May 20, 2014: IAQF/Thalesians Seminar Series

Variable Volatility and Financial Failure

A Talk by Peter Carr

Abstract
Structural models of corporate default (eg. Merton’s model) typically impose a rigid para¬metric specification on the volatility of the firm’s assets. This approach fails to recognize that management can exert some limited control on the level of the assets’ risk at every possible level of their firm’s default probability. In this paper, we assume that management chooses the assets’ volatility level as a non-parametric function of the firms’ risk-neutral default prob¬ability (RNDP). We develop closed form formulas which relate RNDP and equity value to this asset volatility function and to asset price. We also show how to explicitly determine the implied RNDP and the implied asset value from the market price of the equity and from the market prices of co-terminal calls written on the equity. Remarkably, the RNDP formula is independent of both the initial asset level and the debt level.

Biography
Dr. Peter Carr is a Managing Director at Morgan Stanley with over 18 years of experience in the derivatives industry. He was also a finance professor for 8 years at Cornell University, after obtaining his PhD from UCLA in 1989. He is presently the Executive Director of the Math Finance program at NYU’s Courant Institute, the Treasurer of the Bachelier Finance Society, and a trustee for the Museum of Mathematics in New York. He has over 80 publications in academic and industry-oriented journals and serves as an associate editor for 8 journals related to mathematical finance. He was selected as Quant of the Year by Risk Magazine in 2003 and as Financial Engineer of the Year by IAFE/Sungard in 2010. More recently, Institutional Investor has included Dr.Carr in its annual Tech 50 for the last 3 years.