| Option replication is an important way of thinking for an option-pricing model problem. It’s based on the establishment of dynamical hedging position. We can solve the option pricing problem by equating the portfolio (consisting of the current securities, and including risk-free bank deposits, risky stock and so on) and the option.This paper mainly studies option pricing problem in binomial market with transaction costs and dividends for the random environment. Under the condition of complete market, no-arbitrage principle and self-financing strategies, using the method of binomial tree, we get option-pricing model. This model has important theoretical and practical significance of investment decision and risk management. The structure of the paper as the following.First, the paper introduces the development of option and option pricing problem and no-arbitrage principle; Second, it gives the binomial market under the probability measure space with transaction costs; then, it discusses the problem of option replication for self-financing strategies and finds ways to create option replication, therefore deducing the option pricing formula; Finally, it demonstrates uniqueness and existence proof of the theorem for option replication in the condition of self-financing strategies. |
