Essays in option replication

This study examines the effects of time-varying volatility and transaction costs on replication of foreign currency futures options. Evidence in various financial markets, including currency and currency futures markets, clearly indicates that the constant volatility model is inadequate. This evidence motivates us to consider alternatives to the constant volatility model. I consider three models two of which assume that the volatility process follows GARCH(1,1) model and the third alternative assumes that volatility is a mean-reverting process. I construct replicating portfolios, which are rebalanced dynamically, and test if payoff of options is met. To construct the replicating portfolios, I use the derivatives with respect to futures price (delta) and the volatility (vega) prescribed by the models. My results indicate that the models generally replicate smaller strike options fairly accurately while producing somewhat larger errors for larger strike options and that the hypothetical futures contract on a hypothetical volatility index is useful hedging instrument. Of the three alternative models considered, I find that error correction model with GARCH(1,1) volatility is the best model. Since dynamic rebalancing of the replicating portfolio is quite expensive when there are proportional transaction costs, an acceptable alternative should provide optimal tradeoff between transaction costs and replication error. I consider three alternative rebalancing strategies using Black (1976) model and Monte Carlo simulation to examine the transaction costs and replication error with the objective of determining profit or loss from each simulation run. After 10,000 simulation runs, based on the 95th percentile profit, I determined that the rebalancing strategy based on the no-transaction bound on delta of the option suggested by Whalley and Wilmott (1993) gives the best results in terms of profits. Another form of transaction cost is bid-ask spread in the markets for assets underlying options. This spread results in different option prices for buyers and sellers of options; that is, the bid price of the option should be less than or equal to the ask price of the replicating portfolio while the ask price of the option should be greater than or equal to the bid price of the replicating portfolio. I test these equilibrium bounds, violations of which provide arbitrage opportunities, using actual market bid-ask data on both underlying futures and options obtained from Chicago Mercantile Exchange. The market prices generally satisfy the equilibrium bounds though I find in my analysis that choice of volatility used as input for simulation can be critical