Theme
Organizers: Matt Davison and Adam Metzler (UWO)
This
thematic session will focus on the application of quantitative
methods to problems of financial regulation. Specific topics include,
but are not limited to, the burgeoning fields
of financial networks (helpful in identifying institutions that
are too big to fail), systemic risk measures (valuable in designing
more appropriate capital regulations) and contingent capital (a
possible marketbased solution to enforcing discipline and reducing
the burden of costly financial bailouts). Our panel will be truly
interdisciplinary, showcasing speakers with such diverse backgrounds
as physics, mathematics, engineering, economics and business.
In addition, we plan to host at least one session showcasing Ph.D.
students in financial mathematics.
Our
theme will consist of three major parts
1. Invited talks.
2. Roundtable discussion on contingent capital
3. Minisymposium showcasing PhD students in mathematical finance
The
confirmed invited speakers for the first part are:
1. Dilip Madan (plenary), Robert H. Smith School of Business,
University of Maryland at College Park.
2. George Pennacchi, College of Business, University of
Illinois.
3. Matheus Grasselli, Department of Mathematics and Statistics,
McMaster University.
4. Frank Milne, Department of Economics, Queen's University.
5. Kay Giesecke, Department of Management Science and Engineering.
Stanford University.
6. Michael Gordy, Senior Economist (Risk Analysis Section,
Division of Research and Statistics), Board of Governors of the
Federal Reserve System.
7. Bhaskar DasGupta, Department of Computer Science, University
of Illinois at Chicago.
8. David Saunders, Department of Statistics and Actuarial
Science, University of Waterloo.
For the minisymposium we are expecting approximately eleven doctoral
students from the following schools/departments
1. University of Toronto. Department of Statistics and Actuarial
Science, Department of Computer Science.
2. York University. Department of Mathematics and Statistics.
3. McMaster University. Department of Mathematics and Statistics.
4. University of Calgary. Haskayne School of Business.
For
the roundtable discussion we have confirmed participants from the
Bank of Canada, as well as the Office of the Superintendent of Financial
Institutions.
Speaker
Abstracts
Monday,
June 25
10:0010:40
George Pennacchi, University of Illinois
A Structural Model of Contingent Bank Capital
This
paper develops a structural credit risk model of a bank that issues
shortterm deposits, shareholders equity, and xed or oatingcoupon
contingent capital (CoCos). The model assumes that bank assets
follow a jumpdiffusion process, interest rates are stochastic,
and capital ratios are meanreverting. Allowing for sudden declines
in asset val ues, as occur during nancial crises, has distinctive
implications. CoCo credit spreads are higher when: the capital
conversion trigger is lower; the conversion writedown is greater;
and conversion awards a xed, rather than variable, number of shares.
Dual price trigger CoCos are more similar to nonconvertible subordinated
debt. Issuing CoCos can create a debt overhang problem and a moral
hazard incentive for the bank to raise its asset risk, but these
problems are often less than if the bank issued a similar amount
of subordinated debt. In general, incentive problems are least
when contract terms minimize CoCos credit
risk.
10:4011:20
David Saunders, University of Waterloo
Calculating Regulatory Capital for Credit Risk: Mathematical
and Computational Issues
The
inadequacies of methods for calculating credit risk capital, particularly
in the trading book, in the leadup to the global nancial crisis
have led to a reevaluation of regulatory capital, resulting in
the new Basel III requirements. I will discuss mathematical and
computational problems that arise when computing the new capital
requirements for credit risk in the trading book
11:2012:00
Michael B. Gordy, Board of Governors
of the Federal Reserve System
Counterparty Credit Risk and Interconnectedness in CDS Trade
Repository Data
Authors: Celso Brunetti and Michael Gordy
As
evidenced during the financial crisis, OTC derivative markets
can
be an important pathway for the transmission of systemic risk.
The default of a large market participant can impose significant
direct losses on its counterparties, which may cascade to the
counterparties of the defaulted firms' counterparties. Though
more difficult to quantify, a distressed firm's interconnectedness
in OTC markets may be no less a concern. If the firm plays a significant
role in intermediation, then the normal functioning of the OTC
market may be disrupted even if the firm has balanced positions
with all significant counterparties.
