Mean reversion, tax arbitrage and hidden Markov modeling of risk premia

This dissertation is a combination of three chapters on three empirical finance issues. In chapter 1 "Are Term Premia Mean Reverting", we attempt to explain the mean reversion evidence in US Treasury bill (T-bill) forward rates that indicates either market inefficiency or existence of speculative dynamics in models with time invariant term premia. Accepting term premia as time variant and explicitly modeling the forward rates using a multifactor GARCH model under the rational expectation and efficiency market hypotheses, we find that the estimated term premia do exhibit the mean reversion property, thus reconciling the evidence of mean reversion with market efficiency theory.;Chapter 2 "Do Asymmetric Taxes Have a Say on Forward-futures Spreads?---An Empirical Investigation" is aimed to explore whether different tax treatment of ordinary income and capital gains/losses in the US can explain the persistent difference between futures rates and implicit forward rates for 91-day US T-bills.;In chapter 2 we revisit the issue on whether asymmetric taxes on capital gains/losses versus ordinary income affect the relative yields from forward and futures contract for T-bill. Under some stringent assumptions that would establish the asymmetric tax treatment as the only factor determining forward-futures spreads, we derive a formula for implicit forward premia based on the observed forward-futures spreads. Empirically, however, we find that the estimated marginal tax rates from the aforementioned relationship are unrealistically too high, thus implying that the tax-based explanation insufficient. The investigation for a later period of 1987--92 also reveals evidence consistent with findings in earlier periods. We further argue that the market demand and supply imbalance of futures is the most likely explanation for forward-futures spreads, and the high short selling cost in T-bill cash market is the reason behind the demand-supply imbalance.;In chapter 3 "Semiparametric Representation of a Generalized Stochastic Volatility Model and Hidden Markov Approximation", we proposed a stochastic volatility model with a generalized homogeneous volatility process. The purpose is to circumvent model selection problem associated with the volatility process. We also proposed to use a discrete state hidden Markov model (HMM) with continuous range observations to approximate this generalized model. Under this arrangement, estimation of a stochastic volatility model becomes a signal filtration process. The estimation and forecast of hidden Markov model are introduced. Empirically, we use the HMM to model several major exchange rate time series and find it performs quite well comparing with the popular GARCH models.