Density Estimation And Apply Of Options Arbitrage

Discretely rebalanced options arbitrage strategies in the presence of transaction costs have path dependent returns that are difficult to model analytically. I instead use a quasi-analytic procedure that combines the computational efficiency of analytical solutions with the flexibility of simulations. The central feature is the estimation of the distribution of returns of the arbitrage strategy by mapping simulated returns percentiles and the input parameter set. Using the estimated density, I evaluate the tradeoff between transaction costs and risk exposure under generalized transaction costs structures that includes bid-ask spread and brokerage commission. I show that the optimal strategy depends on transaction costs, volatility, and option moneyness. At-the-money and in-the-money options have a higher dollar cost of rebalancing as compared to out-of-the money options. However, as a percentage of the options premium, out-of-the money options incur higher rebalancing costs. These results can be coupled with trading practices in options markets to evaluate conditions under which option prices would generate the implied volatility smile. Transaction costs can be, therefore, one possible explanation for the observed systematic patterns in implied volatilities.