Essays in financial economics

This thesis is the collection of papers studying the relationship between option markets and differences in beliefs (part I) and monetary term structure models (part II). Chapter 1 studies the role of non-redundant options in an economy with differences in beliefs. In traditional no-arbitrage models with deterministic volatility, options are redundant and can be priced by replication. However, these models axe silent about option volumes. Markets are dynamically complete and agents are indifferent about holding options or not. In this chapter we study a heterogeneous economy in which options are held in equilibrium becauseo f information reasons. Agents have different priors on the characteristics of two factors that affect (a) the market price of risk, and (b) the dividend process. Uncertainty makes options non-redundant and heterogeneity creates a link between differences in beliefs and option volumes. In the empirical section we use survey data to build an Index of Dispersion in Beliefs and estimate the structural model. We find that a model which takes into account information heterogeneity can explain the dynamics of option volume better than reduced-form models with stochastic volatility and that both the pricing and hedging performance is at least as good. We find that the Index of Dispersion in Beliefs is correlated with changes in the shape of the smile and it forecasts future realized volatility even after controlling for the current implied volatility. Chapter 2 and 3 study the monetary term structure models. In Chapter 2 we study a dynamics of monetary and real term structures in a continuous time monetary economy with habit formation. A crucial property is that, unlike in affine specifications, the price of risk is not a constant multiple of the volatility of interest rates but it depends on the state of the economy. In bad (good) states, investors become more (less) risk averse. We axe able to derive closed form solution for the both nominal and real bond prices. We take the model to the data and explore its ability to explain the dynamics of the term structure of interest rates. We find that, compared to affine specifications, the model with habit persistence finds it easier to reproduce (i) the empirical Campbell and Shiller (1991) slope coefficients and the documented deviations from the expectation hypothesis, (ii) the extent of the persistency of the conditional volatility of interest rates, (iii) the lead/lag relationship between interest rates and monetary aggregates, and (iv) the dynamics of the inflation risk premium. Chapter 3 analyzes the structural links between inflation and the term structure of interest rates in a monetary economy in which the fiscal system is only partially indexed to inflation shocks. We explore the relation between inflation shocks and nominal interest rates in a structural model generating an endogenous state-dependent market price of risk. We study and quantify the size of the inflation risk premium for different investment horizons. This question is important for a number of reasons: to understand the pricing relationship between nominal and index linked bonds; to extrapolate expectations on future inflation from current interest rates and assets valuation; to understand the welfaxe cost of inflation. We estimate a general equilibrium production economy in which (i) the monetary policy is responsive to both nominal and real shocks, (ii) the stochastic process for inflation is endogenous, (iii) the fiscal system is imperfectly indexed to inflation shocks with taxes payable on nominal income and nominal capital gains, and (iv) the endogenous price of risk is not a constant multiple of the volatility of the factors but state dependent. We find that over the last 40 years, the average inflation risk premium has been 60 basis points. However, the term structure of the inflation risk premium is sharply upward sloping, and it shows substantial time variation over the business cycle, from 20 to 140 basis points. The time-variation of the inflation risk premium is an important explanatory variable of deviations from the expectation hypothesis. We regress the forward risk premium onto the model-implied inflation risk premium and find an RI of 23% at five year horizon. Last, we find that the endogenous state-dependent market price of risk plays a key role in explaining deviations from the expectation hypothesis of interest rates