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Large and moderate deviations for importance sampling in the Heston model

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  • Marc Geha
  • Antoine Jacquier
  • Zan Zuric

Abstract

We provide a detailed importance sampling analysis for variance reduction in stochastic volatility models. The optimal change of measure is obtained using a variety of results from large and moderate deviations: small-time, large-time, small-noise. Specialising the results to the Heston model, we derive many closed-form solutions, making the whole approach easy to implement. We support our theoretical results with a detailed numerical analysis of the variance reduction gains.

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  • Marc Geha & Antoine Jacquier & Zan Zuric, 2021. "Large and moderate deviations for importance sampling in the Heston model," Papers 2111.00348, arXiv.org.
    • Handle: RePEc:arx:papers:2111.00348
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    References listed on IDEAS

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    1. Baldi, P. & Caramellino, L., 2011. "General Freidlin-Wentzell Large Deviations and positive diffusions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1218-1229, August.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Robertson, Scott, 2010. "Sample path Large Deviations and optimal importance sampling for stochastic volatility models," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 66-83, January.
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