Hi, my name is Johannes Fürst and I am one of the financial engineers in the UnRisk developer team. Together with my colleagues, I have been working on a wide range of computational finance projects. My primary duties are the implementation and improvement of numerical methods and algorithms used for the pricing of instruments and model calibration in the UnRisk software package.
In my first blog post, I would like to give a little insight to the calibration of the Black Karasinski model, which assumes that the short interest rate process follows the stochastic differential equation
To be able to fit the current term structure of interest, ϑ is chosen to be time dependent, whereas the reversion speed parameter η and the volatility parameter σ - used for the calibration to option data - are chosen to be constant.
Since (even for simple instruments) there is no analytical formula available in this model, numerical methods have to be applied (even in the calibration process). Using the Ito formula and no arbitrage arguments, the pricing equation - which is a parabolic partial differential equation - can be derived:
More details of the calibration process and results for the Black Karasinski model will be presented in the blog next monday.
