

Actuarial Science and Mathematical Finance
Group Meetings 201011
at the Fields Institute


The Actuarial Science and Mathematical Finance 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. Talks range from original research to reviews
of classical papers and overviews of new and interesting mathematical
and statistical techniques/frameworks that arise in the context
of Finance and Actuarial Science. This seminar series is sponsored
in part by MITACS through the research project Finsurance
: Theory, Computation and Applications.
Meetings are normally held on Thursdays from 2pm to 3:30pm in the
Stewart Library, but check calendar for exceptions. If you are interested
in presenting in this series please contact the seminar organizer:
Prof. Sebastian Jaimungal (sebastian [dot] jaimungal [at] utoronto
[dot] ca).
UPCOMING SEMINARS 
March 10, 2011

Nicolas Merener (School of
Business, Universidad Torcuato Di Tella, Buenos Aires, Argentina)
Efficient Monte Carlo for Discrete Variance Contracts
We develop an efficient Monte Carlo method for the valuation
of a financial contract with payoff dependent on discretely
realized variance. We assume a general model in which asset
returns are random shocks modulated by a stochastic volatility
process. Realized variance is the sum of squared daily returns,
depending on the sequence of shocks to the asset and the realized
path of the volatility process. The price of interest is the
expected payoff, represented as a high dimensional integral
over the fundamental sources of randomness. We compute it
through the combination of deterministic integration over
a two dimensional manifold defined by the sum of squared shocks
to the asset and the path average of the modulating variance
process, followed by exact conditional Monte Carlo sampling.
The deterministic integration variables capture most of the
variability in realized variance therefore the residual variance
in our estimator is much smaller than that in standard Monte
Carlo. We derive theoretical results that quantify the variance
reduction achieved by the method. We test it for the HullWhite,
Heston, and Double Exponential models and show that the algorithm
performs significantly better than standard Monte Carlo for
realistic computational budgets.
(joint work with Leonardo Vicchi, Center of Applied Mathematics,
Universidad Nacional de San Martin, San Martin, Argentina
)

PAST SEMINARS 
Nov. 25, 2010 
Pascal Francois (Department
of Finance, HEC Montreal)
Credit spread changes within switching regimes
Empirical studies on credit spread determinants consider a singleregime
model over the entire sample period and find limited explanatory
power. We model the ratingspecific credit cycle by estimating
Markov switching regimes from credit spread data. Accounting
for endogenous credit cycles significantly enhances the explanatory
power of credit spread determinants for all ratings and up to
67% for BBB spreads. The single regime model cannot be improved
when conditioning on the NBER cycle. Our regimebased model
highlights a positive relation between credit spreads and the
riskfree rate in the high regime. Inverted relations are also
obtained for other determinants including liquidity.
This is joint work with Georges Dionne and Olfa Maalaoui
Chun

Nov. 4, 2010 
Tony Ware (Department of Mathematics
and Statistics, University of Calgary)
Accurate semiLagrangian time stepping for gas storage problems
Stochastic dynamic programming approaches for the valuation
of natural gas storage, and the determination of the optimal
continuoustime injection/withdrawal strategy, give rise to
HJB P(I)DEs which are typically solved using finite differences
[Thompson et. al., 2009]. A semiLagrangian discretization
was analyzed by [Chen and Forsyth, 2007], who demonstrated
firstorder convergence to the viscosity solution.
This talk will show how a semiLagrangian approach for such
problems can be formulated in such a way that it generates
a secondorder accurate discretization in time. Combined with
a hybrid Fourier/finite difference discretization in the remaining
dimensions, the resulting method can provide efficiency gains
over existing approaches.

Oct.21, 2010 
Bruno Rémillard (Department of Management Sciences,
HEC Montreal)
Optimal hedging in discrete and continuous time
In this talk I will do a quick survey of the literature on
meanvariance hedging in discrete and continuous time. Then
I will find the optimal solution of the hedging problem in
continuous time when the underlying assets are modeled by
a regimeswitching geometric Lévy process or a stochastic
volatility model. It is also shown that the continuous time
solution can be approximated by discrete time Markov models
processes. In some cases, the optimal prices corresponds to
prices under an equivalent martingale measure, making that
measure a natural choice for pricing. However, even if the
optimal hedging strategy is not the usual delta hedging, it
can be easily computed by Monte Carlo methods.

Sept. 16, 2010 
Joseph H. T. Kim (Department
of Statistics and Actuarial Science, Waterloo University)
Measuring and Managing Systemic Risk
In the wake of the current financial crisis, there is an
ongoing debate on the importance of managing systemic risk
in the financial sector. Much of the conventional regulation
focuses on the safeguarding of the solvency of individual
firms. The recent crisis has highlighted the importance of
systemic risk and the shortcomings of pure firm specific regulation.
This paper proposes the use of the Co Conditional Tail Expectation(CoCTE)
to measure systemic risk since adapted from CoVaR by Adrian
and Brunnermeier. We explain how CoCTE can be used in constructing
a fund to protect the financial sector in times of severe
crises. The second goal of this paper is to endogenize the
procyclicality of capital requirements. Using a regime switching
model we show how to determine countercyclical risk charge
for systemic insurance fund.
This is joint work with Phelim Boyle

Sept. 23, 2010 
Carole Bernard (Department of Statistics and Actuarial
Science, University of Waterloo)
Explicit Representation of CostEfficient Strategies: Suboptimality
of pathdependent strategies
This paper uses the preference free framework proposed by
Dybvig (1988) and Cox and Leland (1982,2000) to analyze dynamic
portfolio strategies. In general there will be a set of dynamic
strategies that have the same payoff distribution. We are
able to characterize a lowest cost strategy (a “costefficient”
strategy) and to give an explicit representation of it. As
an application, for any given pathdependent strategy, we
show how to construct a financial derivative that dominates
in the sense of firstorder stochastic dominance. We provide
new costefficient strategies with the same payoff distributions
as some wellknown option contracts and this enables us to
compute the relative efficiency of these standard contracts.
We illustrate the strong connections between costefficiency
and stochastic dominance.

Sept. 30, 2010 
Pascale Valery (Department of Finance, HEC Montreal)
Waldtype tests when rank conditions fail: a smooth regularization
approach
Abstract

Past Semainrs 200910
Past Seminars 200809

