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SPX, VIX and scale-invariant LSV\footnote{Local Stochastic Volatility}

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  • Alexander Lipton
  • Adil Reghai

Abstract

Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data. However, the literature misses a potent approach commonly used in physics and works with absolute (dimensional) variables rather than with relative (non-dimensional) ones. While model parameters defined in absolute terms are counter-intuitive for trading desks and tend to be heavily time-dependent, relative parameters are intuitive and stable, making it easy to steer the model adequately and consistently with its Profit and Loss (PnL) explanation power. We propose a specification that first explores historical data and uses physically well-defined relative quantities to design the model. We then develop an efficient hybrid method to price derivatives under this specification. We also show how our method can be used for robust scenario generation purposes - an important risk management task vital for buy-side firms.\footnote{The authors would like to thank Prof. Marcos Lopez de Prado and Dr. Vincent Davy Zoonekynd for valuable comments.}

Suggested Citation

  • Alexander Lipton & Adil Reghai, 2023. "SPX, VIX and scale-invariant LSV\footnote{Local Stochastic Volatility}," Papers 2302.08819, arXiv.org.
  • Handle: RePEc:arx:papers:2302.08819
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    References listed on IDEAS

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    1. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    2. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Alexander Lipton & Artur Sepp, 2022. "Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility," Papers 2202.07849, arXiv.org.
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