The Pricing Of Options With Delay Response And Bayesian Empirical Research

Option pricing has long been a difficult and important topic in financial deriva-tives pricing.The classic Black-Scholes model is the basis of following researches on option pricing,but this model has many limitations,since it was developed under a series of assumptions posed on the financial market.Therefore,how to construct extended models reasonably and do some researches about option pricing are hot topics among scholars.This dissertation conducts research on the pricing of options on the underlying assets with delays,and studies the pricing of options on multiple underlying assets containing many unknown parameters.The adopted Bayesian method provides us with more posterior results than the classic statistical method.Firstly,we provide a numerical simulation method to compute Quanto op-tion prices using Bayesian posterior inference.Quanto option is one of the most complicated options containing two underlying assets,and its option price is in-fluenced by both the foreign underlying asset and the exchange rate.There exists the closed pricing formula for the Quanto option under the Black-Scholes mod-el,but the increase of the number of underlying asset leads to that the Quanto option pricing model includes more unknown parameters.This paper constructs the Bayesian method and posterior sampling algorithm to solve the estimation of unknown parameters and obtain the posterior results for the Quanto option price.By numerical experiments,the constructed Bayesian method is found to have better pricing performance for the Quanto option comparing with some ex-isting classic estimation methods,especially when the available data of underlying assets is limited.Secondly,based on the existing research of the pricing of options on one under-lying asset with delay,we conduct an extending research on the pricing of options on two underlying assets with delays.By taking the exchange option as an exam-ple,we obtain the closed option pricing formula on the subinterval of the option life.According to the local Lipschitz and boundedness conditions required by the volatility function,we find a concrete function form for it,and then the numerical simulation of the pricing of options on the underlying asset with delay is com-pletely solved by using the Euler-Maruyama approximation and the Monte Carlo method in combination.The empirical studies indicate that the delay influences option prices in a complicated way,where the big delay has ignorable effects on option prices,and the small delay has obvious impacts on option prices.Thirdly,based on the existing research about the robustness of the delay on the pricing of options on one underlying asset with delay,we extend this result to the robustness of delay on the pricing of some two-asset options,where the two underlying assets have different delays,and both the drift function and the volatility function contain the delay.By taking the exchange option,the Quanto option and the two-asset Barrier option for examples,we discuss how the delay influences option prices and derive the sufficient conditions for the robustness of delay.We find that the small changes in delay parameters would not result in drastic fluctuations in the prices of three types of considered options.Furthermore,we provide empirical studies using real market data to verify the efficiency of our theoretical proof.Fourthly,we construct the Bayesian method to price options on the underlying asset with delay.The incorporation of delay makes the price process of underlying asset a non-Markovian process and leads to that the closed option pricing formula can only be derived on a subinterval of option life.To solve the problems created by the introduction of delay in the price process of underlying asset,we adopt many techniques in combination,including the Euler-Maruyama approximation scheme,the introduction of missing data between each pairs of underlying asset observations,and the regroup of the discrete underlying price process.We simulate option prices by using Bayesian posterior prediction and Monte Carlo simulation methods.Our constructed Bayesian method provides a systematic research idea for the pricing of options on the underlying asset with delay.We use both the simulated data and the real market data of S&P500 index option to demonstrate the correctness of our proposed method.