| This thesis is concerned with options pricing with transaction costs. Since the publication of Black and Scholes formula in 1973, derivative asset pricing has been intensively studied. A great amount of papers have been written on correcting Black and Scholes type formulae in the presence of transaction costs. We will present an asymptotic approach to derive optimal trading strategies when transaction costs are involved. The terms in the asymptotic expansions we derived for the effect of transaction costs on the prices and hedge ratios of European and American options represent the deviation of the prices from those given by the standard formulae of Black and Scholes type. This gives rise to correction terms which can be easily computed and implemented in practice. It also permits the representation of the hedging error due to transaction costs as a separate security whose price can be inferred from the market. On the basis of this, hedge ratios are found which minimize the additional cost due to transaction.;We organize the thesis as follows. In chapter 2, we introduce Black and Scholes formula and analyze the discrepancies between the model assumption and the real world situation. In chapter 3, we illustrate various methods in correcting Black and Scholes formula. In chapter 4 and chapter 5, we derive optimal trading strategies for European and American options with transaction costs. |