We
have "snapshots" of the credit default swap market on
two dates in 2010 as captured by the CDS trade repository. To
identify
counterparty exposures of potential concern, we sift the data
for the
largest bilateral and multilateral positions at three levels of
market aggregation. We apply network methods to characterize and
quantify patterns of interconnectedness. Broadly speaking, our
aim is to identify firms crucial to the transfer of risk from
endbuyers to endsellers, and to assess the resilience of the
trading network to the loss of one or more crucial
nodes.
(Tentative) Stochastic
TimeChange of Default Intensity Models: Pricing and Estimation
Joint with Ovidiu Costin, Min Huang, and Pawel Szerszen
We
introduce stochastic time change to default intensity models of
credit risk as a parsimonious way to account for stochastic volatility
in credit spreads. We derive two series solutions for the survival
probability function, and show that both methods are applicable
when the intensity follows the widelyused basic affine process.
This leads to straightforward and efficient solutions to bond
prices and CDS spreads. We then estimate the timechanged model
on panels of CDS spreads (across maturity and observation time)
using Bayesian MCMC meth
ods. We find strong evidence of stochastic time change.
2:303:10
Justin Sirignano, Stanford University
Large Portfolio Asymptotics for Loss From Default
Joint with Kostas Spiliopoulos (Brown), Richard Sowers (Illinois),
and Kay Giesecke (Stanford)
We
prove a law of large numbers for the loss from default and use
it for approximating the distribution of the loss from default
in large, potentially heterogenous portfolios. The density of
the limiting measure is shown to solve a nonlinear stochastic
PDE, and certain moments of the limiting measure are shown to
satisfy an innite system of SDEs. The solution to this system
leads to the distribution of the limiting portfolio loss, which
we propose as an approximation to the loss distribution for a
large portfolio. Numerical tests illustrate the accuracy of the
approximation, and highlight its computational advantages over
a direct Monte Carlo simulation of the original stochastic system.
3:10
Bruno Rémillard, HEC Montréal
Optimal hedging in continuous time
In
this talk I will cover the problem of meanvariance optimal hedging
for some continuous time models: regimeswitching geometric Levy
processes and stochastic volatility models. 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.

Tuesday,
June 26
10:0010:40
Frank
Milne, Queen's University
The Anatomy of Systemic Risk
Joint with John Crean (University of Toronto)
Systemic
risk arises almost entirely on credit exposures to real sectors
of the economy. Data in the paper show that such risks are concentrated
in a few systemically important real sectors (SIRS). Typical firms
in all potential SIRS share common characteristics: high fixed
costs, low marginal costs of production, heavy competition and
high leverage. Downturns in such sectors are spasmodic and deep.
The particular sectors that cause systemic risk change from recession
to recession. The paper constructs a dynamic theory that reflects
these characteristics. The model is initially structured without
short term bank deposits. The model generates several conclusions.
Credit crises in SIRS generate the key macroeconomic phenomena
of systemic crises even in the absence of short term funding runs.
In such crises, insolvencies among firms and banks spread unexpectedly.
Effects extend outside the SIRS. Complaints of resale pricing
and credit restrictions are widespread. The introduction of short
term deposits deepens downturns. Liquidity runs on particular
banks cannot be adequately forecast without an explicit analysis
of the SIRS and other credit risks of particular banks. The paper
explains why standard models have difficulty in predicting major
credit and liquidity events. The model outlines the taxonomy of
systemic risk in a manner that enables such risk to be identified
exante. It therefore has important implications for structuring
efficient stress tests.
10:4011:20
Matheus R. Grasselli, McMaster University
An AgentBased Computational Model for Bank Formation and Inter
bank Networks
Joint with Omneia R. H. Ismail (McMaster University)
We
introduce a simple framework where banks emerge as a response
to a natural need in a society of individuals with heterogeneous
liquidity preferences. We examine bank failures and the conditions
for
an interbank market is to be established. We start with an economy
consisting of a group of individuals arranged in a 2dimensional
cellular automaton and two types of assets available for investment.
Because of uncertainty, individuals might change their investing
preferences and accordingly seek their surroundings neighbours
as trading partners to satisfy their new preferences. We demonstrate
that the individual uncertainty regarding preference shocks coupled
with the possibility of not finding a suitable trading partners
when needed give rise to banks as liquidity providers. Using a
simple learning process, individuals decide whether or not to
join the banks, and through a feedback mechanism we illustrate
how banks get established in the society. We then show how the
same uncertainty in individual investing preferences that gave
rise to banks also causes bank failures. In the second level of
our analysis, in a similar fashion, banks are treated as agents
and use their own learning process to avoid failures and create
an interbank market. In addition to providing a bottom up model
for the formation of banks and interbank markets, our model allows
us to address under what conditions bank oligopolies and frequent
banks failures are to be observed, and when an interbank market
leads to a more stable system with fewer failures and less concentrated
market players.
