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Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method

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  • Andrei Cozma
  • Matthieu Mariapragassam
  • Christoph Reisinger

Abstract

We propose a novel and generic calibration technique for four-factor foreign-exchange hybrid local-stochastic volatility models with stochastic short rates. We build upon the particle method introduced by Guyon and Labord\`ere [Nonlinear Option Pricing, Chapter 11, Chapman and Hall, 2013] and combine it with new variance reduction techniques in order to accelerate convergence. We use control variates derived from a calibrated pure local volatility model, a two-factor Heston-type LSV model (both with deterministic rates), and the stochastic (CIR) short rates. The method can be applied to a large class of hybrid LSV models and is not restricted to our particular choice of the diffusion. The calibration procedure is performed on real-world market data for the EUR-USD currency pair and has a comparable run-time to the PDE calibration of a two-factor LSV model alone.

Suggested Citation

  • Andrei Cozma & Matthieu Mariapragassam & Christoph Reisinger, 2017. "Calibration of a Hybrid Local-Stochastic Volatility Stochastic Rates Model with a Control Variate Particle Method," Papers 1701.06001, arXiv.org, revised Mar 2021.
    • Handle: RePEc:arx:papers:1701.06001
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    Cited by:

    1. Andrei Cozma & Christoph Reisinger, 2017. "Strong convergence rates for Euler approximations to a class of stochastic path-dependent volatility models," Papers 1706.07375, arXiv.org, revised Oct 2018.

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