Model-Free Methods in Valuation and Hedging of Derivative Securities

Abstract

In contrast to conventional model-based derivative pricing, a recent stream of research aims to investigate what prices are consistent with absence of arbitrage, given only the current prices of traded options on the same underlying. This paper gives a succinct survey of work in this area. After summarising results on the Black-Scholes model, the volatility surface and the Breedon-Litzenberger (BL) and Dupire formulas, the two main streams of work are described. In the first, marginal distributions of the underlying at a finite number of times are assumed known via the BL formula. The option bounds are obtained using methods based on the Skorokhod embedding or the theory of optimal transport. If, instead, we use only a finite number of traded option prices as input data (not interpolated à la BL) then option bounds are obtained using the duality theory of semi-infinite or doubly-infinite linear programming.

Keywords: model-free methods, derivative pricing, Breedon-Litzenberger formula, Skorokhod embedding, optimal transport, linear programming

JEL Classification: G12, G13