Title

Two essays on fixed income derivatives

Date of Award

2003

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Business Administration

Advisor(s)

Chunchi Wu

Keywords

Bond pricing, Interest rate caps, Tax timing option, Default risk, Capital gains, Fixed income derivatives

Subject Categories

Business | Business Administration, Management, and Operations | Finance and Financial Management

Abstract

This dissertation contains two major parts. In Essay 1, we examine the optimal trading and tax option value of defaultable bonds with asymmetric capital gain taxes. Under current U.S. tax laws, capital gains are not taxed until investors sell their assets and the tax rates applied to capital gains or losses depend on the holding period. Long-term gains are subject to a more favorable tax rate than short-term gains. These tax treatments provide investors an incentive to time the sales of their bonds to minimize tax liability. In reality, investors' tax-timing strategy is complicated by the risk of default. Default forces investors to close their position before maturity and therefore, imposes a constraint on investors' trading strategy. Investors have an incentive to sell their bonds to establish a short-term status to realize future losses short-term in an anticipation of default. Moreover, default increases bond yield and subjects investors to higher income taxes. This paper examines these complicated effects induced by asymmetric capital gain tax treatments on investors' trading behavior and the pricing of defaultable bonds. It incorporates the effects of discount and premium amortization, multiple trading dates, transaction costs, and changes in tax rates and in the level and volatility of interest rates. Contrary to intuition, default does not necessarily reduce the value of the tax-timing option under asymmetric capital gain taxes. The value of tax-timing option depends not only on the probability of default but also on tax rates, coupon size, maturity and the short rate process. Tax option values remain sizable even after accounting for the effects of default and transaction costs. Ignoring the tax-timing option value results in an underestimation of default probability and the implied marginal tax rate from observed bond yields. This bias in estimation increases with maturity and decreases with bond quality.

In Essay 2, we test the term structure models in the HJM class with different volatility functions using cap data with different strike maturities and moneyness. We estimate the implied volatility of these models and evaluate model performance. The choice of a volatility function is quite important for the HJM model. For one-factor models, the exponential and the linear volatility models have the best performance in the pre- and post-September 11 periods, respectively. Compared with one-factor models, two-factor models perform much better when volatility functions are employed to capture the level, maturity, and curvature effects. Among the two-factor HJM models, the linear absolute and proportional volatility model is the best choice to capture the volatility smile in interest rate caps. Finally, we find that term structure effects on the underlying forward rate volatility are time variant. In the pre-September 11 sample, the level and curvature effects are more important while in the post-September 11 sample, the maturity effect is more influential on the forward rate volatility structure.

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