In a discrete setting, we develop a model for pricing a contingent claim in incomplete markets. Since hedging opportunities influence the price of a contingent claim, we first introduce the optimal hedging strategy assuming that a contingent claim has been issued: a strategy implemented by investing initial wealth plus the selling price is optimal if it maximizes the expected utility of the agent’s net payoff, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. Next, we introduce the ‘reservation price’ as a sub jective valuation of a contingent claim. This is defined as the minimum price that makes the issue of the claim preferable to stay put given that, once the claim has been written, the writer hedges it according to the expected utility criterion. We define the reservation price both for a short position (reser- vation selling price) and for a long position (reservation buying price) in the claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu (or Black-Scholes) price. If the claim is non-redundant, then the reservation prices are interior points of the bid-ask interval. We provide also two numerical examples with different utility functions and contingent claims. Some qualitative properties of the reservation price are shown.
File in questo prodotto:
Non ci sono file associati a questo prodotto.