Читать книгу Perturbation Methods in Credit Derivatives - Colin Turfus - Страница 15

Another desk meanwhile trading hybrid products into emerging markets notices that the bank's pricing library now provides production‐quality analytic methods for option pricing under the Black–Karasinski model. They frequently use this model in preference to Hull–White as an interest rate model, as they find it performs better in market conditions with high and volatile interest rates. They are interested in what analytic functions are available and see that in Chapter 5 there are explicit formulae for caplets, swaptions and zero coupon bonds (stochastic discount factors) which they consider could be useful, particularly in the process of model calibration, where pricing of calibration instruments must otherwise be done by repeated Monte Carlo simulation.

They note in addition that results in Chapter 14 allow calibration of the Black–Karasinski model in a multi‐curve framework where the LIBOR spread(s) over the risk‐free rate can be stochastic and potentially correlated with the risk‐free rate. Furthermore, they note that results in Chapter 13 facilitate the extension of Black–Karasinski option pricing formulae enabling the model to be conveniently calibrated to caps referencing backward‐looking risk‐free rates, as and when a market in these inevitably appears in the post‐IBOR world to which the finance industry is currently headed.