Option Pricing With Credit Risk Based On Subfractional Brownian Motion

With the rapid development of contemporary financial economy,the trading of financial derivative products has been developed to varying degrees in various countries around the world,and its role in micro-macro and its finance is very significant.However,the sale of financial derivatives may give Investors bring high returns and are always accompanied by high risks,which may bring huge profits,and it does not rule out many economic disasters.Therefore,before trading any financial derivative products,traders are And the income situation must have an accurate control.Options as the most conventional kind of financial derivatives,it is important to formulate reasonable prices for options under a rigorous and scientific mathematical model.The classic Black-Scholes formula is the top priority of the option pricing process,but this traditional formula relies on the assumption of an efficient market,that is,the entire change process of the underlying asset price is assumed to be independent of each other,and the underlying asset price is regarded as a In the case of time series,the logarithm of the asset price ratio of adjacent times is a normal random variable that is subject to independent and identical distribution.However,in recent years,a lot of research on the stock market can be concluded: the stock market price does not follow the normal Distribution,but a distribution with a "peaky thick tail" feature,and there is a certain correlation between different time periods before and after,therefore,the classic Black-Scholes model is already incapable of describing asset price changes.On the other hand,With the need for risk hedging,many option transactions are conducted off-exchange.OTC options are not guaranteed by third parties like clearing houses.Both buyers and sellers of transactions face the risk of default by the other party.The options traded outside are all credit risk-containing options,and their intrinsic value is lower than the value of in-market options under the same conditions.So with the credit risk option is an adjustment to the idealized market,in order to avoid counterparty default occurs,the option pricing model to build a quantitative credit risk has very important significance.This article takes the sub-score Black-Scholes model that is closer to the real financial market as the theoretical cornerstone,and uses a probabilistic martingale method to solve the pricing problems of standard European options and credit risk-containing options.First,taking the sub-score Brownian motion as the theoretical basis,Then construct the sub-score Black-Scholes model to describe the change process of the underlying asset price(stock),and finally solve the analytical formula for the stock price satisfaction by combining the sub-score formula;secondly,according to the analytical formula for the stock price satisfaction,use the traditional The probabilistic method derives the standard European option pricing display solution.Third,the sub-score Black-Scholes model is used to study the pricing problem of credit risk-containing options,where credit risk-containing options refer to options that default because the company's liabilities exceed assets.This article simply sets the company's debt as a constant,and the company's asset price is based on the sub-fractional Brownian motion theory.Under this model,the probability martingale method is also used to obtain an explicit solution to the price of options with credit risk.Finally,combined with the actual financial market situation in China,Select some data of alternative warrants Construct a suitable estimator to estimate the parameters in the model,and use the estimated parameters to calculate the price of the corresponding alternative warrants,and also compare the error with the actual market value.the results show that the sub-score Black-Scholes model does have a strong advantage in describing financial asset price fluctuations.It can scientifically and rigorously price options,and further verifies the feasibility and effectiveness of the martingale method.Investors provide a reliable basis for predicting option prices and risk control...