The Valuation of Contingent Claims under Portfolio Constraints: Reservation Buying and Selling Prices

With constrained portfolios contingent claims do not generally havea unique price that rules out arbitrage opportunities.Earlier studies have demonstratedthat when there are constraints on the hedge portfolio,a no-arbitrage price interval for any contingent claim exists.I consider the more realistic case where the constraints are imposed on the total portfolio of each investor and define reservation buying and selling prices for contingent claims. I derive propertiesof these prices, show how they can be computed numerically, and study two simple examples in which the reservation prices and the corresponding hedging strategies are compared to the Black–Scholes setting.