Pricing Credit Linked Notes with a modified LIBOR MARKET MODEL

蔡孟軒(Meng-Hsuan Tsai)

指導教授 ： 張焯然

國立清華大學/科技管理學院/科技管理研究所/碩士(2008年)

摘要

Due to the global depression economy with the low interest rate accompanied,
the credit derivatives and interest rate derivatives have been blossoming. Structure
notes are tailor-made products which are created by nancial engineering.
In Lotz and Schlogl (2000), they supposed a model for nite-interval interest
rates, for example, LIBOR (London InterBank Oered Rate) rate, which explicitly
takes into account the possibility of default through the in
uence of a point process
with deterministic intensity. They relate the defaultable interest rate to the
non-defaultable interest rate and to the credit risk characteristics default intensity
and recovery rate in comparison with the forward LIBOR model that can derive the
appropriate model assumption by using the observable market rate to calibrate the
parameter of the model.
Before having modied market model process, we should construct the termstructure
of default intensity in advance that can transform non-defaultable into
defaultable interest rate.
Therefore, the rst aim of this study is to utilize the modied market model to
construct the defaultable LIBOR rate, and to use defaultable cap to calibrate the
instantaneous volatility of defaultable LIBOR used in modied market model as a
parameter. After simulating defaultable LIBOR rate has been developed, the cash

ows of credit linked notes will be identied.
The second aim of this study is following Sch�onbucher (2000), he models effective
default-free forward rates and forward credit spreads as lognormal diusion
processes. Therefore, we also consider that default intensity is stochastic, and analyze
what eects will be produced in dierent correlation coefficient
Keyword : Credit linked notes, LIBOR market model, default intensity

關鍵字

Credit linked notes ； LIBOR market model ； default intensity

參考文獻

[1] Arvanitis, A., J. Gregory, and J. P. Laurent (1999). Building Models for Credit

[2] Brace, A., D. Gatarek., and M. Musiela (1997). The Market Model of Interest

[3] Brigo, D., F. Mercurio., and M. Morini (2003). Di_erent Covariance

[4] Brigo, D. and F. Mercurio (2006). Interest Rate Models Theory and Practice.

interest-rate models to Black volatilities and to the correlation matrix