| Most theories in finance assume perfect and complete assets market. For example, based on these assumptions, Black and Scholes derived an elegant option pricing formula which has perhaps had the biggest impact on the real world of securities trading. However, the Black-Scholes theory does not explain the market bid-ask spreads of options. In the presence of transaction costs, their replicating strategy is infinitely costly. Chapter Two and Three of this dissertation sought to fill the void of option pricing theory in the presence of transaction costs. The author considered binomial lattice model first; then, by taking limits, he solved the continuous-time problem. Two approaches have been taken. The first assumes an infinitely risk-averse dealer pursuing a riskless hedging of existing position in options. Closed-form formulae for bid and ask prices of options are derived for binomial models of arbitrarily large number of periods. In the continuous-time case, the bid-ask spread is shown to be equal to the underlying stock price. To narrow down the spreads, the second approach assumes the dealer is finitely risk-averse. By solving an individual portfolio choice problem with existing positions in the option, the author has shown the optimal strategy is a control limit policy: there exist moving upper and lower boundaries for the number of stock shares held, and the dealer adjusts the portfolio only when it hits one of the boundaries. The derived bid-ask spreads are smaller than those derived in the first approach. In addition, Chapter One derived an exact solution to an optimal investment problem in a Merton type economy with transaction costs. Chapter Four derived a closed-form solution to transactions demand of money which includes earlier works of Baumol-Tobin, Miller-Orr, and Frenkel-Jovanovic as special or limiting cases. |
