Essays on pricing fixed income derivatives and risk management

2000 2000

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Abstract (summary)

This dissertation consists of four essays on pricing fixed income derivatives and risk management. The first essay presents pricing and duration formulas for floating rate bonds and interest rate swaps with embedded options. It combines Briys et al.'s approximation with the extended Vasicek term structure model to value caps and floors. Using this approach, it computes the durations of caps, floors, collars, floating rate bonds with collars and interest rate swaps with collars, and provides comparative statics analyses of these durations with respect to the underlying variables such as the cap rate, the floor rate, the interest rate volatility, and the level of interest rates.

The second essay explores a class of polynomial Taylor series expansions for approximating the bond return function, and examines its implication for managing interest rate risk. The generalized duration vector models derived from alternative Taylor series expansion extend Fong and Fabozzi's M-square model and Nawalkha and Chambers' M-vector model, and the empirical tests show that immunization results can be improved for models g( t) = tα with α less than 1 when higher order generalized duration vectors are used.

The third essay develops a methodology to build recombining trees for pricing American options on bonds under deterministic volatility HJM models. Without imposing the HJM drift restriction, our approach uses the Nelson-Ramaswamy transformation to generate recombining forward rate trees. We show that the option prices obtained from our recombining trees satisfy Merton's bond option PDE when step size approaches zero. Numerical simulations provide evidence that this approach is efficient in pricing both European and American contingent claims.

The fourth essay obtains computationally efficient trees for pricing European options under two types of proportional volatility HJM models. We construct a numeraire economy in which European options are priced using a maturity-specific equivalent martingale measure. We then show that for the two types of proportional volatility models, European option prices are independent of the forward rate drift under this maturity-specific equivalent martingale measure. Our method is particularly beneficial when used to price long-dated caps, floors and collars because these instruments involve a large number of long-dated puts and calls.

Indexing (details)

Securities prices;
Risk management
0508: Finance
0770: Banking
Identifier / keyword
Social sciences; Fixed income derivatives; Pricing; Risk management
Essays on pricing fixed income derivatives and risk management
Zhang, Jun
Number of pages
Publication year
Degree date
School code
DAI-A 61/10, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
0599964243, 9780599964242
Nawalkha, Sanjay
University of Massachusetts Amherst
University location
United States -- Massachusetts
Source type
Dissertations & Theses
Document type
Dissertation/thesis number
ProQuest document ID
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
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