2012
DOI: 10.1080/1350486x.2011.646523
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On the Approximation of the SABR Model: A Probabilistic Approach

Abstract: In this article, we derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general case. Specifically, we focus on capturing the terminal distribution of the underlying process (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a variety of parameters that cover the long-dated opti… Show more

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Cited by 5 publications
(16 citation statements)
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“…Once we fit an appropriate approximation to the underlying's marginal distribution, implied volatilities can be immediately recovered by inverting the option prices. In Kennedy et al (2012), we found that this approach was significantly better than the benchmark approximation proposed in Hagan et al (2002). An advantage for the probabilistic approximation in Kennedy et al (2012) is that it can cope well with very long maturity (up to 30 years) or high volatility of volatility.…”
Section: Introductionmentioning
confidence: 56%
See 4 more Smart Citations
“…Once we fit an appropriate approximation to the underlying's marginal distribution, implied volatilities can be immediately recovered by inverting the option prices. In Kennedy et al (2012), we found that this approach was significantly better than the benchmark approximation proposed in Hagan et al (2002). An advantage for the probabilistic approximation in Kennedy et al (2012) is that it can cope well with very long maturity (up to 30 years) or high volatility of volatility.…”
Section: Introductionmentioning
confidence: 56%
“…In Kennedy et al (2012), we found that this approach was significantly better than the benchmark approximation proposed in Hagan et al (2002). An advantage for the probabilistic approximation in Kennedy et al (2012) is that it can cope well with very long maturity (up to 30 years) or high volatility of volatility. This is a different feature from other current approaches in the literature that rely on the assumption of very small total volatility and usually degrades for longer than 10 years maturity, e.g.…”
Section: Introductionmentioning
confidence: 56%
See 3 more Smart Citations