This paper develops a new econometric method to estimate continuous time processes from discretely sampled data. This method extends the maximum likelihood technique to cases where the transition density of the process cannot be computed in closed form but can nevertheless be computed by simulation. The asymptotic properties of the estimator are obtained, showing it to have the same behavior in large samples of the (unknown) true likelihood estimator. That is, the simulated likelihood estimator is consistent and asymptotically normal. The econometric method is used to estimate the parameters of a broad family of processes for the short-term interest rate and test some restrictions to well-known models of the term structure.

We use a novel pricing model to filter times series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex-ante risk assessed by investors. We find that both components of risk vary substantially over time, are quite persistent, and correlate with each other and with the stock index. Using a simple general equilibrium model with a representative investor, we translate the filtered measures of ex-ante risk into an ex-ante risk premium. We find that the average premium that compensates the investor for the risks implicit in option prices, 10.1 percent, is about twice the premium required to compensate the same investor for the realized volatility, 5.8 percent. Moreover, the ex-ante equity premium that we uncover is highly volatile, with values between 2 and 32 percent. The component of the premium that corresponds to the jump risk varies between 0 and 12 percent.

We investigate the risk and return of a wide variety of trading strategies involving options on the S&P 500. We consider naked and covered positions, straddles, strangles, and calendar spreads, with different maturities and levels of moneyness. Overall, we find that strategies involving short positions in options generally compensate the investor with very high Sharpe ratios, which are statistically significant even after taking into account the non-normal distribution of returns. Furthermore, we find that the strategies’ returns are substantially higher than warranted by asset pricing models. We also find that the returns of the strategies could only be justified by jump risk if the probability of market crashes were implausibly higher than it has been historically. We conclude that the returns of option strategies constitute a very good deal. However, exploiting this good deal is extremely diffcult. We find that trading costs and margin requirements severely condition the implementation of option strategies. Margin calls force investors out of a trade precisely when it is losing money. Taking margin calls into account turns the Sharpe ratio of some of the best strategies negative.

We find that the average excess return in the stock market is higher under Democratic than Republican presidents– a difference of 9 percent per year for the value-weighted portfolio and 16 percent for the equal-weighted portfolio. The difference is economically and statistically significant, does not seem to be due to small sample biases, and is robust in different subsamples. There is a remarkable monotonicity in the difference of returns for size-decile portfolios, from 7 percent for large firms to about 22 percent for small firms. Presidential partisan cycles have a heterogeneous impact on industry returns: the tobacco, telecom, and chemical industries have performed better under Republican presidents, whereas the real estate, construction, and services industries have fared significantly better under Democrats. We test three plausible explanations for these findings. First, the relation might be due to political variables proxying for business-cycle factors. Second, the relation might be attributed to unexpected returns around elections, when information is revealed, rather than to expected returns varying with the political cycle. Lastly, differences in stock market riskiness across presidential regimes could account for the difference in average returns. We reject all three hypotheses. As it stands, the difference in excess returns during Republican and Democratic presidencies is a puzzle that cannot easily be explained. However, the cross-sectional evidence from size-sorted and industry portfolios suggests that the party in the presidency may affect the stock market through differences in fiscal and regulatory policies.

This paper offers a new approach for pricing options on assets with stochastic volatility. We start by taking as given the prices of a few simple, liquid European options. More specifically, we take as given the “surface” of Black-Scholes implied volatilities for European options with varying strike prices and maturities. We show that the Black-Scholes implied volatilities of at-the-money options converge to the underlying asset’s instantaneous (stochastic) volatility as the time to maturity goes to zero. We model the stochastic processes followed by the implied volatilities of options of all maturities and strike prices as a joint diffusion with the stock price. In order for no arbitrage opportunities to exist in trading the stock and these options, the drift of the processes followed by the implied volatilities is constrained in such a way that it is fully characterized by the volatilities of the implied volatilities. Finally, we suggest how to use the arbitrage-free joint process for the stock price and its volatility to price other derivatives, such as standard but illiquid options as well as exotic options, using numerical methods. Our approach simply requires as inputs the stock price and the implied volatilities at the time the exotic option is to be priced, as well as estimates of the volatilities of the implied volatilities.

Exchange rates depreciate by the difference between the domestic and foreign marginal utility growths. Exchange rates vary a lot, st of the variation of average stock risk through time and it is idiosyncratic risk that drives the forecastability of the stock market.” as much as 10% per year. However, equity premia imply that marginal utility growths vary much more, by at least 50% per year. This means that marginal utility growths must be highly correlated across countries - international risk sharing is better than you think. Conversely, if risks really are not shared internationally, exchange rates should vary more than they do - exchange rates are much too smooth. We calculate an index of international risk sharing that formalizes this intuition in the context of both complete and incomplete capital markets. Our results suggest that risk sharing is indeed very high across several pairs of countries.”

We introduce Mixed Data Sampling (henceforth MIDAS) regression models. The regressions involve time series data sampled at different frequencies. Technically speaking MIDAS models specify conditional expectations as a distributed lag of regressors recorded at some higher sampling frequencies. We examine the asymptotic properties of MIDAS regression estimation and compare it with traditional distributed lag models. MIDAS regressions have wide applicability in macroeconomics and �nance.

We present a novel approach to dynamic portfolio selection that is no more difficult to implement than the static Markowitz model. The idea is to expand the asset space to include simple (mechanically) managed portfolios and compute the optimal static portfolio in this extended asset space. The intuition is that a static choice among managed portfolios is equivalent to a dynamic strategy. We consider managed portfolios of two types: “conditional” and “timing” portfolios. Conditional portfolios are constructed along the lines of Hansen and Richard (1987). For each variable that affects the distribution of returns and for each basis asset, we include a portfolio that invests in the basis asset an amount proportional to the level of the conditioning variable. Timing portfolios invest in each basis asset for a single period and therefore mimic strategies that buy and sell the asset through time. We apply our method to a problem of dynamic asset allocation across stocks, bonds, and cash using the predictive ability of four conditioning variables.

We develop an estimation method for the Diagonal Multivariate GARCH model. For a vector of size N unidimensional GARCH processes for the diagonal elements of the conditional covariance matrix, and N(N-1)/2 bivariate GARCH processes for the off-diagonal elements of the conditional covariance matrix. The coefficient matrices are then transformed in such a way that ensures the positive semi-definiteness of the conditional covariance matrix. Under a technical assumption, the estimator has the same asymptotic properties as the univariate and bivariate maximum likelihood GARCH estimators. The method is computationally feasible for large problems, of size N=100 or larger. We do not need to impose any particular simplifying structure on the coefficient matrices. The conditional covariance is ensured to be stationary, and is, in general, well conditioned. We provide an empirical application in the context of international stock markets and offer Monte Carlo evidence of the good small sample properties of the model.

We offer a new model for pricing bonds subject to default risk. The event of default is remodeled as the first time that a state variable that captures the solvency of the issue goes below a certain level. The payoff to the bond in case of default is a constant fraction of the value of a security with the same promised payoffs but without the risk of default. We show that our model is very tractable under different models of interest rate risk and of the interaction between default risk and interest rate risk, with closed-form solutions for corporate bond prices in special cases. The model is seen to produce term structures of default yield spreads and forward spreads with more reasonable properties than other models that have recently been proposed. We illustrate the issue of our model by estimating its parameters and backing up both the default writedown and the state variable that governs default risk from a panel data set of bond prices issued by RJR Nabisco.