Risk Neutral Densities: A Review Stephen

Transcript:Risk Neutral Densities: A Review Stephen:
Risk Neutral Densities: A Review Stephen Figlewski* * Professor of Finance Stern School of Business New York University email: sfiglews@stern.nyu.edu I. Overview II. Options, Probabilities, and Risk Preferences: The P and the Q-densities III. The Evolution of the Data Generating Process and the Risk Neutral Density IV. Overview of Estimation Methodology V. Implied Volatility: The Volatility Risk Premium and the VIX VI. The Volatility Surface VII. The "Pricing Kernel Puzzle" VIII. Two Major Directions for Future Research Outline of Presentation International Risk Management Conference 2018 ©2018 Figlewski The Risk Neutral Density (RND) extends the familiar concept of Implied Volatility (IV) for a single option. Given a set of options with a range of strike prices, you can extract the market's entire (risk neutral) probability distribution over the expiration day stock price ST . The RND (the "Q-distribution") combines the market's estimate of the true probabilities over ST (the "P-distribution") and the market's risk preferences (the "pricing kernel" k(ST)  Q(ST)/P(ST) ). We can "observe" the Q density in the options market. A major challenge is to separate the market's true probability expectations from risk premia. What is the Risk Neutral Density? International Risk Management Conference 2018 ©2018 Figlewski Consider a call option that allows you to buy a share of some underlying stock for a price of 101 one month from now. If the stock price in one month is above 101, you will exercise the option. The market price for this option is $5.00 . There is a second call option that allows you to buy 1 share of the same stock for a price of 100 in one month. The market price for Option 2 is $5.70. For every stock price above 101, the second option pays $1 more than the first option. The market values the extra $1 that option 2 pays if the stock price is above 101 as being worth 5.70 – 5.00 = $0.70. So (roughly speaking) the market is saying the probability the stock price will be above 101 is 70%. If you have a lot of options prices with strikes close together, you can get the whole density. How risk neutral probabilities are extracted from option prices 4 International Risk Management Conference 2018 ©2018 Figlewski How risk neutral probabilities are extracted from option prices International Risk Management Conference 2018 ©2018 Figlewski The P density is what the market really is predicting. Presuming