11:2012:00
Bhaskar
DasGupta, University of Illinois at Chicago
Global Stability of Banking Networks Against Financial Contagion:
Mea
sures, Evaluations and Implications
Instabilities
of major nancial institutions during the recent financial crisis
of 2007 and later have generated renewed interests in evaluating
the stabilities (or, lack thereof) of banking networks among economists,
regulatory authorities and other relevant segments of the population.
In particular, one reason of such type of vulnerabilities to the
socalled financial contagion process in which failures of few
individual banks propagate through the "web of banking dependencies"
to affect a significant part of the entire global banking system.
We initiate a systematic scientific investigation of defining
and evaluating a global stability measure for the nancial contagion
process for several classes of banking
networks, and discuss some interesting implications of our evaluations
of this stability measure.
2:30
pm
(C)Meng Han, University of Toronto
Approximations to Loss Probabilities of Loan Portfolios
Coauthors: Ken Jackson, Alex Kreinin
Credit
risk analysis and management at the portfolio level are challenging
problems for financial institutions due to their portfolios' large
size, heterogeneity and complex correlation structure. The conditional
independence framework is widely used to calculate loss probabilities
of credit portfolios. The existing computational approaches within
this framework fall into two categories: (1) simulationbased
approximations and (2) asymptotic approximations. The simulationbased
approximations often involve a twolevel Monte Carlo method, which
is extremely timeconsuming, while the asymptotic approximations,
which are typically based on the Law of Large Number (LLN), are
not accurate enough for tail probabilities, especially for heterogeneous
portfolios. We give a more accurate asymptotic approximation based
on the Central Limit Theorem (CLT), and we discuss its convergence
and when it can be applied. To further increase accuracy for lumpy
portfolios, we also propose a hybrid approximation, which combines
the simulationbased approximation and the asymptotic approximation.
We test our approximations with some artificial and real portfolios.
Numerical examples show that, for a similar computational cost,
the CLT approximation is more accurate than the LLN approximation
for both homogeneous and heterogeneous portfolios, while the hybrid
approximation is even more accurate than the CLT approximation.
Moreover, the hybrid approximation significantly reduces the computing
time for comparable accuracy compared to simulationbased approximations.
3:00
pm.
(C)Lung Kwan Tsui
Efficient Calculation of Economic and Regulatory Capital
for Structured Credit Instruments
Computing
the economic capital of a portfolio containing CDO and CLO tranche
is a challenging practical problem faced by financial institutes
holding these kinds of securities. Firstly, pricing CDOs and CLOs
for a large number of scenarios is computational intensive. Furthermore,
we have to take into account both the default risk and credit
migration risk embedded in these instruments. We provide a efficient
simulation methodology to compute VaR and CVaR of a portfolio
containing CDOs and CLOs. We first approximate the tranche pricing
function by matching the moments of the distribution of the survival
probabilities of the entities in the collaterals of a CDO or CLO.
We then compute the prices on a sparse multidimension grid which
is used for interpolation. This methodology significantly enhances
the computational efficiency of the Monte Carlo simulation required
for computing the VaR and CVaR.
3:30
pm
(C)Daniel Hackmann, York University
The optimal dividend problem for two families of meromorphic
Levy processes
A recent paper develops a solution to De Finetti's optimal dividend
problem by finding an explicit expression for the value function
in cases when the underlying wealth model is a spectrally negative
Lévy process. The value function is presented in terms
of a socalled scale function which is implicitly defined using
the Laplace transform. For two recently introduced families of
Lévy Processes (the beta and theta families), which can
be modified through an appropriate choice of parameters to have
paths of infinite activity and infinite variation, one can find
manageable series expressions for the scale function. This provides
an opportunity to evaluate the value function through standard
numerical methods. In this talk I will discuss the techniques
used to derive an accurate approximation and compare the results
to the value function of the well known Cramér Lundberg
process with exponentially distributed jumps. The comparison shows
that unless the starting capital of the company is close to zero,
the simpler CramérLundberg model gives nearly identical
results to those calculated for the more complicated beta and
theta processes. Additionally, I will discuss the empirical distribution
of the time of ruin under the optimal reflection strategy when
the wealth model is the CramérLundberg process. The results
of several Monte Carlo simulations show that an interesting avenue
of further research is to consider the optimal dividend problem
when a penalty, in the form of a function of the time of ruin,
is imposed.
