
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR 

Fields
Quantitative Finance Seminar
20122013
held
at the Fields Institute, 222 College St., Toronto
Map
to Fields


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 45minute 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
Talks 20122013
Talks
streamed live at FieldLive


TBA 
Past
Talks 20122013 (Video archive of Talks) 
April 24

Carol Alexander, University of Sussex
Nice Moment Swaps
(slide presentation)
This talk presents the very latest research on moment swaps, starting
with a simple new definition of realised variance that yields discretely
monitored variance swaps with none of the usual pricing errors (viz.
from jumps and from the use of an integral rather than a sum in the
derivation of fair value). We then generalize the set of moment characteristics
which satisfy Neuberger’s aggregation property and explain how
the fair values of such moment swaps may be obtained by pricing some
fundamental contacts (e.g. the log and entropy contracts) based on
vanilla option prices. Our methodology relies solely on the assumption
of an arbitragefree market and is therefore relevant for a wide range
of applications.
(Jointly with Johannes Rauch).
Sergey Nadtochiy, University of Michigan
Weak Reflection Principle and Static Hedging of Barrier
Options (slide
presentation)
The classical Reflection Principle is a technique that allows one
to express the joint distributionof a Brownian motion and its running
maximum through the distribution of the process itself. It relies
on the specific symmetry and continuity properties of a Brownian motion
and, therefore, cannot be directly applied to an arbitrary Markov
process. We show that, in fact, there exists a weak formulation of
this method that allows us to recover the same results on the joint
distribution of a Brownian motion and its running maximum. We call
this method a Weak Reflection Principle and show that it can be extended
to a large class of Markov processes, which do not posses any symmetry
properties and are allowed to have jumps. We demonstrate various applications
of this technique in Finance, Computational Methods, Physics, and
Biology. In particular, we show that theWeak Reflection Principle
provides an exact solution to the problem of hedging Barrier options
with a semistatic position in European type claims. Our method allows
us to find such hedging strategies in the diffusion and L´evybased
models. In addition, we show how it can be used to establish robust
static hedging strategies that are modelindependent. We illustratethe
theory with numerical examples.

Mar 27

Albert S. (Pete) Kyle, University of Maryland
Market Microstructure Invariance: Theory and Empirical Tests
Using the intuition that financial markets transfer risks in business
time, we define “market microstructure invariance” as the
hypothesis that the size distribution of risk transfers (“bets”)
and transaction costs of their implementation are constant across
assets and time. A metamodel suggests that microstructure invariance
is ultimately related to granularity of information flow. Based on
a database of 400,000+ portfolio transition trades, we show that quantitative
predictions of microstructure invariance concerning bets sizes and
transaction costs as functions of observable volume and volatility
closely match the data. We calibrate invariants and discuss implications
for financial markets.
Andreea Minca, Cornell University *Talk
Cancelled
When Do Creditors with Heterogeneous Beliefs Agree to Run?
We explore, in a multiperiod setting, the funding liquidity of a
borrower that finances its operations through short term debt. The
short term debt is provided by a continuum of agents with heterogeneous
beliefs about the prospects of the borrower. In each period, creditors
observe the borrower’s fundamentals and decide on the amount
they invest in its short term debt. We formalize this problem as a
coordination game, and we show that there exists a unique reasonable
Nash equilibrium. We show that the borrower is able to refinance if
and only if the liquid net worth is above an illiquidity barrier,
and we explicitly find this barrier in terms of the distribution of
capital and beliefs across agents.
(joint with Andrey Krishenik and Johannes Wissel).

