| Summary: | 碩士 === 國立臺灣大學 === 資訊工程學研究所 === 87 === Interest rate derivatives are instruments whose payoffs depend in
some way on interest rates. To price them, it involves
constructing a model to describe the probabilistic behavior of
interest rates.
When valuing a derivative, it is customary to assume that there is
no risk of default. However, the no-default assumption is not
defensible, especially in over-the-counter markets. So dealing
with credit risk issues has become more and more important.
This thesis is concerned with the above two topics: calibrating
interest rate models under credit risk. We first use the yields of
default-free and risky zeros to calculate the probabilities of
default, then use the prices of risky zeros and options on risky
bonds to calibrate a tree of possible future short rates. With the
help of forward induction, the calibration process can be done
efficiently. We can use the tree to value interest-rate-sensitive
securities involving credit risk.
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