo models above efficiently avoid the inadequacy in CRR model, andconverge to Black-Scholes formula. Meanwhile, the proof procedure ofconvergence is provided in detail. The process and formula for pricing barrieroptions are provided based on the feature of generalized binomial model withtwo extended parameters. Empirical results from Hong Kong warrants marketshow that the NCRR model has excellent convergence, and its runtime is short.Through the numerical example, we conclude that the generalized binomial model with two extended parameters has significance and convergence. Then,a fuzzy binomial model is proposed for pricing American put options. Thevolatility of underlying assets is replaced by parabolic type fuzzy numbers.Detailed pricing process of the fuzzy binomial method is showed by empiricalresults from domestic warrant market. In addition, a rational fuzzy optionprice interval is evaluated by fuzzy binomial model. The investors can makestrategic decisions by changing the confidence levels and parabolic type fuzzynumbers.In this paper, the improvement to another numerical method for optionpricing-Monte Carlo simulation is focused on the application of variancededuce techniques and exotic options’ pricing. The barrier option is pricedusing complex variance deduce technique which is combined conditionalMonte Carlo simulation with importance sampling technique. The numericalexamples show that the accuracy of Monte Carlo using complex variancededuce technique is better than common Monte Carlo. However, Monte Carlosimulation is not as good as generalized binomial model with two extendedparameters. Least-squares Monte Carlo is applied to price the same Americanwarrant, and the numerical results are close to the market price.