A Study Of Option Pricing With Transaction Costs

Option is a kind of basic financial derivatives, when it appeared in the financial markets, option pricing theory and method have became hot issues. The celebrated B-S option pricing methodology is not suitable for option pricing with transaction costs, though it has many significant application in pricing financial derivatives. There are two main methods for option pricing with transaction costs: no-arbitrage principle and the utility function method.Apply adjusting replicating time in the equal time interval to discrete time model, we get option pricing formula of European call option. You can see, the new option pricing formula is looks like B-S formula, except for volatility. Then we consider about some economic signification of risk management parameters. Furthermore, by establishing the relationships between the adjusted volatility and the stock's volatility, we can find that there are some relationships between option pricing with transaction costs and B-S formula. Fix the time interval on a specific value, B-S formula provides hedging portfolio can still be used, only the flexibility of hedging operation is weak. At last, we also consider the situation of complicated transaction costs.In modern finance, utility function commonly be used to describe the risk priority, a lot of research has confirmed that hedging is the best way to study of option pricing with transaction costs, which is based on utility theory. An efficient algorithm is developed to price European options in the presence of proportional transaction costs, using the optimal portfolio framework of Davis and the relationships between marginal profit of options trading and the optimization portfolio strategy. It is called balanced option pricing method, in which we needn't to solve more complex optimization problems. With the linear utility, the optimal portfolio through time is independent of the wealth held in the bond. Then we can get the expressions of value function H(t, S,y) in the BUY,SELL and NT regions and the optimal portfolio strategy. Option prices are computed numerically using a Markov chain approximation to the continuous time singular stochastic optimal control problem, for the case of exponential utility. The method results in a uniquely specified option price for every initial holding of stock, and the price lies within bounds which are tight even as transaction costs become large.