Vulnerable Option Pricing With Multiscale Stochastic Volatility Model

Credit risk is also known as counterpart risk or default risk which is one of thr major financial risks,referring to the risk that the other party fails to perform it’s due debt or can not perform fully.Vulnerable option is an option with credit risk.Therefore,this article studies the above situations.Since the Global Financial Crisis of 2007 – 2008,people concerns about financial derivatives subject to credit credit risk in the over-the-counter(OTC)markets have grown rapidly,due to there is no organized exchange to guarantee the promised payment in the OTC markets,the option holder is already vulnerable to the credit risk.And nearly 90% of derivatives are OTC in financial derivatives.So it is significant to fix a price for vulnerable option accurately.The main contents are as follows:Part 1: We introduce the research significance and background of vulnerable options and multiscale stochastic volatility model,then we give a introduce to the research status of stochastic volatility,vulnerable options and multiscale analysis methods at home and abroad.Part 2: We introduce the basic knowledge of option pricing and the basic theorem of stochastic process related in this paper.Part 3: Introducing the vulnerable options in the pricing formula under the Klein model.And assuming that the basic asset obeys geometric Brownian motion,the vulnerable option pricing formula under Klein model is derived by using the method of equivalent martingale measure.Part 4: By using otI? formula and martingale method,the partial differential equation of fragile options in multiscale stochastic volatility model is derived.By using the singular perturbation analysis method and the multiscale technique,the exact expression of the first-order approximate price of the vulnerable option in the multscale stochastic volatility model is obtained,and the analytical solution of the principal term and the first-order correction price of the vulnerable option is obtained.Part 5: We summary the main contents of this paper,and look forward to the future research of vulnerable options in the real financial market in terms of option pricing considering random interest rates and the existence of jumps.