Vulnerable Option Pricing With Transaction Cost Under Stochastic Volatility

Due to the loose regulation of over-the-counter trading,option longs may suffer from a possible increase in the risk of short credit defaults.The longs are exposed to both market risk and credit risk.This option with credit risk in over-the-counter trading is called vulnerable options.Compared with traditional European options,vulnerable options are closer to reality.The main results of this paper on European vulnerable options are as follows:By constructing a risk-free portfolio and using the no-arbitrage principle,the pricing model of vulnerable options with transaction costs is obtained,which is a partial differential equation with terminal conditions.Using the difference method,it is transformed into algebraic equations,and a numerical algorithm for the vulnerable option pricing model with transaction cost is given.Through numerical experiments,the influence of each pricing parameter on the value of the option is analyzed.The numerical test results show that the value of the option decreases with the increase of transaction cost,and the correlation coefficient between the underlying asset and the counterparty company’s assets is inversely proportional to the price of the vulnerable option.By comparison,it is found that the option price with transaction cost is lower than the option price without transaction cost.The Hull-White stochastic volatility model is used to replace the constant volatility,and an option with different maturity date and strike price is introduced to a risk-free investment portfolio.The pricing model of European vulnerable options is given by using the Δ-hedging technique.Using the difference method,the numerical algorithm of the model is given and numerical experiments are carried out.The numerical results show that the greater the value of the underlying asset and the counterparty company’s assets,the greater the value of the vulnerable option,and the faster the growth.The default threshold is inversely proportional to the value of the option.The volatility of the underlying asset and the value of the counterparty’s asset value are directly proportional to the value of the option.