Pricing Vulnerable Options Under Scott Model With Stochastic Volatilities

Nowadays,many financial institutions trade their deriv atives with counterparties and other institutions in OTC ma rkets.Credit risk has become a major threat to the stabili ty of the entire financial system due to the systematic def ects and ineffective supervision of OTC transactions.There fore,it is urgent to accurately design various schemes to resist the financial crisis.The standard option pricing fo rmula does not focus on counterparty risk.Therefore,more investors and researchers begin to consider the impact of c ounterparty risk on corporate credit risk and pay attention to the pricing of vulnerable options.Many papers assume the volatility of the underlying ass et as a fixed value,which actually does not conform to the law of the real financial market.Therefore,this paper ex plain how to price vulnerable options when the volatility o f the underlying asset is stochastic.Firstly,this paper i ntroduces the source and background of vulnerable options,then introduces Klein pricing method of vulnerable options,and gives the detailed derivation process of the solution of the equation.It also compares Black-Scholes options pri ce with vulnerable options price.Finally,the pricing equa tion of European options under stochastic volatility of Sco tt model and the analytical solution of the equation is der ived by introducing the concept of market price of risk.Then the volatility of the underlying assets is simulated by Scott model,and the vulnerable option pricing equation wit h boundary conditions is obtained through the method of mar ket price of risk.Finally,the recursive formula of the vu lnerable option price equation is obtained by the finite di fference method,and the pricing method of the vulnerable o ption is found.