金融学系列讲座（2013-04）

题目：What is Risk Neutral Volatility?

报告人：Stephen Figlewski, New York University

时间：2013年4月11日（周四）10:00---11:30

地点：成人直播新楼216

Abstract:A security's expected payoff under the real world distribution for stock returns includes risk

premia to compensate investors for bearing different types of stock market risk. But Black-

Scholes and the great majority of derivatives valuation models developed from it produce the

same option prices as would be seen under modified probabilities in a world of investors who

were indifferent to risk. Implied volatility and other parameters extracted from options market

prices embed these modified "risk neutral" probabilities, that combine investors' objective

predictions of the real world returns distribution with their risk preferences. Under Black-

Scholes assumptions, real world volatility and risk neutral volatility are equal. But Black-

Scholes pricing does not hold in the real world because of unhedgeable risks that bear nonzero

risk premia, and the risk neutral volatility that goes into option prices is not the market's best

estimate of the volatility that will actually occur. This paper explores what factors relating to

both forecasting the empirical distribution of future returns and the risk neutralization process go

into the market's risk neutral volatility parameter. Daily risk neutral densities are extracted from

S&P 500 index options from 1996-2011 using a model-free procedure. We compute both risk

neutral volatility and realized volatility from the observation date through option expiration in

order to compare the sensitivity of the two volatility measures to a wide range of variables

relating to different manifestations of volatility, such as tail risk, and to the risk neutralization

process, such as the general level of consumer confidence and the size of recent volatility

forecast errors.