Explicit Approximations of Multi-Asset Option Prices Including Greeks

Abstract

In this article we give a lower bound approximation to a stochastic program that is typical for many complex financial derivatives, e.g. Bermudan options, Rainbow options and swing contracts. The approximation is based on an algorithm that does not require any simulation but uses a well-known spread option pricing formula. Since the method explicitly computes lower bounds for the claim’s value, sensitivities such as deltas and gammas are available as well as derivatives with respect to correlations and other inputs. Our resulting procedure is a powerful and practical tool for the pricing and risk analysis of exotic payoff structures. As such, it is useful in the day-to-day environment of financial institutions.

Keywords: rainbow option, multi-asset option, swing option, sensitivities, Greeks, pricing, risk analysis

JEL Classification: C61, G13