


Seminar: Spring 2003
Stanford Financial Mathematics Seminar Schedule
Date 
Speaker 
Affiliation 
Talk Title
(click to see Abstract) 
Comments 
4/11 
John Moody 
Professor of Computer Science and Electrical Engineering,Oregon Graduate Institute 
Minimizing Downside Risk via Direct Reinforcement 
Survey article (pdf) 
4/18 
Frank Riedel 
Lynen Research Fellow, Stanford University 
Dynamic Coherent Risk Measures [pdf] 

4/23 (Wed) 4:15 
Andrew Mullhaupt 
Director of Research, SAC Meridian Fund 
Cantelli's Inequality and the Estimation of Transaction Costs [pdf] 
After the talk, meet company representatives and discuss career opportunities. 
4/25 
Peter Bossaerts 
Professor of Economics and Management and Professor of Finance, Caltech 
Prices And Portfolio Choices In Financial Markets: Theory And Experimental Evidence 

5/2 
Sanjiv Das 
Professor of Finance, Santa Clara University 
Simple Comprehensive Models of Default Risk 
Paper: .pdf 
5/9 
Jaksa Cvitanic 
Professor of Mathematics and Economics, USC 
Revisiting Treynor and Black (1973): an Intertemporal Model of Active Portfolio Management 

5/16 
Karim Khiar 
Director, Financial Modeling, Gifford Fong Associates 
Anatomy of Copula Default Models 

5/20 (Tue) 4:15 
Eric Hillebrand 
Department of Mathematics, Stanford University 
Unknown Parameter Changes in GARCH and ARMA Models 
This is a joint Statistics / Financial Mathematics seminar. 
5/23 
Josh Gray 
Derivatives Specialist, Financial Engineering Associates 
Real Options: Theory and Practice 

5/30 
Nassim Taleb 
Founder and Chairman of Empirica Capital 
On the Effect of Distributions Not Being Observable 

6/27 
Nicole El Karoui 
Professor of Mathematics, Université de Paris VI. Professor of Applied Mathematics, Ecole Polytechnique. 
Optimal design of derivatives under dynamic risk measures 
This is a joint Probability / Financial Mathematics seminar. 
Minimizing Downside Risk via Direct Reinforcement 

John Moody ( Department of Computer Science, OGI School of Science & Engineering, Oregon Health & Science University)
Title:
Presenter:
Department of Computer Science
OGI School of Science & Engineering
Oregon Health & Science University
Abstract:
I present reinforcement learning (RL) methods for optimizing
portfolios, asset allocations and trading systems. In this approach,
investment strategies are discovered in simulation via trial and
error exploration.
RL has been developed in the machine learning, neural networks and
control engineering communities since the 1950's. These methods can
find approximate solutions of dynamic programming or stochastic
control problems without a detailed model of the system. Direct
Reinforcement (DR) algorithms are a promising alternative to standard
RL methods. DR enables more natural problem representations, reduces
Bellman's "curse of dimensionality" and offers compelling advantages
in efficiency.
I will demonstrate how Direct Reinforcement can be used to directly
optimize investment performance criteria such as profit, economic
utility or risk adjusted returns. Traders with varying degrees of
risk aversion can be modeled by the choice of performance measure.
The approach is illustrated using the Sharpe ratio and a criterion
that penalizes downside risk, the Downside Deviation ratio. Market
frictions, such as transaction costs or market impact, can be
included easily in the optimizations. The strategies discovered are
shown to depend upon the level of transaction costs and choice of
performance criterion.
Demonstrations of the proposed approach include a monthly asset
allocation system and an intradaily currency trader.
Speaker Biography:
John Moody is a Professor of Computer Science at the OGI School of
Science & Engineering in Portland, Oregon. His research interests
include machine learning, neural and statistical computing, time
series analysis and computational finance. He recently served as
Program CoChair of the IEEE Computational Intelligence in Financial
Engineering 2003 in Hong Kong and Computational Finance 2000 in
London. Moody founded OGI's very successful Computational Finance
program in January 1996 and served as its Director until June 2002.
He previously held positions in Computer Science and Neuroscience at
Yale University and at the Institute for Theoretical Physics in Santa
Barbara. Moody received his B.A. in Physics from the University of
Chicago, and earned his Ph.D. in Theoretical Physics at Princeton.
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Prices And Portfolio Choices In Financial Markets:
Theory And Experimental Evidence 