4:00p.m
(C)Stephen Tse, University of Waterloo
Comparison between the Mean Variance optimal and the Mean
Quadratic Variation optimal trading strategies
Coauthors: Peter Forsyth, Shannon Kennedy, Heath Windcliff
We
compare optimal liquidation policies in continuous time in the
presence of trading impacts by numerical solutions of Hamilton
Jacobi Bellman (HJB) partial differential equations (PDE). We
show quantitatively that the meanquadraticvariation strategy
can be significantly suboptimal in terms of meanvariance efficiency
and that the meanvariance strategy can be significantly suboptimal
in terms of meanquadraticvariation efficiency. Moreover, the
meanquadraticvariation strategy is on average more suboptimal
than the meanvariance strategy, in the above sense. In the semiLagrangian
discretization used for solving the HJB PDEs, we show that interpolating
along the semiLagrangian characteristics results in significant
improvement in accuracy over standard interpolation while still
guaranteeing convergence to the viscosity solution.

Wednesday,
June 27
10:00
Bruno Remillard (100 min tutorial)
Tutorial for graduate students in mathematical finance
Optimal hedging in discrete time
In
this tutorial I will discuss the implementation of meanvariance
optimal hedging for discrete time models. In particular, I will
cover models with independent increments, HMM models and GARCH
models.
2:30
pm (20 minute talks)
(C)Amir
Memartoluie University of Waterloo
Counterparty Credit Risk, a Mass Transportation Approach
In
this work, we propose a new approach for calculating the Conditional
Value at Risk (CVaR) of a portfolio. One of the main issues that
quantitative modellers face in this regard is estimating the joint
distribution of credit risk factors and market risk factors. After
describing the underlying Counterparty Credit Risk problem, we
describe the risk measure which fits our model best. After that
we adapt a new approach which is based on utilizing Transportation
Problem for formulating our optimization problem. We finish by
presenting our numerical results.
3:00
(C)Duy Minh Dang (University of Waterloo)
An efficient numerical PDE approach for pricing foreign exchange
interest rate hybrid derivatives
Coauthors: Duy Minh Dang, Christina Christara, Ken Jackson, and
Asif Lakhany.
We
discuss efficient pricing methods via a Partial Differential Equation
(PDE) approach for longdated foreign exchange (FX) interest rate
hybrids under a threefactor multicurrency pricing model with
FX volatility skew. The emphasis of the paper is on PowerReverse
DualCurrency (PRDC) swaps with popular exotic features, namely
knockout and FX Target Redemption (FXTARN). Challenges in pricing
these derivatives via a PDE approach arise from the highdimensionality
of the model PDE, as well as from the complexities in handling
the exotic features, especially in the case of the FXTARN provision,
due to its pathdependency. Our proposed PDE pricing framework
for FXTARN PRDC swaps is based on partitioning the pricing problem
into several independent pricing subproblems over each time period
of the swap's tenor structure, with possible communication at
the end of the time period. Each of these pricing subproblems
can be viewed as equivalent to a knockout PRDC swap, and requires
a solution of the model PDE, which, in our case, is a timedependent
parabolic PDE in three space dimensions. Finite difference schemes
on nonuniform grids are used for the spatial discretization of
the model PDE, and the Alternating Direction Implicit (ADI) timestepping
methods are employed for its time discretization. Numerical examples
illustrating the convergence properties and efficiency of the
numerical methods are provided.
(C)
3:30
Zhenyu Cui, University of Waterlo
Nearly
Exact Option Price Simulation using Characteristic Functions
Coauthors: Carole Bernard (University of Waterloo), Don Mcleish
(University of Waterloo)
This
paper presents a new approach to perform a nearly unbiased simulation
using inversion of the characteristic function. As an application
we are able to give unbiased estimates of the price of forward
starting options in the Heston model and of continuously monitored
Parisian options in the BlackScholes framework. This method of
simulation can be applied to problems for which the characteristic
functions are known but the corresponding probability density
functions are complicated.
4:00
p.m.
