Removing Maturity Effects of Implied Risk Neutral Densities and Related Statistics
AbstractWhen studying a time series of implied Risk Neutral Densities (RNDs) or other implied statistics, one is faced with the problem of maturity dependence, given that option contracts have a fixed expiry date. Therefore, estimates from consecutive days are not directly comparable. Further, we can only obtain implied RNDs for a limited set of expiration dates. In this paper we introduce two new methods to overcome the time to maturity problem. First, we propose an alternative method for calculating constant time horizon Economic Value at Risk (EVaR), which is much simpler than the method currently being used at the Bank of England. Our method is based on an empirical scaling law for the quantiles in a log-log plot, and thus, we are able to interpolate and extrapolate the EVaR for any time horizon. The second method is based on an RND surface constructed across strikes and maturities, which enables us to obtain RNDs for any time horizon. Removing the maturity dependence of implied RNDs and related statistics is useful in many applications, such as in (i) the construction of implied volatility indices like the VIX, (ii) the assessment of market uncertainty by central banks (iii) time series analysis of EVaR, or (iv) event studies.
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Bibliographic InfoPaper provided by University of Essex, Department of Economics in its series Economics Discussion Papers with number 609.
Date of creation: 22 Feb 2006
Date of revision:
Postal: Discussion Papers Administrator, Department of Economics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, U.K.
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-03-11 (All new papers)
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