David S. Bates

Post-'87 crash fears in the S&P 500 futures option market

Abstract Post-crash distributions inferred from S&P 500 future option prices have been strongly negatively skewed. This article examines two alternate explanations: stochastic volatility and jumps. The two option pricing models are nested, and are fitted to S&P 500 futures options data over 1988–1993. The stochastic volatility model requires extreme parameters (e.g., high volatility of volatility) that are implausible given the time series properties of option prices. The stochastic volatility/jump-diffusion model fits option prices better, and generates more plausible volatility process parameters. However, its implicit distributions are inconsistent with the absence of large stock index moves over 1988–93.

Empirical option pricing: a retrospection

This article provides an overview and discussion of empirical option pricing research: how we test models, what we have learned, and what are some key issues. Some suggestions for future research are provided.

The market for crash risk

This paper examines the equilibrium when stock market crashes can occur and investors have heterogeneous attitudes towards crash risk. The less crash averse insure the more crash averse through options markets that dynamically complete the economy. The resulting equilibrium is compared with various option pricing anomalies: the tendency of stock index options to overpredict volatility and jump risk, the Jackwerth [Recovering risk aversion from option prices and realized returns. Review of Financial Studies 13, 433-451] implicit pricing kernel puzzle, and the stochastic evolution of option prices. Crash aversion is compatible with some static option pricing puzzles, while heterogeneity partially explains dynamic puzzles. Heterogeneity also magnifies substantially the stock market impact of adverse news about fundamentals.

Valuing the Futures Market Clearinghouse's Default Exposure During the 1987 Crash

Futures market clearinghouses are intermediaries that make large volume trading between anonymous parties feasible. During the October 1987 market crash rumors spread that a major clearinghouse might fail. This paper presents estimates of three measures of the default exposure on the popular S&P500 futures contract traded on the Chicago Mercantile Exchange. We estimate the traditional summary statistic for risk exposure: the tail probabilities that the change in the futures price exceeds the margin. And we estimate two economic measures of the risk--the expected value of the payoffs in the tails and expected value of the payoffs in the tails conditional on landing in the tail. The economic measures of risk reveal exposure from low probability large payoff events--like a crash--that does not show up tail probabilities. The tail probabilities only capture the likelihood of a crash, not the expected loss. The estimated measures of risk follow directly from estimates of the conditional distribution of futures price changes. We infer a jump-diffusion process and a log-normal rocess from the prices of traded options and we estimate a jump-diffusion process from time-series data on futures prices. After the crash the forward-looking jump-diffusion model inferred from traded options reflects the fears of another crash voiced by market participants. The model indicates another jump is unlikely, but if it occurred it would be big and negative. The tail probabilities are small, less than 2%. But, the day after the crash the model estimates the expected value of payoffs in the tails conditional on landing in the tail equals of 55% of the S&P500 futures price. According to this estimate roughly

Financial markets' assessments of EMU

10.5 billion in liquid reserves would be required to weather another crash. On October 20 the Federal Reserve announced it stood ready to supply the necessary liquidity.

How Crashes Develop: Intradaily Volatility and Crash Evolution

Abstract This paper reviews the assumptions and methodologies underlying “EMU probability calculators,” which infer from financial data the probability of specific countries joining the European Monetary Union. Some historical evidence is presented in support of the expectations hypothesis for intra-European interest-rate differentials underlying most calculators, while various potential biases are deemed negligible. The various EMU calculators differ primarily in their scenarios for intra-European interest-rate differentials conditional upon EMU not occurring. This paper also discusses what can be inferred from financial data regarding future policies of the European Central Bank.

Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options

This paper explores whether affine models with volatility jumps estimated on intradaily SP self‐exciting but short‐lived volatility spikes capture intradaily and daily returns better. Multifactor models of the evolution of diffusive variance and jump intensities improve fits substantially, including out‐of‐sample over 2009 to 2016. The models capture reasonably well the conditional distributions of daily returns and realized variance outliers, but underpredict realized variance inliers. I also examine option pricing implications.