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Calibrating Local Volatility Models With Stochastic Drift And Diffusion

Author

Listed:
  • ORCAN ÖGETBIL

    (Corporate Model Risk, Wells Fargo, 100 Park Ave, 2nd Floor New York, NY 10017-5516, USA)

  • NARAYAN GANESAN

    (Corporate Model Risk, Wells Fargo, 100 Park Ave, 2nd Floor New York, NY 10017-5516, USA)

  • BERNHARD HIENTZSCH

    (Corporate Model Risk, Wells Fargo, 100 Park Ave, 2nd Floor New York, NY 10017-5516, USA)

Abstract

We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems and list the required input data and steps for calibration. We give conditions under which a local volatility can exist given European option prices, stochastic interest rate model parameters, and correlations. The models are posed in a foreign exchange setting. The drift term for the exchange rate is given as a difference of two stochastic short rates, domestic and foreign; each modeled by a Gaussian one-factor model with deterministic shift (G1 + +) process. For stochastic volatility, we model the variance for the exchange rate by a Cox–Ingersoll–Ross (CIR) process. We include tests to show the convergence and the accuracy of the proposed algorithms.

Suggested Citation

  • Orcan ÖGetbil & Narayan Ganesan & Bernhard Hientzsch, 2022. "Calibrating Local Volatility Models With Stochastic Drift And Diffusion," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 25(02), pages 1-43, March.
    • Handle: RePEc:wsi:ijtafx:v:25:y:2022:i:02:n:s021902492250011x
    DOI: 10.1142/S021902492250011X
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    Cited by:

    1. Orcan Ogetbil & Bernhard Hientzsch, 2022. "A Flexible Commodity Skew Model with Maturity Effects," Papers 2212.07972, arXiv.org.
    2. Arun Kumar Polala & Bernhard Hientzsch, 2023. "Parametric Differential Machine Learning for Pricing and Calibration," Papers 2302.06682, arXiv.org, revised Feb 2023.

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