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The Fields Institute 2006-2007
Seminar Series on Quantitative Finance
sponsored by
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The Quantitative
Finance Seminar has been a centerpiece of the Commercial/Industrial
program at the Fields Institute since 1995. Its mandate is to arrange
talks on current research in quantitative finance that will be of
interest to those who work on the border of industry and academia.
Wide participation has been the norm with representation from mathematics,
statistics, computer science, economics, econometrics, finance and
operations research. Topics have included derivatives valuation, credit
risk, insurance and portfolio optimization. Talks occur on the last
Wednesday of every month throughout the academic year and start at
5 pm. Each seminar is
organized around a single theme with two 45-minute talks and a half
hour reception. There is no cost to attend these seminars and everyone
is welcome.
To be informed of speakers and titles for upcoming seminars and
financial mathematics activities, please subscribe to the Fields
mail list.
Upcoming Seminars
June 6, 2007
5:00 p.m. Reception
5:20 p.m. Kay Giesecke, Stanford University
Pricing, hedging and calibrating credit from the top down
A credit derivative is a contingent claim on the aggregate financial
loss in a portfolio of credit sensitive instruments such as loans,
bonds or credit swaps. We summarize our recent results on the
pricing, hedging and calibration of credit derivatives using point
processes. Topics include the representation of the conditional
transform of a point process, Markovian projection, random thinning,
time changes and simulation. The material is based on joint work
with
Xiaowei Ding, Eymen Errais, Lisa Goldberg, Baeho Kim and Pascal
Tomecek.
April 25, 2007
Bjorn Flesaker, Bloomberg
Robust Replication of Default Contingent Claims
We demonstrate how to replicate a broad class of single
name credit derivatives with static positions in standard credit
default swaps and a self-financing money market account balance.
The survival contingent money market account balance is given
as the solution to a certain second order linear (backward)
ordinary differential equation, subject to terminal boundary
conditions. The absence of arbitrage determines a linear valuation
operator, and we derive the forward equation for its Green's
function. We provide examples of closed form solutions for special
cases, give an example of applications to credit index arbitrage,
and show how the results motivate current market practice for
credit curve stripping under essentially arbitrary default dynamics.
The talk is based on joint work with Peter Carr.
and
Lane Hughston, King's College London
Information, Inflation, and Interest
We propose a class of discrete-time stochastic models for the
pricing of inflation-linked assets. The paper begins with an
axiomatic scheme for asset pricing and interest rate theory
in a discrete-time setting. The first axiom introduces a risk-free
asset, and the second axiom determines the intertemporal pricing
relations that hold for dividend-paying assets. The nominal
and real pricing kernels, in terms of which the price index
can be expressed, are then modelled by introducing a Sidrauski-type
utility function depending on (a) the aggregate rate of consumption,
and (b) the aggregate rate of real liquidity benefit conferred
by the money supply. Consumption and money supply policies are
chosen such that the expected joint utility obtained over a
specified time horizon is maximised subject to a budget constraint
that takes into account the value of the liquidity benefit associated
with the money supply. For any choice of the bivariate utility
function, the resulting model determines a relation between
the rate of consumption, the price level, and the money supply.
The model also produces explicit expressions for the real and
nominal pricing kernels, and hence establishes a basis for the
valuation of inflation-linked securities.
Key words: Inflation, interest rate models, partial information,
price level, money supply, consumption, liquidity benefit, utility,
transversality condition.
Working paper (coauthored with Andrea Macrina) downloadable
at: www.mth.kcl.ac.uk/research/finmath/
March 28, 2007
David Saunders, University of Waterloo
Pricing CDO Tranches of Bespoke Portfolios
We present a robust and practical CDO valuation framework
based on weighted Monte Carlo techniques used in option pricing.
