Bounds on Derivative Prices in an Intertemporal Setting with Proportional Transaction Costs and Multiple Securities

Abstract:     
The observed discrepancies of derivative prices from their theoretical, arbitrage-free values are examined in the presence of proportional transaction costs. Analytic upper and lower bounds on the reservation write and purchase prices, respectively, are obtained when an investor's preferences exhibit constant relative risk aversion between zero and one. The economy consists of multiple primary securities with the stationary returns, a constant rate of interest, and any number of American or European derivatives with path-dependent arbitrary payoffs. The price processes of the primary securities are modelled either as jump/diffusions in a continuous-time framework, or as arbitrary processes in a discrete-time framework.

Keywords: derivative pricing, transaction costs, multi-securities, american claims, exotic options, utility maximization, volatility smile.

JEL Classifications: G13, G14, D84, D52

Working Paper Series