Articlegreen2006

Expensive martingales

28 citations0/0 files storedQuantitative Finance

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Stochastic processes and financial applications Financial Markets and Investment Strategies Risk and Portfolio Optimization

Abstract

We characterize strictly arbitrage-free markets of European options where only a discrete set of options is traded. We then construct martingales which reprice all given options and which are ‘most expensive’ among all martingales with this property. We also present algorithms to adjust real-life market data and to construct expensive martingales while taking into account additional ‘weak’ information: estimated prices of more exotic products such as, for example, forward started options.

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References

1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 2003Monte Carlo Methods in Financial Engineering 1981Martingales and stochastic integrals in the theory of continuous trading 1999Infinite Dimensional Analysis 1998The fundamental theorem of asset pricing for unbounded stochastic processes 2006Moment explosions in stochastic volatility models 2002Stochastic Finance 2007Equity Hybrid Derivatives

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