The inverse volatility problem for American options

Ian Knowles; Ajay Mahato

doi:10.3934/dcdss.2020235

Article Contents

2020, Volume 13, Issue 12: 3473-3489. Doi: 10.3934/dcdss.2020235

This issue Previous Article On hyperbolic mixed problems with dynamic and Wentzell boundary conditions Next Article A Zaremba-type criterion for hypoelliptic degenerate Ornstein–Uhlenbeck operators

The inverse volatility problem for American options

Ian Knowles^, and
Ajay Mahato

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

^* Corresponding author
^* Corresponding author

Received: August 31, 2018

Early access: January 2020

Published: August 2020

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Abstract

The problem of determining equity volatility from a knowledge of American option prices for a range of exercise (strike) prices and expirations is solved by minimization of a convex functional.

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Mathematics Subject Classification: Primary: 35K10; Secondary: 65N21.

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Figure 1. Flowchart

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Figure 2. GOOGLE put option data, 19th April, 2013

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Figure 4. Maturity interval $ 14\le T\le 21 $: iterations of $ g(S_0, t_0, K, T) $

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Figure 5. The functional $ G $ for maturity $ 14\le T\le 21 $

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Figure 3. Recovered Google Volatility

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Figure 6. Comparing option and recovered prices from the Dupire Equation

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