Gurdip Bakshi

Baby Boom, Population Aging, and Capital Markets

This article tests how demographic changes affect capital markets. The life-cycle investment hypothesis states that at an early stage an investor allocates more wealth in housing and then switches to financial assets at a later stage. Consequently, the stock market should rise but the housing market should decline with the average age, a prediction supported in the post-1945 period. The second hypothesis that an investors risk aversion increases with age is tested by estimating the resulting Euler equation and supported in the post-1945 period. A rise in average age is found to predict a rise in risk premiums. Copyright 1994 by University of Chicago Press.

Pricing and hedging long-term options

Recent empirical studies find that once an option pricing model has incorporated stochastic volatility, allowing interest rates to be stochastic does not improve pricing or hedging any further while adding random jumps to the modeling framework only helps the pricing of extremely short-term options but not the hedging performance. Given that only options of relatively short terms are used in existing studies, this paper addresses two related questions: Do long-term options contain different information than short-term options? If so, can long-term options better differentiate among alternative models? Our inquiry starts by first demonstrating analytically that differences among alternative models usually do not surface when applied to short term options, but do so when applied to long-term contracts. For instance, within a wide parameter range, the Arrow-Debreu state price densities implicit in different stochastic-volatility models coincide almost everywhere at the short horizon, but diverge at the long horizon. Using regular options (of less than a year to expiration) and LEAPS, both written on the S&P 500 index, we find that short- and long-term contracts indeed contain different information and impose distinct hurdles on any candidate option pricing model. While the data suggest that it is not as important to model stochastic interest rates or random jumps (beyond stochastic volatility) for pricing LEAPS, incorporating stochastic interest rates can nonetheless enhance hedging performance in certain cases involving long-term contracts.

A Theory of Volatility Spreads

This study formalizes the departure between risk-neutral and physical index return volatilities, termed volatility spreads. Theoretically, the departure between risk-neutral and physical index volatility is connected to the higher-order physical return moments and the parameters of the pricing kernel process. This theory predicts positive volatility spreads when investors are risk averse, and when the physical index distribution is negatively skewed and leptokurtic. Our empirical evidence is supportive of the theoretical implications of risk aversion, exposure to tail events, and fatter left-tails of the physical index distribution in markets where volatility is traded.

Understanding the Role of Recovery in Default Risk Models: Empirical Comparisons and Implied Recovery Rates

This article presents a framework for modeling defaultable debt under alternative recovery conventions (for a wide class of processes describing recovery rates and default probability). These debt models have the ability to differentiate the impact of recovery rates and default probability, and can be utilized to invert the market expectation of recovery rates implicit in bond prices. Among potential applications, the framework can be used for pricing and hedging credit derivatives that are contingent on the default event and/or recovery levels. Empirical implementation of these models suggests two central findings. First, the recovery concept that specifies recovery as a fraction of the discounted par value has broader empirical support. Second, parametric debt valuation models can provide a useful assessment of recovery rates embedded in bond prices. This article has attempted to model recovery and comprehend their impact on debt values.

Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels

When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing region of the kernel. Using returns of (i) S&P 500 index calls, (ii) calls on major international equity indexes, (iii) digital calls, (iv) upside variance contracts, and (v) a theoretical construct that we denote as kernel call, we find broad support for the implications of U-shaped pricing kernels. A possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short-selling.

Investigating the Role of Systematic and Firm-Specific Factors in Default Risk: Lessons from Empirically Evaluating Credit Risk Models

This paper proposes and empirically investigates a family of credit risk models driven by a two-factor structure for the short interest rate and an additional factor for firm-specific distress. The firm-specific distress factors include leverage, book-to-market, profitability, equity-volatility, and distance-to-default. Our estimation approach and performance yardsticks show that interest rate risk is of first-order importance for explaining variations in single-name defaultable bond yields. When applied to low-grade bonds, a credit risk model that takes leverage into consideration reduces absolute yield mispricing by as much as 30%. A strategy relying on Treasury instruments is effective in dynamically hedging credit exposures.

Volatility Risk Premiums Embedded in Individual Equity Options: Some New Insights

The accumulation of trading experience and empirical evidence since the original Black-Scholes (BS) model was developed, have made it increasingly evident that volatility is not a constant parameter, as BS assumed, but stochastic. With a second random factor associated with volatility affecting security returns, it would not be surprising if investors cared about bearing risk related to that factor. And there is considerable evidence from analysis of real world options that volatility risk is indeed a priced factor, with a negative price. That is, investors will pay extra for (accept lower returns on) securities like options whose values increase when volatility goes up. In that case, Black-Scholes implied volatilities will tend to be higher than actual volatilities, which provides one measure of the market price of volatility risk. Research on stochastic volatility has focused largely on stock index options, but modern portfolio theory makes a strong distinction between stochastic factors that are correlated with the market portfolio and those that are not, whose risk can be diversified. In this article, Bakshi and Kapadia look at the pricing of individual stock options to explore the effects of market volatility risk versus firm-specific volatility risk. They find that volatility risk is priced, negatively as expected, and that market volatility risk is more important than firm-specific risk.

Predictability of Currency Carry Trades and Asset Pricing Implications

This paper studies the time series predictability of currency carry trades, constructed by selecting currencies to be bought or sold against the US dollar, based on forward discounts. Changes in a commodity index, currency volatility and, to a lesser extent, a measure of liquidity predict in-sample the payoffs of dynamically re-balanced carry trades, as evidenced by individual and joint p-values in monthly predictive regressions at horizons up to six months. Predictability is further supported through out-of-sample metrics, and a predictability-based decision rule produces sizable improvements in the Sharpe ratios and skewness profile of carry trade payoffs. Our evidence also indicates that predictability can be traced to the long legs of the carry trades and their currency components. We test the theoretical restrictions that an asset pricing model, with average currency returns and the mimicking portfolio for the innovations in currency volatility as risk factors, imposes on the coefficients in predictive regressions.

Estimation of Continuous-Time Models with an Application to Equity Volatility Dynamics

The treatment of this article renders closed-form density approximation feasible for univariate continuous-time models. Implementation methodology depends directly on the parametric-form of the drift and the diffusion of the primitive process and not on its transformation to a unit-variance process. Offering methodological convenience, the approximation method relies on numerically evaluating one-dimensional integrals and circumvents existing dependence on intractable multidimensional integrals. Density-based inferences can now be drawn for a broader set of models of equity volatility. Our empirical results provide insights on crucial outstanding issues related to the rank-ordering of continuous-time stochastic volatility models, the absence/presence of nonlinearities in the drift function of equity volatility, and the desirability of pursuing more flexible diffusion function specifications.

Improving the predictability of real economic activity and asset returns with forward variances inferred from option portfolios

This paper presents an option positioning that allows us to infer forward variances from option portfolios. The forward variances we construct from equity index options help to predict (i) growth in measures of real economic activity, (ii) Treasury bill returns, (iii) stock market returns, and (iv) changes in variance swap rates. Our yardstick for measuring predictive ability is both individual and joint parameter statistical significance within a market, as well as across a set of markets.