Premium
THE WIENER–HOPF TECHNIQUE AND DISCRETELY MONITORED PATH‐DEPENDENT OPTION PRICING
Author(s) -
Green Ross,
Fusai Gianluca,
Abrahams I David
Publication year - 2010
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2010.00397.x
Subject(s) - hindsight bias , mathematics , black–scholes model , lévy process , random walk , valuation of options , gaussian , barrier option , path (computing) , path integral formulation , mathematical economics , mathematical optimization , econometrics , computer science , physics , statistics , quantum mechanics , volatility (finance) , psychology , quantum , cognitive psychology , programming language
Fusai, Abrahams, and Sgarra (2006) employed the Wiener–Hopf technique to obtain an exact analytic expression for discretely monitored barrier option prices as the solution to the Black–Scholes partial differential equation. The present work reformulates this in the language of random walks and extends it to price a variety of other discretely monitored path‐dependent options. Analytic arguments familiar in the applied mathematics literature are used to obtain fluctuation identities. This includes casting the famous identities of Baxter and Spitzer in a form convenient to price barrier, first‐touch, and hindsight options. Analyzing random walks killed by two absorbing barriers with a modified Wiener–Hopf technique yields a novel formula for double‐barrier option prices. Continuum limits and continuity correction approximations are considered. Numerically, efficient results are obtained by implementing Padé approximation. A Gaussian Black–Scholes framework is used as a simple model to exemplify the techniques, but the analysis applies to Lévy processes generally.