光华讲坛——社会名流与企业家论坛第 5091 期
主题：Variable Volatility & Financial Failure
主讲人：Professor Peter Carr, New York University
主办单位：中国金融研究中心 经济数学学院 科研处
Dr. Peter Carr is the Chair of the Finance and Risk Engineering Department at NYU Tandon School of Engineering. He has headed various quant groups in the financial industry for the last twenty years. He also presently serves as a trustee for the National Museum of Mathematics and World Quant University. Prior to joining the financial industry, Dr. Carr was a finance professor for 8 years at Cornell University, after obtaining his Ph.D. from UCLA in 1989. He has over 85 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 Financial Engineer of the Year by IAQF/Sungard in 2010. From 2011 to 2014, Dr. Carr was included in Institutional Investor's Tech 50, an annual listing of the 50 most influential people in financial technology.
Peter Carr 纽约大学工学院金融与风险工程系主任，国家数学博物馆、World Quant University理事，金融科技领域最具影响力人物Top 50。1989年获UCLA博士学位，后任教于康奈尔大学（Cornell University）。在学术与产业界期刊发表文章超85篇，同时在多个数学金融学相关杂志担任副主编，是数量化投资领域最权威的专家之一。
Structural models of corporate default (eg. Merton’s model) typically impose a rigid parametric specification on the volatility of the firm’ 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 probability (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.