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Unifying exotic option closed formulas

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  • Esquível, Manuel L.
  • Veiga, Carlos
  • Wystup, Uwe

Abstract

This paper aims to unify exotic option closed formulas by generalizing a large class of existing formulas and by setting a framework that allows for further generalizations. The formula presented covers options from the plain vanilla to most, if not all, mountain range exotic options and is developed in a multi-asset, multi-currency Black-Scholes model with time dependent parameters. The general formula not only covers existing cases but also enables the combination of diverse features from different types of exotic options. It also creates implicitly a language to describe payoffs that can be used in industrial applications to decouple the functions of payoff definition from pricing functions. Examples of several exotic options are presented, benchmarking the closed formulas' performance against Monte Carlo simulations. Results show a consistent over performance of the closed formula reducing calculation time by double digit factors.

Suggested Citation

  • Esquível, Manuel L. & Veiga, Carlos & Wystup, Uwe, 2010. "Unifying exotic option closed formulas," CPQF Working Paper Series 23, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    • Handle: RePEc:zbw:cpqfwp:23
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    2. Inklaar, Robert & Koetter, Michael & Noth, Felix, 2012. "Who's afraid of big bad banks? Bank competition, SME, and industry growth," Frankfurt School - Working Paper Series 197, Frankfurt School of Finance and Management.
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