The methodology can be used to value consistently CDOs of bespoke
portfolios, CDO-squared and cash CDOs. Under a multi-factor
conditionally independent credit modelling framework, we use
prices of liquid credit portfolio instruments to imply the "risk
neutral" distributions for the underlying set of systematic
factors driving joint obligor defaults. The methodology can
be seen as an extension to the implied copula methodology (Hull
and White 2006), where sector concentration risk of bespoke
portfolios is modelled explicitly using a multi-factor credit
model. The technique is illustrated by computing implied factor
distributions for a Gaussian copula model using prices of standard
tranches on CDS indices. Extensions to other static factor models
and dynamic credit portfolio models are also discussed.
*This research is joint work with Dan Rosen of the Fields
Institute and R2 Financial Technologies.
and
Jaksa Cvitanic, California Institute of Technology
Numerical estimation of volatility values from discretely
observed diffusion data
We consider a Black-Scholes type model, but with volatility
being a Markov Chain process. Assuming that the stock price
is observed at discrete, possibly random times, the goal is
to estimate the current volatility value. The model parameters,
that is, the possible volatility values and transition probabilities,
are estimated using the Multiscale Trend Analysis method of
Zaliapin, Gabrielov and Keilis-Borok, adapted to our framework.
Once these are given, the volatility is estimated using the
filtering formula developed in our previous work Cvitanic, Liptser
and Rozovskii (2006).
Our numerical implementation shows that the estimation is of
very high quality under a range of conditions. Joint work with
B. Rozovski and I. Zalyapin.
February 28, 2007
Ronnie Sircar, Princeton University
Utility Valuation of Credit Derivatives
We discuss the effect of investor risk-aversion on the valuation
of single-name and multi-name credit derivatives. In particular,
we analyze the utility-indifference pricing mechanism applied
to defaultable bonds and CDOs. In the case of complex multi-dimensional
products like CDOs, risk-aversion acts as an effective correlator
of the times of the credit events of the various firms, which
we illustrate from examples, including recent results with stochastic
intensities.
Joint work with Thaleia Zariphopoulou (University of Texas at
Austin).
and
Marcel Rindisbacher, University of Toronto
Dynamic Asset Allocation: a Portfolio Decomposition Formula
and Applications
This paper establishes a new decomposition of the optimal
portfolio policy in dynamic asset allocation models with arbitrary
vNM preferences and Ito prices. The formula rests on a change
of numéraire which consists in taking pure discount bonds
as units of account. When expressed in this new numéraire
the dynamic hedging demand is shown to have two components.
If the individual cares solely about terminal wealth, the first
hedge insures against fluctuations in a long term bond with
maturity date matching the investor's horizon and face value
determined by bequest preferences. The second hedge immunizes
against fluctuations in the volatility of the forward density.
When the individual also cares about intermediate consumption
the first hedging component becomes a coupon-paying bond with
coupon payments tailored to consumption needs. The decomposition
formula is applied to examine the existence of preferred habitats,
portfolio separation, the investment behavior of extremely risk
averse individuals, the demand for long term bonds, the optimal
international asset allocation rule, the preference for I-bonds
in inflationary environments and the integration of fixed income
management and asset allocation.
November 29, 2006
"CANCELLED"
October 25, 2006
Michael J. Brennan, The Anderson School, UCLA
Asset Pricing and Mispricing
We develop models for stock returns when stock prices are
subject to stochastic mispricing errors. We show that expected
rates of return depend not only on the fundamental risk that
is captured by a standard asset pricing model, but also on the
type and degree of asset mispricing, even when the mispricing
is zero on average. Empirically, the mispricing induced return
bias, proxied either by Kalman filter estimates or by volatility
and variance ratio of residual returns, are shown to be significantly
associated with realized risk adjusted returns. This talk is
based on joint work with Ashley Wang.
Thomas S. Salisbury, York University
GMWBs
Guaranteed Minimum Withdrawal Benefits already exist as
a form of income insurance on a large fraction of variable annuity
retirement savings plans in the US. Similar products are now
beginning to be available in Canada. I'll discuss some of the
valuation and risk management issues associated with such guarantees,
both from the point of view of the issuer and the client. This
talk is based on joint work with Moshe Milevsky.
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