
Actuarial Science and Mathematical Finance Group Meetings
200607

My research group
meets on a regular basis to discuss various problems and methods that
arise in Finance and Actuarial Science. These informal meetings are
held at the Fields Institute for Mathematical Sciences and are open
to the public. Typically intendees come from Rotman Business School
of Management, Dept. Mathematics, Statistics, Computer Science and
Engineering.
Sebastian Jaimungal, Department of Statistics and Associate Director,
Mathematical Finance Program, University of Toronto
Meetings are held from 2pm to 3:30pm room 210 at The Fields Institute
for Mathematical Sciences.
May 23, 2007 
Alvaro Cartea, CoDirector Commodities Finance Centre,
Birkbeck College, University of London
How Do Waiting Times or Duration Between Trades of Underlying
Securities Affect Option Prices
We propose a model for stock price dynamics that explicitly
incorporates (random) waiting times, also known as duration,
and show how option prices are calculated. We use ultrahigh
frequency data for bluechip companies to justify a particular
choice of waiting time or duration distribution and then calibrate
riskneutral parameters from options data. We also show that
implied volatilities may be explained by the presence of duration
between trades.

Apr 25, 2007 
Yan Bai
Forward PIDE for European options with fixed fractional
jumps
We consider the model of European stock with jumps. A
partial integro differential equation, which related the price
of a calendar spread to the prices of butterfly spreads, is
derived. The functions describing the evolution of the process
are also given. The evolution functions are the forward local
variance rate and forward local default arrival rate. We specialize
the case where the only jump which can occur reduces the underlying
stock price by a fixed fraction of its predefault value.
In particular using a few calendar dates, we derive closed
form expressions for both the local variance and the local
default arrival rate.
[ This is a review of the article by Peter Carr and Alireza
Javaheri ]

Apr. 18, 2007 
Alex Badescu
Option valuation, GARCH models and riskneutral measures
Option pricing based on GARCH models is typically obtained
under the assumption that the random innovations are standard
normal (normal GARCH models). However, these models fail to
capture the skewness and the leptokurtosis observed in financial
data, so a number of various other distributions have been
proposed. Since under GARCH models the markets are incomplete,
there are an infinite number of risk neutral measures for
pricing contingent claims. The impact of the choice of an
appropriate martingale measure on option pricing has yet to
be addressed in these setups. The present work investigates
the applicability of some wellknown risk neutral measures
for various GARCH models.
Since only a few papers have studied the pricing performance
of nonnormal driving noise, we propose a new semiparametric
GARCH option pricing model. Our approach is to compute option
prices based on a nonparametric density estimator for the
unknown distribution of the innovations based on standardized
residuals. An empirical study regarding European Call option
valuation on S&P500 Index shows our semiparametric model
outperforms the normal GARCH option pricing models.

Apr 11, 2007 
Simon Lee
Discounted penalty at ruin in a jumpdiffusion and
its application
We consider the jumpdiffusion that is obtained if an
independent Wiener process is added to the surplus process
of classical ruin theory. In this model, we examine the expected
discounted value of a penalty at ruin. It can be shown that
the solution satisfies a defective renewal equation which
has probabilistic interpretation. As an application, we determine
the optimal exercise boundary for a perpetual put option.

Mar 28, 2007 
Quantitative
Finance Seminar Series instead 
Mar 23, 2007 *Location :
History Conference Room, Sidney Smith Hall, (enter through 2096)

Chris Rogers, Cambridge University
Pathwise Stochastic Optimal Control
This talk approaches optimal control problems for discretetime
controlled Markov processes by representing the value of the
problem in a dual Lagrangian form. This approach is a completely
novel way to look any stochastic optimal control problem,
independent of (but complementing) the classical dynamicprogramming/valuefunction
approach. The representation obtained opens up the possibility
of numerical methods based on Monte Carlo simulation which
may be advantageous in highdimensional problems, or in problems
with complicated constraints.

Mar 21, 2007 
Simon Lee  POSTPONED to April 11

Mar 14 , 2007 
Hamidreza Arian
Stochastic Correlation Models
The data from financial markets show that
the correlation, which is typically assumed to be constant,
is a stationary stochastic process. Very little has been published
on stochastic correlation models so far. In this talk, I will
discuss the obstacles for considering correlation as a stochastic
process and illustrate how to price options with stochastic
correlations.

Feb 28, 2007 
Quantitative
Finance Seminar Series instead 
Feb 21, 2007 
Eddie Ng
Stochastic Volatlity Models: Overview, Model Calibration,
and all that...
This talk will provide an overview for the GARCH and Heston
Model, including their mathematical formulation, stylized
facts, and methods for model calibration.

Feb 14, 2007 
Benjamin Verschuere
A MCMCMLE Algorithm for Hidden Markov Process in Financial
Time Series
Many time series are affected by a hidden process. An interesting
example can be found in the financial markets which experience
in alternance periods of stress and calm; and accordingly
period of high and low volatility. When modelling the volatility
of stock returns it is sensible to take into consideration
the above mentioned hidden process. The goal of this presentation
is to explain how we can identify the hidden process which
is responsible for the fluctuation of volatility between two
states (high and low) by adopting a Bayesian approach. We
then use simulation to asses the efficiency of our method.

Dec 6, 2006 
Sheldon X. Lin
Analytical Methods for Insurance Risk Models
In this talk, I will discuss some analytical methods developed
in the past few years for insurance risk models. One of the
advantages for using such analytical methods is that they
require little probabilistic argument and hence can easily
be understood by nonprobabilists. These methods also allow
us to utilize results in analysis and differential equations.
Another is that it can some time handle more complex risk
models, especially the risk models with dividend policies,
for which probabilistic reasoning might be difficult. I will
also briefly discuss some potential applications in option
pricing.

Nov 22, 2006 
Bill Bobey
Affine and Quadratic Term Structure Models: Model survey
and comparisons
The discussion will present and contrast affine and quadratic
riskfree rate term structure models. It will highlight the
key differences in the models both in terms of financial interpretation
and mathematical representation. Specific attention will be
paid to the representative Riccati equations. Issues related
to parameter estimation and numerical modelling will be discussed.
Comments regarding extensions to corporate bond modelling
will also be provided. This presentation will draw from two
primary references, (Dai and Singleton, 2000) and (Ahn et
al, 2002), and results related to research requiring the use
of the key results of these papers.

Nov 8, 2006 
Wanhe Zhang
Forward starting Collaterized Debt Obligations 

