Rational Bounds on the Prices of Exotic Options

Finance

IFA Working Paper

1998

In this paper we provide a technique for pricing exotics relative to the instruments used for hedging them, while making minimal assumptions about price processes. The issue we address is this: given the prices of a set of hedging assets (such as a stock and a set of traded European options on that stock), what restrictions can be place on the price of an exotic option? The question has a natural formulation as a linear program. We show how to get price bounds. We also show the corresponding robust strategies which enforce those bounds. The strategies allow agents to write exotics and put a floor on their losses in all states of the world. For some common exotics such as a digital barrier option and a lookback, we provide simple characterizations for the bounds and the hedging strategies. For others, notably the forward straddle, we show numerical solutions.

Institute of Finance and Accounting

FIN 281

IFA Working Paper

No