On the duality principle in option pricing: semimartingale setting
The question is: assuming some dynamics about the evolution of the exchange rate (or even the price process of a stock or an index), what are the dynamics of the reciprocal rates? The duality principle provides the answer to this question. The duality principle states that the calculation of the price of a call option for a model with some process is equivalent to the calculation of the price of a put option for a suitable dual model with respect to the dual measure. The authors model asset prices as general exponential semimartingales, hence they work in the widest possible framework, as far as arbitrage theory is concerned. The appropriate tool to express the answer turned out to be the triplet of predictable characteristics of a semimartingale. The central result provides the explicit form of the triplet of predictable characteristics of the dual process under the dual martingale measure. The duality principle is derived for European options and can be applied to American options and to exotic derivatives - a typical example is Russian option.
scientific article; zbMATH DE number 5290185
scientific article