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Short-maturity Asian options in local-stochastic volatility models

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  • Dan Pirjol
  • Lingjiong Zhu

Abstract

We derive the short-maturity asymptotics for Asian option prices in local-stochastic volatility (LSV) models. Both out-of-the-money (OTM) and at-the-money (ATM) asymptotics are considered. Using large deviations theory methods, the asymptotics for the OTM options are expressed as a rate function which is represented as a two-dimensional variational problem. We develop a novel expansion method for the variational problem by expanding the rate function around the ATM point. In particular, we derive series expansions in log-moneyness for the solution of this variational problem around the ATM point, and obtain explicit results for the first three terms. We give the ATM volatility level, skew and convexity of the implied volatility of an Asian option in a general local-stochastic volatility model, which can be used as an approximation for pricing Asian options with strikes sufficiently close to the ATM point. Using numerical simulations in the SABR, Heston and an LSV model with bounded local volatility, we show good performance of the asymptotic result for Asian options with sufficiently small maturity.

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  • Dan Pirjol & Lingjiong Zhu, 2024. "Short-maturity Asian options in local-stochastic volatility models," Papers 2409.08377, arXiv.org.
    • Handle: RePEc:arx:papers:2409.08377
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    References listed on IDEAS

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    1. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
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    14. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
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