On Option Pricing In Binomial Market With Transaction Costs

The problem of option pricing is one of key problems in financial mathematics. Based on the assumption of arbitrage-free financial market, there are 3 opinions for option pricing: hedging, replicating and mean value. The most famous Black-Scholes formula is foundation on the third opinion. After that, many study especially Merton's form two others. They contribute greatly to the development and generalization of B-S.In this thesis, we study the problem of binomial market option pricing on the condition of complete market and arbitrage-free financial market. A complete market means every option can be replicated by combination of stocks and bonds. Based on replicating, our aim is to find self-financing strategy to replicate option to solve a group of option pricing problems with stocks and bonds both transaction costs.The main work is:(1)For discrete time situation, establish option pricing model with transaction costs in binomial security market.(2)Study the strategy of investor in the self-financing conditions, and express the equivalence of it;(3)Prove that on the especial transaction costs condition exist the only self-financing strategy to replicate the option;(4)According to self-financing strategy, get the pricing formula for option with stocks and bonds both transaction costs.