Koç University, Mathematics Seminar
Date & Time: Monday, May 16, 14:00-15:00
Place: SCI 129
Speaker: Deniz Sezer (University of Calgary)
Title: Illiquidity, Credit Risk and Merton's Model
Abstract: In this talk I am going to introduce a new model for pricing of
corporate bonds which is a modification of the classical model of Merton. In
Merton's model, a corporate bond is a contingent claim on the assets of a
firm. A geometric Brownian motion models
the value of the firm's assets which are assumed to be liquidly traded in the
market. This assumption makes the pay-off replicable with the firm's assets and
the money market account; and a pricing formula is easily obtained. In this new model we drop the liquidity
assumption, and instead assume that there is an asset in the market which is
correlated with the firm's value, and all portfolios can be constructed using
solely this asset and the money market account. We formulate the price of the corporate bond
as the price of the optimal replicating portfolio * exp(- k * replication
error), where k is a positive constant.
The interpretation is that the investor accepts the price of the optimal
replicating portfolio as a benchmark, however, requests compensation for the
non-replicable risk. We show that if the
replication error is measured relative to the firm's value, the resulting
formula is arbitrage free.
Speaker's Brief Biography: Deniz Sezer is a faculty member at the University of Calgary, Department of Mathematics and Statistics. She completed her Ph.D at Cornell University under the supervision of Philip Protter. Her research is in probability theory and stochastic processes, in particular, Markov processes and applications.