zoro20171002 / heston

Option pricing function for the Heston model based on the implementation by Christian Kahl, Peter Jäckel and Roger Lord. Includes Black-Scholes-Merton option pricing and implied volatility estimation. No Financial Toolbox required.

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