Peter Bossaerts (Caltech)
This paper reports on experiments designed to test the basic principles of
modern asset pricing theory. Prices in the experiments generally conform
to the implications of standard assetpricing theory (CAPM in particular),
although risk premia are (perhaps surprisingly) large. However, portfolio
choices in these experiments are strikingly at variance with the
predictions of standard theory (portfolio separation). This is puzzling
because the price predictions of standard theory depend critically on the
portfolio predictions. The paper proposes a theoretical explanation of
this priceportfolio paradox, extending the standard model to include
perturbation terms in individual demands. When the number of traders is
large  as is the case in the experiments reported here  these
perturbation terms largely cancel out, and the model yields pricing
predictions identical with those of standard theory but portfolio
predictions that are quite different. The predictions of the extended
model are consistent with the experimental data. The individual choices
in the experiments shed light on the nature of the perturbation terms.
Revealed preference analysis and analysis of expectedutilityequivalent
experiments without uncertainty suggest that the errors do not arise from
noise, subject confusion, lack of experience or inattention.
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Simple Comprehensive Models of Default Risk 

Sanjiv Das (Santa Clara University)
In this talk, I will first introduce some important aspects about default
risk modeling, and then present the paper titled "A simple unified model
for pricing derivative securities with equity, interest rate, default and
liquidity risk".
This paper develops a model for pricing securities that may be a function
of several different sources of risk, namely, equity, interestrate,
default and liquidity risks. The model is also useful for extracting
probabilities of default (PD) functions from market data.
The model is not based on the stochastic process for the value of the
firm, but on the stochastic process for interest rates and the equity
price, which are observable. The model comprises a riskneutral setting
in which the joint process of interest rates and equity are modeled
together with the default conditions for security payoffs. The model is
embedded on a recombining lattice which makes implementation of the
pricing scheme feasible with polynomial complexity. We present a simple
approach to calibration of the model to market observable data. The
framework is shown to nest many familiar models as special cases.
The model is extensible to handling correlated default risk and may be
used to value distressed convertible bonds, debtequity swaps, and
credit portfolio products such as CDOs. We present several numerical
and calibration examples to demonstrate the applicability and
implementation of our approach.
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Revisiting Treynor and Black (1973): an Intertemporal Model
of Active Portfolio Management 

Jaksa Cvitanic (University of Southern California)
Authors: Jaksa Cvitanic, Ali Lazrak, Lionel Martellini and
Fernando Zapatero
In the line of Treynor and Black (1973), we provide a closedform
solution to the problem of an investor with nonmyopic CRRA utility who
selects an optimal portfolio when assets offer an abnormal expected
return.
In the model of portfolio optimization with partial information in
continuous time, we assume that the investor has a normal prior on the
abnormal returns of the securities and upgrades those priors in a
Bayesian way. We allow the priors to be correlated and show that the
correlation between priors is an important parameter in the determination
of optimal holdings. The time horizon of the investor is another
important parameter. We also account for the presence of portfolio
constraints. These results provide a formal model for long/short
investment strategies and have implications for the active management
industry.
Our findings suggest that low beta hedge funds may serve as natural
substitutes for a significant portion of an investor riskfree asset
holdings. We calibrate the model to a database of hedge funds data,
and find that the optimal portfolios roughly agree with the market
practice.
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Anatomy of Copula Default Models 

