FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
Fields Quantitative Finance Seminar
at the Fields Institute, 222 College St., Toronto
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
Talks 2014-2015 Talks
streamed live at
|April 29, 2015
at 5 p.m.
Marcel Nutz - Columbia University
Optimal Transport and Robust Finance
After a brief introduction to classical optimal transport, we shall
focus on the so-called martingale optimal transport and its connection
to finance, the problem of robust semi-static hedging. Some differences
with the classical transport problem will be highlighted, in particular
the failure of duality in the usual sense. We explain how to obtain
a complete duality theory using notions related to Knightian uncertainty
about pricing models. Based on joint work with Mathias Beiglböck
and Nizar Touzi.
Joe Langsam - University of Maryland
Most financial disasters are a result of either outright fraud or
some form of concentration risk. Concentration risk as it impacts
financial firms can be classified into three categories: a firm in
a well-diversified market whose capital is exposed to one (or a small
number) of risk, a firm (or small number of firms) who have taken
one side of a risk while facing a large market on the other side of
the risk, a market where a sizeable amount of banking capital is exposed
to a small number of highly correlated risks. The first of these represents
little risk to the system with the possible exception that the exposed
firm is a SIFI. If the risks prove too great for this firm, it will
go out of business. The market, being well diversified can absorb
this. The second, which can generate a fire sale, can be of systemic
concern. The third type of concentration, one that we saw in the recent
crisis where so great a part of the system was exposed to real estate
risk, poses the greatest systemic risk. How to measure these concentrations
remains, to my knowledge, an open question. A bank's risk manager
may know the bank's exposures, but is unlikely to have sufficient
knowledge of how these risks are distributed in the market place.
Now is a good time for complete disclosure: I am not as interested
in finding the answer to measuring these risks as I am to finding
the answer as to why these risks continue to evolve.
It is far easier, and much less useful, to identify risk concentrations
after an event. In this talk, I will explore possible means for measuring
concentration risks examining both data and modeling requirements.
What I will not do is answer the important questions of why it exists.
That is beyond my current knowledge, but an important step for designing
regulatory actions that reduce the likelihood and severity of future
crisis without seriously reducing the effectiveness of the capital
|March 25, 2015
at 5 p.m.
Sasha Stoikov - Cornell University
Estimating the cost of latency in trading
Starting with a diffusion model for the evolution of the best bid
and ask sizes of an asset, we compute the probability that the next
price move is upward. This probability is a function of the ratio
of the best bid to ask sizes, the correlation between changes in the
bid/ask sizes and a hidden liquidity parameter. We then formulate
a trade execution problem and solve it using dynamic programming.
The objective is to sell a single lot of an asset in a short time
horizon, while monitoring the ratio of bid to ask sizes. The optimization
problem takes into account the latency of the trading algorithm, which
affects the prices at which the asset is traded. Identifying good
trading times is equivalent to solving an optimal stopping problem,
where the objective is to stop whenever the best bid to ask size ratio
is small. The solution divides the state space into a ``trade'' and
``no-trade'' region. We calculate the cost of latency per lot traded
and demonstrate that the advantage of observing the limit order book
can dissipate quickly as latency increases.
Yaacov Mutnikas - Bank of England
Financial Networks and Systemic Risk
|February 25, 2015
at 5 p.m.
Joe Campolieti - Wilfrid Laurier
Dual Families of Solvable Diffusion Models: Applications to Modelling
and Derivative Pricing in Finance
In this talk I will firstly present a framework for the construction
and classification of a class of dual families of solvable diffusion
models. The dual models have highly nonlinear volatility specifications.
One main family is characterized by an affine drift specification,
while the other has a nonlinear drift specification. The models with
affine drift are useful for modelling asset prices, while those with
nonlinear drift specification are useful for modelling other quantities
such as interest rates. The nonlinearity features, together with the
multiply adjustable parameters in the models, are desirable for model
calibration to market data such as option data. In the second part
of my talk I will discuss the derivation of closed-form spectral expansions
for various transition densities, first hitting time distributions,
joint distributions of the process value and its maximum or minimum,
as well as distributions and expected values for occupation times
of the solvable diffusion processes. As an application of the closed-form
spectral expansions, I will present some results for pricing barrier,
lookback and occupation-time options. The talk will conclude with
a brief discussion of some future extensions and applications of the
Terry Rockafellar - University of Washington
Risk, Utility and Regression
Maximizing the expected utility of a random variable representingprofit
or gain is a widely used approach to financial decision-making.Alternatively,
portfolios can be put together to minimize risk ascaptured by the
choice of a measure of risk as a functional applied torandom variables
representing costs or losses. Some connections areknown between the
two approaches, but there is a deeper linkage, not yetfully appreciated,
in which a measure of risk can very broadly be portrayedas coming
from trade-off rules with respect to "utility" as afunctional
on a space of random variables.
That requires extending beyond just expectations and on the other
hand considering utility to be relative to some benchmark. Such extension
opens remarkable connections between utility and statistical analysis
using generalized regression tuned to particular types of risk.
|January 28, 2015
at 5 p.m.
