Event Date Details:
Refreshments served at 3:15 p.m.
- Sobel Seminar Room; South Hall 5607F
- CFMAR Seminar Series
Abstract: In this paper, a new class of dynamic market models called Dynamic Conditional Distribution (DCD) models is introduced to describe a financial market driven by Brownian motion consisting of a bank account, a stock, a set of zero coupon bonds and a set of European type contingent claims with the stock as the underlying asset. The approach suggested in this paper is different from that of previous dynamic market models since here, the dynamics of the market will be prescribed by choosing the dynamics of the risk neutral measure under which all assets are priced through the dynamics of the cumulants of the log return to the stock. This is done simultaneously for all time horizons and hence a DCD model can alternatively by seen as a dynamic term structure model. The main result of this paper is a set of drift conditions on the mean and variance of the log return which on one hand insures that the model is well-specified and on the other hand provides a tool for constructing DCD models in practice. If additionally, it is assumed the market is driven by a set of factors and that the cumulants are functions of these, higher order cumulants can be computed by recursively solving a set of PDE's and a wide range of interesting models constructed. The class of DCD factor models is illustrated by means of two examples. First, the Quadratic Ornstein-Uhlenbeck DCD model, which allows for explicit computation of the distribution of the cumulants as well as prices of European call- and put options and second the Nelson-Siegel Term Structure Model which allows for the control of the term structure of the cumulants.