Mathematical Finance Seminar

April 25, 2002 5:30 PM to 7:00 PM

Roberto Baviera, MPS Finance Banca Mobiliare

Option Prices in Presence of Transaction Costs

We Provide closed formulas for European call option ask and bid prices in presence of transaction costs. Underlying prices have the same dynamics of Black-Scholes model and a bid-ask spread proportional to bid price. We suppose that a market maker has to quote a bid and ask price for an option in a perfect competition market. Under these conditions derivate prices are obtained imposing the No Almost Sure Arbitrage Principle: the market maker fixes bid (ask) price as the highest buying (lowest selling) price that can be accepted by an investor who maximizes the growth rate of his portfolio.