Option Pricing With Transaction Costs/Transaction Constraints

Classic Black-Scholes option pricing formula is built on lots of assumptions, but the real world economy is not perfect apparently. How to release these assumptions is the main focus of this paper. The paper mainly discusses option pricing with transaction costs/transaction restraints. This transaction costs framework can also includes CEV (constant elasticity of variance) process which allows heteroscedasticity.This paper first reviews systematically the research on option pricing. Then based on the assumption of geometric Brown motion, this paper classifies and studies the ways of option pricing with transaction cost in two categories: local-in-time models (including Leland method and Boyle-Vorst method) and globe-in-time model (utility indifference method). And this dissertation gives numerical comparison and analysis of these methods. In additional, this paper tries to apply this method to Chinese warrants market.Moreover, this dissertation weakens the condition of geometric Brown motion. The framework dealing transaction costs includes CEV process. Suppose that stock price follows CEV process, we present the numerical computing approach of option pricing with proportional transaction costs. And the result is illustrated. Along with the idea of utility indifference, this paper gives option pricing under portfolio constraints and properties in chapter 5. Chapter 6 introduces a simplified general equilibrium model and gives an arbitrage-free interval of option price with the short-sales constraints on the stock.In conclusion, this paper synthetically apply stochastic process, dynamic programming, financial engineering, statistics and computer science, as the embodiment of multi-subject combination characteristic, and try to get better results which can direct the financial practices.