Vulnerable European Option Pricing With The Time Dependent For Jump Diffusion Process

Option is a unique financial instrument. It plays an important role in businessareas, such as investment, risk aversion and asset management. Founded the ChicagoBoard Options Exchange (CBOE) in April1973, It makes the modern sense of theoptions market-the birth of exchange markets. In China, if the2013year is called"Option simulation first year", then2014will be "the first year of the Option Floor".Since the U.S. subprime mortgage crisis in2008, The option of credit risk has becomethe most popular field of study. Many scholars are in-depth research in vulnerableoption pricing issues, but most of these studies focus on the stock price and thecompany value and the parameters in the model are mostly constant. This paperstudies vulnerable European option pricing with the time-dependent for jumpdiffusion process, and this paper build the model which is about the stock price andthe company’s assets-debt ratio. Details are as follows:Firstly, under the company’s value-based credit risk models, we give vulnerableoption pricing formula with the stock price followed a jump diffusion and constantcompany debt. Application Ito formula derives from the relationship of S,SD, SV, and it is important for the question of vulnerable European option pricingwith the time-dependent for single jump diffusion process. Application of risk-neutralpricing, full expectation formula and Measure transform normal random variable. Wegive vulnerable option pricing formula.Secondly, we build the model which is about the stock price and the company’sassets-debt ratio, taking into account the stock price and the company’s assets-debtratio are all followed the jump diffusion process. It makes the model more concise.Applying Ito Lemma and risk-neutral pricing in the martingale measure method,then using two dimensional normal distribution function of each part of the conditionsof expectations, we get the double jump diffusion process in the form of an infiniteseries of time-dependent vulnerable European option pricing formula.Finally, numerical examples analyze various pricing factors affecting the value ofthe option, obtaining a time-dependent vulnerable option pricing model caneffectively reduce the constant parameter model pricing brought deviation, It can bemore accurate prices vulnerable European options.