Please join us for the the BBQ Keynote Talk.
We apply abstract algebra to arbitrage-free valuation of derivative securities. We first focus on the standard problem of developing an arbitrage-free valuation formula for a derivative security paying off the larger of two or more non-negative prices, eg. a convertible bond. We develop an alternative to a probabilistic approach based on the properties of power norms. We then show that our valuation recipe can be interpreted as addition in a monoid. We then extend the monoid into a semi-field to price a larger class of path-independent non-negative payoffs. To remove the non-negativity restriction, we develop an alternative monoid that can be used to price a derivative security paying off the larger of two or more real-valued prices, eg. a call option on a spread. We then extend this monoid into a semi-field to price a larger set of path-independent real-valued payoffs.
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 WorldQuant 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.