Methods and Applications of Analysis

Volatility calibration with American options

Yves Achdou, Govindaraj Indragoby, and Olivier Pironneau

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Abstract

In this paper, we present two methods in order to calibrate the local volatility with American put options. Both calibration methods use a least-square formulation and a descent algorithm. Pricing is done by solving parabolic variational inequalities, for which solution procedures by active set methods are discussed.

The first strategy consists in computing the optimality conditions and the descent direction needed by the optimization loop. This approach has been implemented both at the continuous and discrete levels. It requires a careful analysis of the underlying variational inequalities and of their discrete counterparts. In the numerical example presented here (American options on the FTSE index), the squared volatility is parameterized by a bicubic spline.

In the second approach, which works in low dimension, the descent directions are computed with Automatic Differentiation of computer programs implemented in C++.

Article information

Source
Methods Appl. Anal., Volume 11, Number 4 (2004), 533-556.

Dates
First available in Project Euclid: 13 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.maa/1144939946

Mathematical Reviews number (MathSciNet)
MR2195369

Zentralblatt MATH identifier
0205.41803

Subjects
Primary: 91B28
Secondary: 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 60H10: Stochastic ordinary differential equations [See also 34F05] 60H30: Applications of stochastic analysis (to PDE, etc.)

Citation

Achdou, Yves; Indragoby, Govindaraj; Pironneau, Olivier. Volatility calibration with American options. Methods Appl. Anal. 11 (2004), no. 4, 533--556. https://projecteuclid.org/euclid.maa/1144939946


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