On martingale measures and pricing for continuous bond-stock market with stochastic bond

Details On martingale measures and pricing for continuous bond-stock market with stochastic bond On martingale measures and pricing for continuous bond-stock market with stochastic bond

2011-08-03

arxiv.org/abs/1108.0719v1

Economy

Quantitative Finance

Pricing of Securities

22 pages

Scientific paper

This paper studies pricing of stock options for the case when the evolution of the risk-free assets or bond is stochastic. We show that, in the typical scenario, the martingale measure is not unique, that there are non-replicable claims, and that the martingale prices can vary significantly; for instance, for a European put option, any positive real number is a martingale price for some martingale measure. In addition, the second moment of the hedging error for a strategy calculated via a given martingale measure can take any arbitrary positive value under some equivalent measure. Some reasonable choices of martingale measures are suggested, including a measure that ensures local risk minimizing hedging strategy.

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