
Financial Mathematics Seminars  April 24, 2002
Abstracts
Audio
of Talks
Affine Processes and Applications in Finance

Damir Filipovic,
Princeton University

This talk provides a definition and complete characterization
of regular affine processes, a class of Markov processes that has
arisen from a large and growing range of useful applications in
finance, although until now without succinct mathematical foundations.
The key ``affine'' property is roughly that the characteristic function
of the transition distribution of such a process is exponentialaffine
with respect to the initial state. This includes continuousstate
branching processes with immigration and processes of the OrnsteinUhlenbeck
type in particular. Some common financial applications of the properties
of a regular affine process include: the term structure of interest
rates, the pricing of options and credit risk. Prominent examples
are the Vasicek and CoxIngersollRoss short rate models and Heston's
stochastic volatility model.

Modelling Credit Risk In Convertible
Bonds

Gerald Quinlan, Sungard Trading and Risk Systems

The correct way of including credit risk in convertible bond
pricing has always been a source of confusion. One approach is
to use a model that considers the full 'value of the firm', including
information about the issuer's distance to default. These models
require information about the issuer's capital structure, however,
and must make simplifying assumptions to reduce the problem to
a tractable form. The more commonly used approach is to add a
credit spread to the riskfree yield curve. Several adhoc procedures
have been proposed for splitting the credit spread between the
bond and option parts of the convertible. These are reviewed and
compared with a more consistent treatment of credit risk in the
convertible security. The use of stockdependent credit spreads
is shown to be necessary for matching price profiles of real convertibles.
A different approach is required for exchangeable bonds  convertibles
for which the stock and bond are issued by different firms. Conclusions
are drawn for the measurement and hedging of credit risk in convertible
portfolios.


