The C++ code for Heston and CEV implied vol approximations is now available for download HERE. Available also on QuantLib. Implied Volatility formulas are derived from "Explicit implied vols for multifactor local-stochastic vol models" http://ssrn.com/abstract=2283874
New Implied Vol for any Local-Stochastic Vol Model (January 29, 2014)
In this website, we collect some material, papers and Mathematica CDF files (get here the free CDF Player) on analytical approximation methods in option pricing. The notebooks available for download have been recently updated to include higher order approximations as well as non-zero interest rates. Specifically, we have pricing and implied volatility formulas for the following models:
– CEV local volatility
– Quadratic local volatility
– Heston stochastic volatility
– 3/2 stochastic volatility
– JDCEV (bond prices and credit spreads)
– general local-stochastic vol model
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Implied vol for any local-stochastic vol model [by M. Lorig, S. Pagliarani and A. Pascucci]
Implied Vol for any Local-Stochastic Vol Model (June 24, 2013)
In this website, we collect some material, papers and Mathematica CDF files (get here the free CDF Player) on analytical approximation methods in option pricing. The most recent results are universal approximation formulas for the Implied Vol in any Local-Stochastic volatility model. We have also studied a simplified approach to the approximation of the transition density in a general local volatility model for European and Asian options.
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- Implied vol for any local-stochastic vol model [by M. Lorig, S. Pagliarani and A. Pascucci]
Mathematica CDF
This notebook contains implied vol formulas for the following models:
– CEV local volatility
– Quadratic local volatility
– Heston stochastic volatility
– SABR local-stochastic volatility
– 3/2 stochastic volatility
– general local-stochastic vol models.
– Quadratic local volatility
– Heston stochastic volatility
– SABR local-stochastic volatility
– 3/2 stochastic volatility
– general local-stochastic vol models.
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-European options in local Lévy models [by S. Pagliarani, A. Pascucci and C. Riga]
-European options in local volatility models [by S. Pagliarani and A. Pascucci] Preprint "Analytical approximation of the transition density in a LV model" Mathematica CDF
-Approximations for LSV models with Jumps [by S. Pagliarani and A. Pascucci] Preprint "Approximation Formulas for Local Stochastic Volatility with Jumps" Mathematica CDF
-Asian options in local volatility models [by P. Foschi, S. Pagliarani and A. Pascucci] Preprint "Black-Scholes formulae for Asian options in LV models" Mathematica CDF
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Feel free to contact the authors for any question concerning the preprints or the Mathematica code.
On request, we provide the Mathematica code for specific volatility models.
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The proposed methodology is sufficiently flexible to be extended
to much more general settings.
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We plan to put on this website other results and
the related Mathematica CDF files in the near future.
ExplicitSolutions 