Mihai Sirbu, Carnegie Mellon -- A Two-Person Game for Pricing Convertible Bonds
Abstract: A firm issues a convertible bond. At each subsequent time, the bond- holder must decide whether to keep the bond, thereby collecting coupons, or to convert it to stock. The bondholder wishes to choose a conversion strategy to maximize the bond value. Subject to some restrictions, a convertible bond can be called by the issuing firm, which presumably acts to maximize equity value and thus to minimize the bond value. This creates a two-person game, and we model the bond price as the value of this game. We show, however, that under our standing assumption (dividends are paid at a lower rate than the money market rate) this game reduces to one of two optimal stopping problems, and the relevant stopping problem can be determined a priori, i.e., without first solving the convertible bond pricing problem. Because of dividend payments, the partial differential equation describing the pricing function becomes nonlinear. This means that our analysis involves a fixed point problem. We also prove that for large time to maturity the value of the convertible bond approaches the value of the perpetual convertible bond The presentation is based on joint work with Steven E. Shreve.
Organizational Meeting
Aytac Ilhan, Princeton -- Optimal Investment with Derivative Securities
Abstract: We consider an investor who maximizes expected exponential utility of wealth from a static position in derivative securities and a dynamic trading strategy in stocks. Our main result, obtained by studying the strict concavity of the utility-indifference price as a function of the static positions, is that, in a quite general incomplete arbitrage-free market, there exists a unique optimal strategy for the investor.
Alec Kercheval, FSU -- The Fundamental Theorem of Asset Pricing, after Schachermayer
Alec Kercheval, FSU -- The FTAP, after Schachermayer, II
Alec Kercheval, FSU -- The FTAP, after Schachermayer, III
Spring Break
Yevgeny Goncharov, Michigan -- Mortgages
Alec Kercheval, FSU -- The FTAP, after Schachermayer, IV
Alec Kercheval, FSU -- The FTAP, after Schachermayer, V
Juan Moreno, FSU -- Pricing Foreign Currency Derivatives
Wenbo Hu, FSU -- Portfolio Credit Risk
Abstract: Copulas are introduced in the pricing of portfolio risk. We calculate default probabilities for the "first to default" product based on five different copulas, and compare results.
Wenbo Hu, FSU -- Portfolio Credit Risk, II