Feb. 27

Ulrich Bindseil, European
Central Bank
Central bank liquidity provision, risktaking and economic efficiency
That in financial crises, central banks should become lenders of
last resort to the economy, while taking into account fi nancial risk
management and moral hazard concerns, is well known ever since the
19th century experience of the Bank of England as documented in Bagehot
(1873) or King (1936). In this paper, we develop further the relevant
tradeo ffs. First, we argue that the credit riskiness of counterparties
and issuers is endogenous to central bank's financial crisis measures
and the related risk control framework. It is shown that ignoring
this can lead to suboptimal risk management decisions. Second, extending
the problem of the central bank from a pure risk management perspective
to one considering economic efficiency, the central bank also needs
to consider how to avoid to the extent possible (a) defaults of viable
but illiquid institutions, and (b) the preservation through central
bank lending of lossmaking and nonviable institutions. Finally,
we formalize these ideas by providing a stylized model capturing the
effects of central bank collateral haircuts on both central bank risktaking
and economic efficiency. The model illustrates that (i) central bank
risktaking can decrease or increase when haircuts are increased;
(ii) economic efficiency and central bank risktaking are in many
cases nonmonotonous functions of haircuts on collateral; (iii) that,
as expected, central bank risktaking and economic efficiency are
not necessarily aligned. The model explains why in a financial crisis,
in which liquidity shocks become more erratic and the social costs
of defaults increase, central banks tend to make the collateral framework
less restrictive (CGFS, 2008).
Central bank liquidity provision,
risktaking and economic efficiency
Mike Lipkin (Katama Trading and Columbia University)
Market turbulence, monetization, and universality.
Shocks in financial markets create regions of turbulence which are
outofequilibrium. Prices in this region are frequently monetizable.
Are there universal properties? Some of the work presented here was
done by Columbia University students in the course Experimental Finance.

Feb. 6

Julien Guyon, Bloomberg (presentation)
(video archive of the talk)
Stochastic Volatility's Orderly Smiles
We consider multifactor stochastic volatility models and derive
the volatility smile at order two in the volatilityofvolatility.
At this order, the smile is quadratic in logmoneyness and depends
on three effective quantities within which the dynamics of the spot
and forward variances of any particular model is condensed. We supply
explicit expressionsof these quantities for a family of Hestonlike
models as well as a 2factor version of the Bergomi model. For this
model, comparison with the exact smiles shows good agreement for volatilityofvolatility
levels that are typical ofequity underlyings. Finally we derive short
term asymptotics and highlight the structural dependence of the level
of ATM skew and curvature on the ATM volatility, and we link the decay
of ATM skew and curvature for long maturities to the time decay of
spot/variance and variance/variance covariance functions.
Jon Gregory, Solum Financial Partners (video
archive of the talk)
Why CDOs Work
Prior to the beginning of the global financial crisis in 2007, the
CDO was a successful financial innovation. However, CDOs have been
blamed for causing the crisis, pricing models for CDOs have been heavily
criticised, litigation has been rife and investor demand has almost
disappeared. All players in the CDO market, notably banks, rating
agencies as well as investors have suffered as a result. An obvious
question to ask is whether the concept of a CDO is flawed and the
market was doomed to eventual failure or if CDOs, like many other
financial investments, were simply a casualty of a largely unforeseen
and completely unprecedented global financial crisis. In this talk,
I provide an answer to this question based on empirical analysis of
corporate default rates and a typical CDO structure.

Nov. 28

Paul Ormerod (Volterra Partners LLP) (presentation)
(video archive of the talk)
Trying to Make Economics a Science: Key Empirical Features of Recessions
and Thoughts on How to Explain Them
The current financial crisis has attracted a huge amount of attention.
But economic recessions are not new. There have been over 200 individual
examples across the individual Western countries since the late 19th
century. Mainstream economic models, with their focus on equilibrium,
are quite unable to explain the key empirical features such as distribution
of duration and size. How might we go about building models which
do? Feedback is essential, and agent based models also allow diversity
of behaviour. These seem promising ways of moving forward.

