Can Standard Preferences Explain the Prices of Out of the Money S&P 500 Put Options, Issue 11861
National Bureau of Economic Research, 2005 - Options (Finance) - 41 pages
Prior to the stock market crash of 1987, Black-Scholes implied volatilities of S&P 500 index options were relatively constant across moneyness. Since the crash, however, deep out-of-the-money S&P 500 put options have become 'expensive' relative to the Black-Scholes benchmark. Many researchers (e.g., Liu, Pan and Wang (2005)) have argued that such prices cannot be justified in a general equilibrium setting if the representative agent has 'standard preferences' and the endowment is an i.i.d. process. Below, however, we use the insight of Bansal and Yaron (2004) to demonstrate that the 'volatility smirk' can be rationalized if the agent is endowed with Epstein-Zin preferences and if the aggregate dividend and consumption processes are driven by a persistent stochastic growth variable that can jump. We identify a realistic calibration of the model that simultaneously matches the empirical properties of dividends, the equity premium, the prices of both at-the-money and deep out-of-the-money puts, and the level of the risk-free rate. A more challenging question (that to our knowledge has not been previously investigated) is whether one can explain within a standard preference framework the stark regime change in the volatility smirk that has maintained since the 1987 market crash. To this end, we extend the model to a Bayesian setting in which the agent updates her beliefs about the average jump size in the event of a jump. Note that such beliefs only update at crash dates, and hence can explain why the volatility smirk has not diminished over the last eighteen years. We find that the model can capture the shape of the implied volatility curve both pre- and post-crash while maintaining reasonable estimates for expected returns, price-dividend ratios, and risk-free rates.
What people are saying - Write a review
We haven't found any reviews in the usual places.
1987 market crash 500 Put Options aggregate Appendix approximate Arbitrage Asset Pricing at-the-money options Bakshi Bansal baseline Bates Bayesian updating Black-Scholes Brownian motions Chernov Collin-Dufresne consumption and dividend consumption process crash dates crash occurs define Dividend Claim dividend dynamics Duffie Economics equation equity premium Eraker evidence expected growth rate FairTax Financial Studies Goldstein implied volatility Intertemporal Substitution intuition Jackwerth Journal of Econometrics Journal of Finance jump distribution jump intensity jump process jump-diffusion KPEZ model predicts month to maturity NBER Working Papers obtain optimal option prices out-of-the-money put options parameters Poisson jump price-dividend ratio pricing kernel Recursive Utility representative agent Review of Financial risk aversion risk premium risk-free rate risk-neutral dynamics Robert S&P 500 options simulated Skiadas solution Specifically SPX prices standard preferences stochastic differential equation stochastic differential utility Stochastic Volatility stock market stock prices subscription updates her beliefs utility index volatility smirk