Discontinuous payoff option pricing by Mellin transform: A probabilistic approach

Henryk Gzyl (), M. Milev and A. Tagliani

Finance Research Letters, 2017, vol. 20, issue C, 281-288

Abstract: The Mellin transform technique is applied for solving the Black-Scholes equation with time-dependent parameters and discontinuous payoff. We show that the option pricing is equivalent to recovering a probability density function on the positive real axis based on its moments, which are integer or fractional Mellin transform values. Then the Mellin transform can be effectively inverted from a collection of appropriately chosen fractional (i.e. non-integer) moments by means of the Maximum Entropy (MaxEnt) method. An accurate option pricing is guaranteed by previous theoretical results about MaxEnt distributions constrained by fractional moments. We prove that typical drawbacks of other numerical techniques, such as Finite Difference schemes, are bypassed exploiting the Mellin transform properties. An example involving discretely monitored barrier options is illustrated and the accuracy, efficiency and time consuming are discussed.

Keywords: Barrier options; Black-Scholes equation; Discontinuous payoff; Fractional moments; Maximum entropy; Mellin transform (search for similar items in EconPapers)
JEL-codes: C02 C65 G13 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:finlet:v:20:y:2017:i:c:p:281-288

DOI: 10.1016/j.frl.2016.10.011

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