COMMERCIAL AND INDUSTRIAL MATHEMATICS

September 17, 2014

The Fields Institute 2006-2007
Seminar Series on Quantitative Finance

sponsored by

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.


Past Seminars (audio recording of talks)

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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