(C)Nadia Saad, University of Ottawa
Compound Wishart Matrices and Noisy Covariance Matrices:
Risk Underestimation
Coauthors: B. Collins and D. McDonald
In
finance, Covariance matrices are used to compute the weights
and the risk of the optimal portfolio. Random Matrix Theory
shows that Covariance matrices determined from empirical financial
time series contain a high amount of noise. Using Random matrices
techniques, we derive the asymptotic formula of the effect of
this noise, resulting from estimating the Covariance matrix,
on determining the risk of the Markowitz's problem and hence
we get a perfect estimating of the risk of the optimal portfolio.
The advantage of our result is that it deals not only with independent
observations but also with correlated ones.
Thursday,
June 28
10:00
(C)Dimby
Ramarimbahoaka University of Calgary
A stochastic discount function modeled by a finite state
Markov chain and the perpetual American option
Robert
J.Elliott and John van der Hoek in 2010 investigated the theory
of asset pricing using a stochastic discount function process
where uncertainties in the economy are modeled by a Markov chain.
Stock price models, futures pricing etc were derived. In a later
paper (2011), in the same framework, they discussed finite maturity
American options where prices are obtained as solutions of a finite
dimensional variational inequality which is expressed in terms
of a system of ordinary differential equation. With Robert J.Elliott,
we give a discussion on the perpetual American option case.
10:30
Almas Nassem, University of Western
Ontario
Analysis of Taxdeductible Interest Payments for ReAdvanceable
Canadian Mortgages
Coauthors: Mark Reesor
According
to Canadian tax law the interest on loans used for investment
purposes is tax deductible while interest on personal mortgage
loans is not. One way of transforming from nontax deductible
to tax deductible interest expenses is to borrow against home
equity to make investments. A readvanceable mortgage is a
product specifically designed to take advantage of this tax
discrepancy. Using simulation we study the risk associated
with the readvanceable mortgage strategy to provide a better
description of the mortgagor’s position. We assume that
the mortgagor invests the borrowings secured by home equity
into a single risky asset (e.g., stock or mutual fund) whose
evolution is described by geometric Brownian motion (GBM).
With a readvanceable mortgage we find that the average mortgage
payoff time is less than the original mortgage term. However,
there is considerable variation in the payoff times with a
significant probability of a payoff time exceeding the original
mortgage term. Higher income homeowners enjoy a payoff time
distribution with both a lower average and a lower standard
deviation than lowincome homeowners. Thus this strategy is
most beneficial to those with the highest income. We also
find this strategy protects the homeowner in the event of
job loss. This work is important to lenders, financial planners
and homeowners to more fully understand the benefits and risk
associated with this strategy.
(C)11:00
Bernardo Reis Carneiro da Costa Lima, McMaster University
Dynamical Model for an Economy with Credit Expansion, Asset
Price Bubbles and Fragility
Steve
Keen's mathematical formulation of Hyman Minsky's financial
instability hypothe
sis provides a framework to study the effect of credit expansion
on the economy. Speculation is also studied in an enhanced model,
demonstrating its destabilizing effect, much in line with Minsky's
ideas. We propose a second extension of Keen's model, including
a stock index price process that is partially driven by the
level of speculation. Using jumpdiffusion dynamics, we are
able to capture the doubleedged effect of Ponzi investors in
the stock market. In turn, the cost of borrowing fluctuates
inversely with the stock price, providing a feedback effect
to the economy. I will discuss the stability properties of the
first two models, along with interesting features of the proposed
stochastic system.
11:30
(C)Adrian Walton, University of Western Ontario
Market Composition and Price Dynamics
We
derive a model from microeconomic principles that describes
how an asset's price fluctuates around its fair value in continuous
time. These dynamics depend on the relative market power and
perceptions of different classes of traders such as value investors,
highfrequency traders and hedgers. We show how our model is
useful for assessing the impact of trading strategies on an
asset's returns and volatility and present a mechanism for the
formation of price bubbles.
Jason
Ricci, University of Toronto
Calibration of the Generalized Hawkes Processes with Latent
Point Types
It
is well known that the classical Hawkes Process has modeling
applications in many fields including biology, neuroscience,
seismology, and finance. Motivated by highfrequency finance
and algorithmic trading, we propose a larger class of marked
point processes that may better represent the DGP for realworld,
natural systems. In this class, points are classified as those
that influence the underlying intensity process (influential)
and those that do not (noninfluential), where such classification
is latent. Moreover, we provide efficient quasimaximumlikelihood
calibration methods that makes calibration of parameters in
large data sets possible. Finally, modified Sequential Monte
Carlo estimators are used for realtime estimation of the
state of the corresponding intensity process.
