Pricing Of Fragile Two-value Options Under The System Transformation Model

As a kind of financial derivatives,option plays an important role in the financial markets.Therefore,an accurate and effective pricing of option is very necessary.In the 1970s Black and Scholes put forward the famous Black-Scholes option pricing mod-el.The model had a profound impact for traders about how to price and hedge options and promote the development of financial engineering.However,with the fast develop-ments of the financial market,the inherent defects of Black-Scholes option model began to emerge,which restricted the further development of options market.The credit risk in the process of options trading is one of the most obvious defects.Hence,how to ad-just the option Prices to reflect the counter party credit risk has become a serious problem,which is the so-called vulnerable option pricing problem.The article considers underlying asset stock price,trader's company value and company liabilities are subordinated to Markov-modulated geometric brownian motion model.the market interest rate,the average rate of return and stochastic volatility of the risk assets depend on the states of the economy which are modelled by a continuous-time finite-state Markov chain.At this time,the market is incomplete in general,the equivalent martingale measure is not unique.We employ the regime switching Esscher transform to determine the martingale measure and derive the pricing formula of vulnerable binary options.In addition,Supposed that the underlying asset stock price is subordinated to Markov-modulated jump-diffusion model,the other conditions are invariant and the continuous part and the part with jump are independent,we also derive the pricing formula of vulnerable binary options.At last,numerical illustrations are given.