Hedging Strategies of Financial Intermediaries: Pricing Options with a Bid‐Ask Spread

This paper uses a model similar to the Boyle‐Vorst and Ritchken‐Kuo arbitrage‐free models for the valuation of options with transactions costs to determine the maximum price to be charged by the financial intermediary writing an option in a non‐auction market. Earlier models are extended by recognizing that, in the presence of transactions costs, the price‐taking intermediary devising a hedging portfolio faces a tradeoff: to choose a short trading interval with small hedging errors and high transactions costs, or a long trading interval with large hedging errors and low transactions costs. The model presented here also recognizes that when transactions costs induce less frequent portfolio adjustments, investors are faced with a multinomial distribution of asset returns rather than a binomial one. The price upper bound is determined by selecting the trading frequency that will equalize the marginal gain from decreasing hedging errors and the marginal cost of transactions.