Nov. 23

Peter Carr (Morgan Stanley) (presentation)
(video archive of the talk)
Risk, Return and Ross Recovery
The risk return relation is a staple of modern finance. When risk
is measured by volatility, it is well known that option prices convey
risk. One of the more influential ideas in the last twenty years is
that the conditional volatility of an asset price can also be inferred
from the market prices of options written on that asset. Under a Markovian
restriction, it follows that riskneutral transition probabilities
can also be determined from option prices. Recently, Ross has shown
that realworld transition probabilities of a Markovian state variable
can be recovered from its riskneutral transition probabilities along
with a restriction on preferences. In recent work with Jiming Yu,
we show how to recover realworld transition probabilities in a bounded
diffusion context in a preferencefree manner. Our approach is instead
based on restricting the form and dynamics of the numeraire portfolio.

Oct. 24

Paul Kaplan ( Morningstar) presentation
(video archive of the talk)
Alpha, Beta, and Now... Gamma
When it comes to generating retirement income, investors arguably
spend the most time and effort on selecting 'good' investment funds/managersthe
so called alpha decisionas well as the asset allocation, or beta,
decision. However, alpha and beta are just two elements of a myriad
of important financial planning decisions, many of which can have
a far more significant impact on retirement income. We introduce a
new concept called "Gamma" designed to quantify the additional
expected retirement income achieved by an individual investor from
making more intelligent financial planning decisions. Gamma will vary
for different types of investors, but in this article we focus on
five fundamental financial planning decisions/techniques: a total
wealth framework to determine the optimal asset allocation, a dynamic
withdrawal strategy, incorporating guaranteed income products (i.e.,
annuities), taxefficient decisions, and liabilityrelative asset
allocation optimization. We estimate a retiree can expect to generate
29% more income on a "utilityadjusted" basis using a Gammaefficient
retirement income strategy when compared to our base scenario, which
assumes a 4% constant real withdrawal and a 20% equity allocation
portfolio. This additional income is equiva lent to an annual arithmetic
return increase of +1.82% (i.e., Gamma equivalent alpha), which represents
a significant improvement in portfolio efficiency for a retiree. Unlike
traditional alpha, which can be hard to predict, we find that Gamma
(and Gamma equivalent alpha) can be achieved by anyone following an
efficient financial planning strategy.
***This month's seminar will host one speaker and end at 6:30 p.m.

Sept. 26

Yacine AitSahalia (Princeton University) (presentation)
(video archive of the talk)
The Term Structure of Variance Swaps, Risk Premia and the Expectation
Hypothesis
We study the term structure of variance swaps, which are popular
volatility derivative contracts. A modelfree analysis reveals a significant
jump risk component embedded in variance swaps. The variance risk
premium is negative and has a downward sloping term structure. Variance
risk premia due to negative jumps present similar features in quiet
times but have an upward sloping term structure in turbulent times.
This suggests that shortterm variance risk premia mainly reflect
investors' fear of a market crash. Theoretically, the Expectation
Hypothesis does not hold, but biases and inefficiencies are modest
for short time horizons. A simple trading strategy with variance swaps
generates significant returns.
This is a joint work with Mustafa Karaman and Loriano Mancini.
Carole Bernard (University of Waterloo) (presentation)
(video archive of the talk)
MeanVariance Optimal Portfolios in the Presence of a Benchmark and
Application to Fraud Detection
We first study meanvariance efficient portfolios when there are
no trading constraints. Optimal strategies amount to holding a short
position in the stochastic discount factor used for pricing. We show
that optimal strategies perform poorly in bear markets. We then depart
from the traditional setting and assume investors use a stochastic
benchmark (linked to the market) as a reference portfolio. Preferences
become statedependent and we are able to accomodate for this. Precisely,
we derive meanvariance efficient portfolios when investors aim to
achieve a given correlation (or a given dependence structure) with
a stochastic benchmark. We also provide bounds on Sharpe ratios and
show how these can be useful for fraud detection. For example it is
shown that under some conditions it is not possible for investment
funds
to display negative correlation with the financial market and to have
a positive Sharpe ratio.

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