Paolo Guasoni - Boston University and Dublin City University
Nonlinear Price Impact and Portfolio Choice
In a market with price-impact proportional to a power of the order
flow, we derive optimal trading policies and their implied welfare
and trading volume, for long-term investors with constant relative
risk aversion, who trade one safe asset and one risky asset that follows
geometric Brownian motion. These quantities admit asymptotic explicit
formulas up to a structural constant that depends only on the price-impact
exponent. As with linear impact, trading rates are finite, but they
are lower near the target portfolio, and higher away from the target.
The model nests the square-root impact law and, as extreme cases,
linear impact and proportional transaction costs.
Anna Obizhaeva - University of Maryland (coauthors: Torben
G. Andersen, Oleg Bondarenko, Albert S. Kyle)
High-Frequency Trading Invariance for Equity-Index Futures
The high-frequency trading patterns of the S&P500 E-mini futures
contracts between January 2008 and November 2011 are consistent with
the following invariance relationship: the number of transactions
is proportional to a product of dollar volume and volatility in 2/3
power. Equivalently, the return variation per transaction is log-linearly
related to trade size, with a slope coecient of -2. This factor of
proportionality deviates sharply from those associated with prior
hypotheses relating volatility to the transactions count or trading
volume. High-frequency trading invariance is, a priori, motivated
by the notion of market microstructure invariance introduced by Kyle
and Obizhaeva (2013), though it does not follow from it directly.
|November 26, 2014
at 5 p.m. .
Yuri Lawryshyn - University of Toronto (coauthor: Sebastian
Jaimungal, University of Toronto) (Slides)
Incorporating Managerial Cash-Flow Estimates and Risk Aversion to
Value Real Options Projects
Real options analysis (ROA) is widely recognized as a superior method
for valuing projects with managerial flexibilities, yet, its adoption
within industry remains limited due to varied difficulties in its
implementation. Models proposed by practitioners often lack financial
rigour, while the more rigorous mathematical models are not conducive
to practical implementation. In this work, we propose a method that
matches managerial cash-flow estimates, consisting of arbitrary distributions
that can be integrated within many of the rigorous mathematical model
frameworks. We achieve this by introducing an observable, but not
traded, market stochastic driver process which drives the cash-flows.
We present our methodology first in a practical real options setting,
then expand the model to account for managerial risk aversion.
(D. Saunders talk has been postponed)
David Saunders - University
Applications of Quantitative Finance to Private Pension Plan Valuation
Private pensions have undergone a dramatic upheaval
in recent years. The needs of providers to avoid the risks associated
with defined benefit (DB) structures have led to an exodus from
these plans and into defined contribution (DC) arrangements. However,
employees under DC plans suffer from greater volatility, and lack
the benefits of security and risk pooling associated with traditional
DB pensions. These concerns have led to the rise of hybrid designs,
which seek to combine features of both DB and DC plans. The methods
of quantitative finance have much to say about the valuation and
management of these plans, and their many embedded options. In particular,
we will discuss two examples: cash balance plans, offered by many
private employers in the U.S., and variable payout life annuities,
such as the one offered by the University of British Columbia.
|October 31, 2014
at 5 p.m.
Damiano Brigo - Imperial College London.
Nonlinear valuation under credit gap risk, collateral margins, funding
costs and multiple curves (Slides)
Following a quick introduction to derivatives markets and the classic
theory of valuation, we describe the changes triggered by post 2007
events. We re-discuss the valuation theory assumptions and introduce
valuation under counterparty credit risk, collateral posting, initial
and variation margins, and funding costs. A number of these aspects
had been investigated well before 2007. We explain model dependence
induced by credit effects, hybrid features, contagion, payout uncertainty,
and nonlinear effects due to replacement closeout at default and possibly
asymmetric borrowing and lending rates in the margin interest and
in the funding strategy for the hedge of the relevant portfolio. Nonlinearity
manifests itself in the valuation equations taking the form of semi-linear
PDEs or Backward SDEs. We discuss existence and uniqueness of solutions
for these equations. We present an invariance theorem showing that
the final valuation equations do not depend on unobservable risk free
rates, that become purely instrumental variables. Valuation is thus
based only on real market rates and processes. We also present a high
level analysis of the consequences of nonlinearities, both from the
point of view of methodology and from an operational angle, includin
deal/entity/aggregation dependent valuation probability measures and
the role of banks treasuries. Finally, we hint at how one may connect
these developments to interest rate theory under multiple discount
curves, thus building a consistent valuation framework encompassing
most post-2007 effects.
Paul Glasserman - Columbia University.
Hidden Illiquidity with Multiple Central Counterparties (Slides)
The ongoing transformation of the swaps market from over-the-counter
trading to central clearing reduces counterparty risk but may create
systemic risk by concentrating risk in central counterparties (CCPs).
Margin requirements provide the first line of defense against the
failure of a CCP. To reflect liquidation costs in the event of a clearing
members failure, initial margin should be convex in the size
of a position. But convex margin requirements create an incentive
for dealers to split positions across multiple CCPs, leading each
CCP to underestimate potential liquidation costs. We analyze the problem
of correcting for this effect. We show that CCPs may set different
yet consistent margin requirements provided they agree on true liquidation
costs. Different views on true liquidation costs create a potential
race to the bottom in which lower margin requirements drive out higher
margin requirements. This is joint work with Ciamac Moallemi and Kai
September 24, 2014
at 5 p.m.
|No seminar scheduled this month
(click here for the Quantitative
Finance Career Fair and for
a Public Lecture in Economics)
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