On the Forward Smile

15 Pages Posted: 31 Jul 2019 Last revised: 21 Apr 2020

See all articles by Thomas Roos

Thomas Roos

Quantitative Financial Consulting

Date Written: July 30, 2019


Using short-time expansion techniques, we obtain analytic implied volatilities for European and forward starting options for a family of stochastic volatility models with arbitrary local volatility component and time dependent (piecewise constant) parameters. The formulas can be used to efficiently calibrate the model to European options at two expiries and to calculate the spanning forward starting option price.

Keywords: Forward Starting Options, Stochastic Volatility, SABR, Implied Volatility

JEL Classification: G13

Suggested Citation

Roos, Thomas, On the Forward Smile (July 30, 2019). Available at SSRN: https://ssrn.com/abstract=3429050 or http://dx.doi.org/10.2139/ssrn.3429050

Thomas Roos (Contact Author)

Quantitative Financial Consulting ( email )

United Kingdom

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