KTH Matematik |

Seminarierummet 3721, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7.
Karta!
We then move on to the main objective of the thesis and present three approaches for pricing inflation derivatives, where we focus in particular on two popular models. The first one, is a so called HJM approach, that models the nominal and real forward curves and relates the two by making an analogy to domestic and foreign fx rates. By the choice of volatility functions in the HJM framework, we produce nominal and real term structures similar to the popular interest-rate derivatives model of Hull-White. This approach was first suggested by Jarrow and Yildirim[1] and it’s main attractiveness lies in that it results in analytic pricing formulas for both linear and non-linear benchmark inflation derivatives. The second approach, is a so called market model, independently proposed by Mercurio[2] and Belgrade, Benhamou, and Koehler[4]. Just like the - famous - Libor Market Model, the modeled quantities are observable market entities, namely, the respective forward inflation indices. It is shown how this model as well - by the use of certain approximations - can produce analytic formulas for both linear and non-linear benchmark inflation derivatives. The advantages and shortcomings of the respective models are eveluated. In particular, we focus on how well the models calibrate to market data. To this end, model parameters are calibrated to market prices of year-on-year inflation floors; and it is evaluated how well market prices can be recovered by theoretical pricing with the calibrated model parameters. The thesis is concluded with suggestions for possible extensions and improvements. References: [1] Jarrow, R. and Yildirim, Y., Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model. 2003: Journal of Financial and Quantitative Analysis 38(2), 409 - 430. [2] Mercurio, F., Pricing inflation-indexed derivatives. 2005: Quantitative Finance 5(3), 289 - 302. [4] Belgrade, N., Benhamou, E., and Koehler, E., A Market Model for Inflation. 2004: ssrn.com/abstract=576081. |

Sidansvarig: Filip Lindskog Uppdaterad: 25/02-2009 |