Pricing Vulnerable Option Based On Uncertainty Theory

As a kind of exotic option,vulnerable option was first proposed by Johnson and Stulz.It considers the risk of counterparty default,namely the impact of credit risk on option price.In the current complex financial environment,credit risk has always been a hot topic.Based on the uncertainty theory,this thesis will deeply study the pricing of vulnerable options in the financial market,reasonably optimize the pricing formula of vulnerable options,and maximize the fairness of both investors.The research contents are as follows:First of all,we consider the pricing of vulnerable options in the uncertain stock model with jumps.The evolution of the company’s value is no longer regarded as a continuous and uncertain process,but as a discontinuous processes.And then we price the European vulnerable option.Taking the European vulnerable call option as an example,the influence of relevant parameters on the option price is analyzed.Secondly,we consider the pricing of vulnerable options under the uncertainty volatility model.Volatility is an important factor that affects the option price.The change of volatility not only reflect the risk and return of the market,but also reflect people’s optimism about the market.Therefore,in general,the volatility should not be a constant.In this thesis,we assume that it follows an uncertain mean regression model.Based on this model,the pricing formula of European vulnerable options is given and taking the European vulnerable call option as an example,the risk analysis of options is carried out from four aspects of delta,gamma,rho and theta.Thirdly,we consider the pricing of vulnerable options under the uncertain interest rate model.This section obtains the solution of the uncertain Cox-Ingersol-Ross(CIR)interest rate model in the sense of distribution.Based on this model,the pricing formula of European vulnerable option is given,the corresponding numerical algorithm is designed,the corresponding numerical examples are given,and the monotonicity of important parameters is analyzed.Finally,we consider the pricing problem of vulnerable options under the uncertain fractional order model.The solution of Caputo uncertain fractional differential equation with initial values condition under multiple factors is solved.Based on the multi-factor Caputo fractional order model,the pricing of European vulnerable options is carried out,and the specific prices of European vulnerable options under different order are given.