An Endogenous Volatility Approach to Pricing and Hedging Call Options with Transaction Costs

Standard delta hedging fails to exactly replicate a European call option in the presence of transaction costs. We study a pricing and hedging model similar to the delta hedging strategy with an endogenous volatility parameter for the calculation of delta over time. The endogenous volatility depends on both the transaction costs and the option strike prices. The optimal hedging volatility is calculated using the criterion of minimizing the weighted upside and downside replication errors. The endogenous volatility model with equal weights on the up and down replication errors yields an option premium close to the Leland (1985) heuristic approach. The model with weights being the probabilities of the option's moneyness provides option prices closest to the actual prices. Option prices from the model are identical to the Black-Scholes option prices when transaction costs are zero. Data on S\&P 500 index cash options from January to June 2008 illustrate the model