Mass at Zero and Small-Strike Implied Volatility Expansion in the SABR Model
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Date
2015-02Type
- Working Paper
ETH Bibliography
yes
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Abstract
We study the probability mass at the origin in the SABR stochastic volatility model, and derive several tractable expressions for it, in particular when time becomes small or large. In the uncorrelated case, tedious saddlepoint expansions allow for (semi) closed-form asymptotic formulae. As an application - the original motivation for this paper - we derive small-strike expansions for the implied volatility when the maturity becomes short or large. These formulae, by denition arbitrage-free, allow us to quantify the impact of the mass at zero on currently used implied volatility expansions. In particular we discuss how much those expansions become erroneous. Show more
Publication status
publishedExternal links
Publisher
ElsevierOrganisational unit
03845 - Teichmann, Josef / Teichmann, Josef
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ETH Bibliography
yes
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