Mathematical Finance Seminar

Fri, 20/05/2005 14:15	Kees Oosterlee (Delft)	Mathematical Finance Seminar	DH 3rd floor SR
	Evaluation of European and American options under de Variance Gamma process with grid stretching and accurate discretization.
	In this talk, we present several numerical issues, that we currently pursue, related to accurate approximation of option prices. Next to the numerical solution of the Black-Scholes equation by means of accurate finite differences and an analytic coordinate transformation, we present results for options under the Variance Gamma Process with a grid transformation. The techniques are evaluated for European and American options.

Fri, 03/06/2005 14:15	Steven Shreve (Carnegie Mellon University)	Mathematical Finance Seminar	DH 3rd floor SR
	Modelling Credit Spread, Implied Volatility, and Optimal Capital Structure with Endogenous Default and Jump Risk
	We propose a model for credit risk with endogenous default and jump risk. The model has four attractive features. It can generate flexible credit spread curves. It leads to flexible implied volatility curves, thus providing a link between credit spread and implied volatility. It implies that high tech firms tend to have very little debts. It yields analytical solutions for debt and equity values. This is a joint work with Nan Chen (a Ph.D. student at Columbia University).

Fri, 17/06/2005 14:15	Steve Kou (Columbia University (New York))	Mathematical Finance Seminar	DH 3rd floor SR
	Modelling Credit Spread, Implied Volatility, and Optimal Capital Structure with Endogenous Default and Jump Risk
	A firm issues a convertible bond. At each subsequent time, the bondholder must decide whether to continue to hold 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, the bond can be called by the issuing firm, which presumably acts to maximize the equity value of the firm by minimizing the bond value. This creates a two-person game. We show that if the coupon rate is below the interest rate times the call price, then conversion should precede call. On the other hand, if the dividend rate times the call price is below the coupon rate, call should precede conversion. In either case, the game reduces to a problem of optimal stopping. This is joint work with Mihai Sirbu.

Forthcoming Seminars