Heston Option Pricing Calibration

Heston1993KahlJaeckelLordRev3 is the Heston option pricing function based on the implementation by Christian Kahl, Peter Jäckel and Roger Lord. The standard Heston formula exhibits a high numerical instability of the integral which is remedied in this implementation.

This function works for plain vanilla (European-style) put and call options and also implements an automatic estimation of the optimal alpha required for the integrand. A user generated alpha can also be used as an optional last argument.

Included are also a Black-Scholes-Merton (BSM) function (bsmec.m) to price European vanilla options and bsmivec.m for calculating the BSM implied volatilites - in case the Financial Toolbox is not available.

References

• Roger Lord, Christian Kahl. Optimal Fourier inversion in semi-analytical option pricing. 2007
• Roger Lord, Christian Kahl. Why the Rotation Count Algorithm Works. 2006
• Christian Kahl, Peter Jäckl. Not-so-complex logarithms in the Heston model. 2009
• Steven L. Heston. A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. 1993

Usage

Run HestonCalibration.m to perform a sample calibration.

Usage of Heston1993KahlJaeckelLordRev3:

Input: (PC till q can be vectorized)

•  PC: 1 for Calls, 2 for Puts
  

•  S: Spot
  

•  K: Strike
  

•  T: Maturity
  

•  t: start date
  

•  r: interest rate
  

•  q: dividend
  

•  v0: initial variance
  

•  theta: long run mean variance
  

•  kappa: mean reversion speed of  volatility
  

•  sigma: volatility of volatility
  

•  rho: correlation between returns volatility
  

•  (alpha:) vector of alphas. if unset function generates alphas
  

  Output:

•  Price for each option
  

•  (Alphas)
  

Tips

Smaller upper boundaries of [100 100 1-eps 100 100 ] instead of [Inf Inf 1-eps Inf Inf ] and trying different starting parameters might help if the calibration gets stuck in a local minimum.

Contributing

1. Fork it!
2. Create your feature branch: git checkout -b my-new-feature
3. Commit your changes: git commit -am 'Add some feature'
4. Push to the branch: git push origin my-new-feature
5. Submit a pull request :D

History

30/04/2016: added the bsmec.m and bsmivec.m functions

License

MIT