## New Directions in Financial Risk Management

## Titles and Abstracts

Andrew Aziz, Vice President, Professional Services, Algorithmics
Inc.

**Title: **A Unified Framework for Enterprise Risk and Reward

**Abstract:** It is clear that it makes no sense for financial institutions
to price, hedge, measure risk, allocate capital and compute asset allocations
using different methods based on different assumptions.. Yet that is
what happens today. There is no mathematical consistency in most financial
institutions. We believe that consistency can be achieved and if implemented,
has great value. This talk is about our Mark-to-Future, the culmination
of our efforts in this direction.

**Phelim Boyle**, University of Waterloo

**Title:** Pricing new securities in an incomplete market: The catch
22 of derivative pricing

**Abstract:** There are two radically different approaches to the
valuation of a new security in an incomplete market. The first approach
is common in the mathematical finance literature. This method takes
the prices of the existing traded securities as fixed and uses no arbitrage
arguments to derive the set of equivalent martingale measures that are
consistent with the initial prices of the traded securities. The price
of the new security is obtained by invoking some preference assumption
or appealing to certain arbitrary criteria. The second method prices
the new secturity using a general equilibrium approach. In this case
the prices of all the existing securities will normally change. This
talk clarifies the distinction between the two approaches and also outlines
a proof that the introduction of the new security will typically change
the prices of all the existing securities.

**Hélyette Geman**, Université Paris IX Dauphine
and ESSEC

**Title:** Stochastic Time Changes, Lévy Processes and Asset Price
Modelling

**Abstract: **We investigate the relative importance of diffusion
and jumps in a new jump diffusion model for asset returns. In contrast
to the standard modelling of jumps for asset returns, the jump component
of our process can display finite or infinite activity, and finite or
infinite variation. Empirical investigations of time series indicate
that index dynamics are essentially devoid of a diffusion component,
while this component may be present in the dynamics of individual stocks.
This result leads to the conjecture that the risk-neutral process should
be free of a diffusion component for both indices and individual stocks.
Empirical investigation of options data tends to confirm this conjecture.
We conclude that the statistical and risk-neutral processes for indices
and stocks tend to be pure jump processes of infinite activity and finite
variation.

**Lane P. Hughston**, King's College, London

**Title:** Entropy and Information in the Interest Rate Term Structure

**Abstract:** Associated with every positive interest term structure
there is a probability density function over the positive half line.
This fact can be used to turn the problem of term structure analysis
into a problem in the comparison of probability distributions, an area
well developed in statistics, known as information geometry. The key
idea is to take the square-root of the density function, which embeds
the space of densities into a Hilbert space. As a consequence, Hilbert
space operations can be employed to study the structure of interest
rate models. Some of the information-theoretic and geometric aspects
of term structures thus arising will be illustrated. In particular,
we introduce a new term structure calibration methodology based on maximisation
of entropy, and also present some new families of interest rate models
arising naturally in this context. (Joint work with D. C. Brody, Imperial
College, London)

**Dilip B. Madan**, Robert H. Smith School of
Business, University of Maryland

**Title:** Stochastic Volatility for Levy Processes

**Abstract:** Three processes reflecting persistence of volatility
are formulated by evaluating three Levy processes at a time change given
by the integral of a square root process. Stock price models are considered
by exponentiating and mean correcting these processes or by stochastically
exponentiating these processes. The resulting chracteristic functions
for the log price yield option pricing systems via the fast Fourier
transform. Results on index options and single name options suggest
advantages to employing higher dimensional Levy systems for index options
and lower dimensional structures for single names. In general mean corrected
exponentiation performs better than employing the stochastic exponential.
Martingale laws for the mean corrected exponential are also studied
and two new concepts termed Levy and martingale marginals are introduced.

**Moshe Milevsky**, Schulich School of Business,
York University

**Title: **Personal Value-at-Risk: An Overview of the Real Options
in Your Life.

**Abstract:** In this presentation, I will describe how many of
the quantitative techniques originally developed in the area of corporate
risk management, can be applied to the individual vis a vis their portfolio
of human and financial capital. I argue that consumers are naturally
endowed with Real Options to 'time' various irreversible 'investments'
that share a striking resemblance to classical decisions in corporate
finance. Whether or not these options should be priced risk-neutrally
is quite independent of the fact that they exist. I will provide some
examples as they relate to insurance and asset allocation decisions
over the life-cycle, and discuss some of the interesting stochastic
modeling problems that emerge....

Marcel Rindisbacher, Joseph L. Rotman School
of Management, University of Toronto

**Title: **A Monte-Carlo Method for Optimal Portfolios

**Abstract: **This paper provides (i) simulation-based approaches
for the computation of asset allocation rules,(ii) economic insights
on the behavior of the hedging components and (iii) a comparison of
numerical methods.

For general utility functions with wealth-dependent risk aversion and
diffusion state variable processes, hedging demands are conditional
expectations of random variables depending on the parameters of the
model, which can be estimated using standard simulation methods. We
propose a modified simulation approach which relies on a simple transformation
of the underlying state variables an improves the performance of Monte
Carlo estimators of portfolio rules. Our approach is flexible and applies
to arbitrary utility functions, any finite number of state variables,
general diffusion processes for state variables and any finite number
of assets. The procedure is implemented for a class of multivariate
nonlinear diffusions for the market price of risk (MPR), the interest
rate (IR) and other factors (such as dividends). After calibrating the
models to the data we document the portfolio behavior. Intertemporal
hedging demands are found to (i) significantly increase the demand for
stocks and (ii) exhibit low volatility. (iii) Non-linearities are shown
to be important: significant biases in allocation rules are documented
if one uses typical (affine/or square root) processes calibrated to
the data. (iv) Dividend predictability is found to have negligible effect.
Portfolio policies are also computed and examined for (v) HARA utility
functions and (vi) in markets with a large number of state variables
and mutual funds.

**Luis Seco**, Mathematics, University of Toronto

**Title:** Mark-to-Future in non-gaussian markets.

**Abstract:** After the initial success of the RiskMetrics methodology,
effective risk management practices in non-gaussian markets leads to
a number of interesting mathematical questions. This talk will review
a number of business situations and the associated mathematical tools
relevant to each of them.