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December 2016 Large-time option pricing using the Donsker–Varadhan LDP—correlated stochastic volatility with stochastic interest rates and jumps
Martin Forde, Rohini Kumar
Ann. Appl. Probab. 26(6): 3699-3726 (December 2016). DOI: 10.1214/16-AAP1189

Abstract

We establish a large-time large deviation principle (LDP) for a general mean-reverting stochastic volatility model with nonzero correlation and sublinear growth for the volatility coefficient, using the Donsker–Varadhan [Comm. Pure Appl. Math. 36 (1983) 183–212] LDP for the occupation measure of a Feller process under mild ergodicity conditions. We verify that these conditions are satisfied when the process driving the volatility is an Ornstein–Uhlenbeck (OU) process with a perturbed (sublinear) drift. We then translate these results into large-time asymptotics for call options and implied volatility and we verify our results numerically using Monte Carlo simulation. Finally, we extend our analysis to include a CIR short rate process and an independent driving Lévy process.

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Martin Forde. Rohini Kumar. "Large-time option pricing using the Donsker–Varadhan LDP—correlated stochastic volatility with stochastic interest rates and jumps." Ann. Appl. Probab. 26 (6) 3699 - 3726, December 2016. https://doi.org/10.1214/16-AAP1189

Information

Received: 1 November 2014; Revised: 1 February 2016; Published: December 2016
First available in Project Euclid: 15 December 2016

zbMATH: 1357.91047
MathSciNet: MR3582815
Digital Object Identifier: 10.1214/16-AAP1189

Subjects:
Primary: 60G99, 60J25, 60J60

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 6 • December 2016
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