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An Analytic Approximation of the Implied Risk-Neutral Density of American Multi-Asset Options

Author

Listed:
  • Juan C. Arismendi

    (ICMA Centre, Henley Business School, University of Reading)

  • Marcel Prokopczuk

    (ICMA Centre, Henley Business School, University of Reading)

Abstract

The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle can not be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalised Edgeworth expansion (MGEE), where the moments of the American density are obtained by a reverse engineering application of the Longstaff and Schwartz (2001) least-squares method (LSM). The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness, and kurtosis swaps.

Suggested Citation

  • Juan C. Arismendi & Marcel Prokopczuk, 2014. "An Analytic Approximation of the Implied Risk-Neutral Density of American Multi-Asset Options," ICMA Centre Discussion Papers in Finance icma-dp2014-07, Henley Business School, University of Reading.
    • Handle: RePEc:rdg:icmadp:icma-dp2014-07
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    More about this item

    Keywords

    Multi-asset Risk-neutral Density; American Multi-asset Options; Higher-order Moments;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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