This paper extends the class of stochastic volatility diffusions for asset returns to encompass Poisson jumps of time-varying intensity. We find that any reasonably descriptive continuous-time model for equity-index returns must allow for discrete jumps as well as stochastic volatility with a pronounced negative relationship between return and volatility innovations. We also find that the dominant empirical characteristics of the return process appear to be priced by the option market. Our analysis indicates a general correspondence between the evidence extracted from daily equity-index returns and the stylized features of the corresponding options market prices. MUCH ASSET AND DERIVATIVE PRICING THEORY is based on diffusion models for primary securities. However, prescriptions for practical applications derived from these models typically produce disappointing results. A possible explanation could be that analytic formulas for pricing and hedging are available for only a limited set of continuous-time representations for asset returns

We especially thank an anonymous referee and Rob Stambaugh, the editor, for helpful suggestions that greatly improved the article. Andrew Ang and Bob Hodrick both acknowledge support from the NSF.

We study optimal investment strategies given investor access not only to bond and stock markets but also to the derivatives market. The problem is solved in closed form. Derivatives extend the risk and return tradeoffs associated with stochastic volatility and price jumps. As a means of exposure to volatility risk, derivatives enable non-myopic investors to exploit the time-varying opportunity set; and as a means of exposure to jump risk, they enable investors to disentangle the simultaneous exposure to diffusive and jump risks in the stock market. Calibrating to the S&P 500 index and options markets, we find sizable portfolio improvement from derivatives investing.

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Limiting cases of our GARCH processes consist of models where both asset returns and local volatility follow jump diffusion processes with correlated jump sizes. Convergence of the GARCH models to their continuous time limits is extremely fast. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process. Since the state variables are fully determined by the path of prices, once the parameters have been estimated, option prices can readily be computed. We find that option prices, even 50 weeks after the parameters are estimated are fairly precise. In addition to pricing tests, we examine hedging effectiveness, and provide evidence that the hedges can be maintained very well over time.

We introduce a new method to price American-style options on underlying investments governed by stochastic volatility models. The method combines a standard gridding ap-proach to solving the associated dynamic programming problem, with a sequential Monte Carlo scheme to estimate required posterior distributions of the latent volatility process. The method represents a refinement of previous algorithms since it does not require the volatil-ity process to be directly observable. Instead, the sequential Monte Carlo scheme provides accurate estimates of the required conditional distributions. Furthermore, the method incorpo-rates market price of volatility risk, and is generalizable to handle different kinds of stochastic volatility models. We also demonstrate that with historical data for two stocks, and appropri-ately chosen market price of volatility risk, the algorithm yields option prices which are highly consistent with market data.

We price options when there are jumps in the pricing kernel and correlated jumps in returns and volatilities. A limiting case of our GARCH process consists of a model where both asset returns and local volatility follow jump di#usion processes with correlated jump sizes. When the jump processes are shut down our model reduces to Duan's (1995) GARCH option model; when the stochastic volatility process is shut down, our model reduces to a form that nests Merton 's (1976) jump di#usion model. Our general model permits conditional return distributions that are skewed and have fat tails. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process and improves the precision of option prices. We conduct hedging tests and provide evidence that hedges can be maintained very well over time.

Abstract: The authors study time-variation in the co-movements between daily stock and Treasury bond returns over 1986 to 2000. Their innovation is to examine whether variation in stock-bond return dynamics can be linked to non-return-based measures of stock market uncertainty, specifically the implied volatility (IV) from equity index options and detrended stock turnover (DTVR). The authors investigate two empirical questions suggested by recent literature on stock market uncertainty and cross-market hedging. First, from a forward-looking perspective, they find that the levels of IV and DTVR are both negatively associated with the future correlation between stock and bond returns. The probability of a negative correlation between daily stock and bond returns over the next month is several times greater following relatively high values of IV and DTVR. Second, from a contemporaneous perspective, the authors find that bond returns tend to be relatively high (low) during days when IV increases (decreases) and during days when stock turnover is unexpectedly high (low). Their findings suggest that stock market uncertainty has cross-market pricing influences that play an important role in understanding joint stock-bond price formation. Further, our results imply that stock-bond diversification benefits increase with stock market uncertainty.

This paper considers the modelling of option prices by using the pricing function's parameter processes. Our pricing function is derived by using transformation analysis and by assuming a jump-diffusion process for the underlying asset. According to our numerical example with S&P 500 options, the parameters related to the down jumps affect the prices more significantly than those governing stochastic volatility or the up jumps. In our example, hedging the uncertainties in the parameters improves the performance of a simple delta hedge on average by 14.3 percent. Uncertainty in the stochastic volatility parameters is most important in hedging the options, although on average it has a smaller effect on option prices than the down jumps.

We estimate the parameters of pricing kernels that depend on both aggregate wealth and state variables that describe the investment opportunity set, using FTSE 100 and S&P 500 index option returns as the returns to be priced. The coefficients of the state variables are highly significant and remarkably consistent across specifications of the pricing kernel, and across the two markets. The results provide further evidence that, consistent with Merton’s (1973) Intertemporal Capital Asset Pricing Model, state variables in addition to market risk The failure of simple complete markets option pricing models of the Black-Scholes (1973) type points to the importance in option pricing of state variables other than the underlying asset price. Despite increasing evidence that state variables other than the market index are important for pricing both

We provide evidence that trading frictions have an economically important impact on the execution and the profitability of option strategies that involve writing out-of-the money put options. Margin requirements, in particular, limit the notional amount of capital that can be invested in the strategies and force investors to close down positions and realize losses. The economic effect of frictions is stronger when the investor seeks to write options more aggressively. Although margins are effective in reducing counterparty default risk, they also impose a friction that limits investors from supplying liquidity to the option market.