Pricing Currency Derivatives Under the Benchmark Approach
25 Pages Posted: 18 Sep 2013 Last revised: 5 Oct 2013
Date Written: October 5, 2013
Abstract
This paper considers the realistic modelling of derivative contracts on exchange rates. We propose a stochastic volatility model that recovers not only the typically observed implied volatility smiles and skews for short dated vanilla foreign exchange options but allows one also to price payoffs in foreign currencies, lower than possible under classical risk neutral pricing. The main reason for this important feature is the strict supermartingale property of benchmarked savings accounts, which the calibrated parameters identify under the proposed model. Using a real dataset on vanilla option quotes, we calibrate our model on a triangle of currencies and find that the risk neutral approach fails for the calibrated model, while the benchmark approach still works.
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