Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information

Abstract

We show how inter-asset dependence information derived from observed market prices of liquidly traded options can lead to improved model-free price bounds for multi-asset derivatives. Depending on the type of the observed liquidly traded option, we either extract correlation information or we derive restrictions on the set of admissible copulas that capture the inter-asset dependencies. To compute the resultant price bounds for some multi-asset options of interest, we apply a modified martingale optimal transport approach. In particular, we derive an adjusted pricing-hedging duality. Several examples based on simulated and real market data illustrate the improvement of the obtained price bounds and thus provide evidence for the relevance and tractability of our approach.

On Intermediate Marginals in Martingale Optimal Transportation

“…The authors from [33] compare within a sole example the influence of additional marginal information on price bounds with the influence of this information in combination with the homogeneity of an underlying process. Further, in the recent works [3], [6], [29], [33], [50], [51], [52], [58], and [61] improvements of robust and modelfree price bounds either via the inclusion of prices of other derivatives, market information or via additional assumptions on the underlying process are studied. However, to the best of our knowledge, to explicitly study the influence of intermediate marginals on model-free price bounds is a novelty.…”