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Recovering a Piecewise Constant Volatility from Perpetual Put Option Prices

Part of: Stochastic processes Mathematical finance

Published online by Cambridge University Press:  14 July 2016

Bing Lu
Bing Lu*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden. Email address: [email protected]
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Abstract

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In this paper we present a method to recover a time-homogeneous piecewise constant volatility from a finite set of perpetual put option prices. The whole calculation process of the volatility is decomposed into easy computations in many fixed disjoint intervals. In each interval, the volatility is obtained by solving a system of nonlinear equations.

Keywords

Perpetual put optioncalibration of modelspiecewise constant volatility

MSC classification

Secondary: 91G20: Derivative securities 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 680 - 692
Copyright
Copyright © Applied Probability Trust 2010 

References

[1] Alfonsi, A. and Jourdain, B. (2009). {Exact volatility calibration based on a Dupire-type Call-Put duality for perpetual American options.} Nonlinear Differential Equations Appl. 16, 523–554.Google Scholar
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[3] Dupire, B. (1994). {Pricing with a smile}. Risk 7, 18–20.Google Scholar
[4] Ekström, E. and Hobson, D. (2009). {Recovering a time-homogeneous stock price process from perpetual option prices.} Preprint. Available at http://arxiv.org/abs/0903.4833v1.Google Scholar