EconPapers    
Economics at your fingertips  
 

From Smile Asymptotics to Market Risk Measures

Ronnie Sircar and Stephan Sturm

Papers from arXiv.org

Abstract: The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be integrated into the theoretical framework of convex monetary measures of risk. In particular, we make use of indifference pricing by dynamic convex risk measures, which are given as solutions of backward stochastic differential equations (BSDEs), to establish a link between these two approaches to risk measurement. We derive a characterization of the implied volatility in terms of the solution of a nonlinear PDE and provide a small time-to-maturity expansion and numerical solutions. This procedure allows to choose convex risk measures in a conveniently parametrized class, distorted entropic dynamic risk measures, which we introduce here, such that the asymptotic volatility skew under indifference pricing can be matched with the market skew. We demonstrate this in a calibration exercise to market implied volatility data.

New Economics Papers: this item is included in nep-rmg and nep-upt
Date: 2011-07, Revised 2012-07
References: View references in EconPapers View complete reference list from CitEc
Citations View citations in EconPapers (1) Track citations by RSS feed

Published in Math. Finance 25:2, 400-425 (2015)

Downloads: (external link)
http://arxiv.org/pdf/1107.4632 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1107.4632

Access Statistics for this paper

More papers in Papers from arXiv.org
Series data maintained by arXiv administrators ().

 
Page updated 2017-09-29
Handle: RePEc:arx:papers:1107.4632