Karim Khiar (Gifford Fong Associates)
Default models are critical for pricing bonds, credit derivatives and
structured finance products driven by defaults. In this framework,
practitioners extensively use default models.
In this discussion, I will focus on the copula default models. These
models (and more precisely the normal copula model) are very common in
credit default modeling. These models are dominant due to their
tractability. We will examine their mathematical properties.
First, we will analyze the different components necessary to implement a
default model. We will examine the correlation parameter, the asset
model, and term structure of default.
Next, we will describe the single step default model based on
multivariate normal distribution and we will illustrate its limitations.
Then, we will describe the multistep approach. The approach will
explicitly introduce a time dimension in the default model. We will
characterize the advantages and its limitations. To illustrate important
differences between these models, the single step outputs are compared to
a multi step model.
Finally, through several examples, we will emphasize the impact of these
different parts (such as maturity, rating, correlation, etc.) on the
multistep model. These examples are based on current practices in the
field of structured finance to design and manage the risk of credit
portfolios. Based on this simple example, I will illustrate the misuse
and misconception of current practices.
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Unknown Parameter Changes in GARCH and ARMA Models 

Eric Hillebrand (Stanford University)
A common finding in the empirical financial literature is that the
volatility of financial data exhibits high persistence, or slow mean
reversion of the order of months. In GARCH models, this is represented
by the fact that the sum of the estimates of the autoregressive
parameters is close to one when sample periods are considered that cover
several years.
It has been documented in simulations, however, that parameter changes
in the datagenerating process lead to exactly this phenomenon. It has
also been reported that segmentations of financial time series and local
GARCH estimations on the segments considerably reduce the estimated
persistence, that is, the sum of the estimated autoregressive parameters
is below one. One possible explanation is that the datagenerating
persistence within segments of constant parameters is relatively low and
that the globally measured high persistence is caused by the parameter
changes.
I will show that in GARCH models of orders up to GARCH(2,2), unknown
parameter changes in the datagenerating process in fact cause the sum
of the estimated autoregressive parameters to be close to one. This is a
consequence of the geometry of the estimation problem, not of the
statistical properties of the estimators, about which little is known.
This particular estimation problem is not confined to GARCH models, the
arguments are readily generalized to ARMA models of orders up to
ARMA(2,2). I will illustrate this effect using synthetic and market
data.
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Real Options: Theory and Practice 

Josh Gray (Financial Engineering Associates)
Real Options Theory is an attempt to map an asset, a contract or a
project into the parlance of the BlackScholes treatment of options. As
such, the theory is widely used in energy markets where the valuation and
hedging of certain contracts, with embedded or explicit optionality, are
managed through this simplifying and tractable translation of the real
world into the financial.
In this talk, we will discuss several examples of real options theory,
including swing contracts (american options), natural gas storage
(calendar spread options), and tolling agreements (spark spread options),
while pointing out the strengths, weaknesses and uncharted areas for
exploration.
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On the Effect of Distributions Not Being Observable 

Nassim Taleb (Empirica Capital)
The generator of a random process is seldom observable in the social
sciences, only its realizations, which may or may not reveal its nature.
Yet knowledge about the generator is what is needed to infer the true
moment properties of the process (expectation, variance). Distinguishing
between Knightian risk and Knightian uncertainty becomes impossible. We
present through the use of Gedanken experiments mathematical and
epistemological problems that arise in the process of attaining knowledge
about such needed properties.
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Optimal design of derivatives under dynamic risk measures 

Nicole El Karoui (Université Paris VI & Ecole Polytechnique)
We develop a methodology to optimally design a financial issue F to reduce
the exposure of an agent A towards a non tradable risk X. The constraint
is that an agent B only enters the transaction if her risk level remains
below a given threshold. Both agents have also the opportunity to invest
on financial markets.
In an entropic framework, the optimal solution is to transfer a constant
proportion of the initial exposure. This constant is a function of
the risk aversion coefficient, and not of the distribution of the risks.
The key assumption is that both agents may invest in the same market.
In the general case, the same results hold if both agents assess their
risk through convex risk measures (in the sense of Foellmer and Schied)
with proportional penalty functions. If not, the solution is more
complex. For dynamic risk measures characterized by their local
decomposition as semimartingales, we characterize the solution in terms
of Backward Stochastic Differential equations.
Joint work with Pauline Barrieu.
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