Journal of Risk

Risk.net

Estimating the tail shape parameter from option prices

Kam Hamidieh

  • In this paper, a method to estimate the tail shape parameter of the risk neutral density from option prices is developed.  
  • Closed form pricing formulas for out-of-the-money European style options are derived.  
  • The method can be used without interpolating the implied volatility, or even the knowledge of the current index value or the dividend yield or the risk-free rate.
  • In a case study, the estimation of the tail shape of S&P 500 index just prior to the market turmoil of the September 2008 showed a thickening of the left tail but a thinning in the midst of the turmoil.

In this paper, a method to estimate the tail shape parameter of the risk-neutral density from option prices is developed and closed-form pricing formulas for out-of-the money European style options are derived. The pricing formulas satisfy many well-known model-free no-arbitrage properties for the options. Our focus is only on the tails of the risk-neutral density and not on the entire body of the density. Our method is quite general, and applies to a large class of risk-neutral densities. Unlike all other methods of estimating the risk-neutral density, it can be used without interpolating the implied volatility, or even without the knowledge of the current index value, the dividend yield or the risk-free rate. A case study using Standard & Poor’s 500 (S&P 500) index options is given. In particular, the estimation of the tail shape of the S&P 500 index shows a thickening of the left tail just prior to the market turmoil of September 2008, but a thinning of the left tail in the midst of the turmoil.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to Risk.net? View our subscription options

You need to sign in to use this feature. If you don’t have a Risk.net account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here