COMMERCIAL AND INDUSTRIAL MATHEMATICS

Past Seminars 2011-2012 (Audio and slides of talks)

Rogemar Mamon, University of Western Ontario

A weak hidden Markov chain-modulated model for asset allocation
A discrete-time weak hidden Markov model (WHMM) is proposed to capture both the switching of economic regimes and memory property of time series data. The drifts and volatilities of asset returns switch over time according to the WHMM dynamics. A multivariate filtering technique in conjunction with the Expectation-Maximisation algorithm is developed to obtain estimates of model parameters. An analysis of ``switching" and "mixed" strategies in asset allocation is presented. The use of financial signal processing via filtering aids investors in determining the optimal investment strategy for the next time step. Numerical implementation is carried out on the datasets of Russell 3000 value and growth indices. We benchmark portfolio performances using three classical investment measures.

Joint work with:
Matt Davison (Departments of Applied Mathematics, Statistical & Actuarial Sciences, and Richard Ivey School of Business, UWO) and Jean Xi (Department of Applied Mathematics, UWO)

====================================
Steve Shreve, Carnegie Mellon University

Optimal Execution in a General One-Sided Limit Order Book
We construct an optimal execution strategy for the purchase of a large number of shares of a financial asset over a fixed interval of time. Purchases of the asset have a nonlinear impact
on price, and this is moderated over time by resilience in the limit-order book that determines the price. The limit-order book is permitted to have arbitrary shape. The form of the optimal execution strategy is to make an initial lump purchase and then purchase continuously for some period of time during which the rate of purchase is set to match the order book resiliency. At the end of this period, another lump purchase is made, and following that there is again a period of purchasing continuously at a rate set to match the order book resiliency. At the end
of this second period, there is a final lump purchase. Any of the lump purchases could be of size zero. A simple condition is provided that guarantees that the intermediate lump purchase is of size zero. This is joint work with Gennady Shaikhet and Silviu Predoiu.

Abel Cadenillas, Mathematics, University of Alberta
A Theory for the Optimal Government Debt Control
Motivated by the current debt crisis in the world, we consider a government that wants to end the optimal control of its debt ratio. The debt generates a cost for the country. The government can reduce the debt ratio, but there is a cost associated with this reduction. We obtain a solution for the government debt problem. This is joint work with Ricardo Huaman.

====================================
**Paul Embrechts, Mathematics, ETH Zurich
Four Theorems and a Financial Crisis
In this talk I will give my personal assessment of the financial crisis (crises) and discuss where quantitative risk management (QRM) went wrong. I will formulate four mathematical theorems/research areas which have relevance for financial crises in general. Related to these theorems, key issues to be discussed are:
1) financial alchemy on Wall street
2) risk measurement for catastrophic risks
3) clustering of extremal events, and
4) beware of linear correlation.

** Note Tuesday, March 27, 2012
Paul Embrechts, will be speaking at McMaster University
Venue: 15:30 - 16:30 in Hamilton Hall 109, McMaster University
The Financial Crisis as a Crisis of Financial Mathematics?

Wed. March 7, 2012**
5:00 p.m.
Fields Institute,
Room 230

Lecture Notes

***Please note the change in date

Alex Levin, Director, Methodology, Market & Trading Credit Risk, RBC Financial Group

Some Approaches to Modeling Wrong-Way Risk in Counterparty Credit Risk Management and CVA
Current Risk Management methods focus on Credit Value Adjustment (CVA) for pricing credit risk of derivative portfolios and Counterparty Credit Risk (CCR) measurement, and are especially concerned with issues related to modeling Wrong-Way Risk (WWR) - dangerous positive correlation between the exposure to a counterparty and its default probability. In this talk, we will explore several new Counterparty Credit Risk measures that account well for Wrong-Way Risk and Right-Way Risk. I will then introduce a multifactor "Gaussian - jump of arbitrary sign" default intensity framework for modeling Wrong/Right-Way Risk and credit rating transitions (credit triggers) for large derivative portfolios with thousands of counterparties with or without collateral agreements. We will look at some calibration examples of this model, following a procedure based on a Volterra integral equation for the hitting time distributions. We will develop a sufficiently general Monte Carlo simulation algorithm for model calibration based on the idea of sequential fitting the drift to a term structure of CDS spreads. Finally, I will describe a new approach to Portfolio CCR and bilateral CVA calculations we call the "Gamma-Factor Copula".

Bruno Dupire, Head of Quantitative Research, Bloomberg

Functional Ito Calculus and Risk Management
We introduce the Functional Ito Calculus, which gives a natural setting for defining the Greeks for path dependent options and gives a generalized PDE for the price of path dependent options, even in the case of non Markov dynamics. It leads to a variational calculus on volatility surfaces and a fine decomposition of the volatility risk as well to links with super-replication strategies. We examine a few practical examples and analyze the ability to hedge (or not) some popular structures.

Peter Carr, Morgan Stanley

Optionality and Volatility
We propose two new concepts in option pricing called optionality and money vol. We provide financial interpetations of each in the context of various models.
We show how money vol can be used to generate dynamics for the underlying which is consistent with a given smile.

=================
Alexander Lipton, Bank of America

Filling the Gaps
The calibration of local volatility models to market data is one of the most fundamental problems of financial engineering. Under the restrictive assumption that the entire implied volatility surface is known, this problem can be solved by virtue of the so-called Dupire equation. In reality, however, the number of available data points is very limited and construction of a non-arbitrageable implied volatility surface is difficult, if not impossible, since it requires both interpolation and extrapolation of the market data. Thus, it is more natural to build the local volatility surface directly. In this talk we present a generic semi-analytical approach to calibrating a parametric local volatility surface to the market data in the realistic case when this data is sparse. This approach also allows one to build a non-arbitrageable implied volatility surface. The power of the method is illustrated by considering layered local volatility and generating local and implied volatility surfaces for options on SX5E.
This is a joint work with Artur Sepp.

Wed. October 26, 2011
5:00 p.m.

Matheus Grasselli , McMaster University

A dynamical systems model for credit expansion, asset price bubbles and financial fragility
Hyman Minsky's main contribution to economics - the financial instability hypothesis - links the expansion of credit to fund new investment to the increase in asset prices and the inherent fragility of an over-leveraged financial system. In this talk I describe an attempt to mathematize his model. I start by reviewing the main properties of the Goodwin model for employment and wages - a simple two-dimensional ODE system with globally stable cycles. I then describe the extension of this model proposed by Steve Keen to incorporate financing through a banking system. This three-dimensional system exhibits both a good equilibrium with a finite level of debt and a bad one where debt grows without bounds. I analyze the stability properties of this system, in particular with respect to interest rates. A further extension connects this system to asset prices and shows the destabilizing effect of Ponzi financing, that is, the purchase of assets with borrowed money for purely speculative purposes. In the final part of the talk I describe the stabilizing effects of countercyclical government spending and capital requirements.

=================
Bill Janeway, Senior Research Associate, Centre for Financial Analysis and Policy, University of Cambridge and Senior Advisor, Warburg Pincus

Tolerating Waste in the Innovation Economy or Putting the 'Creative' in Creative Destruction
Over 250 years, economic development has been driven by waves of transformational technology. This talk explores the three phases of the Innovation Economy: (1) "upstream" discovery and invention; (2) deployment of networked infrastructure; and (3) "downstream" exploration of the new economic space thereby created. Since the first and third phases are necessarily implemented through repeated exercises in trial and error, "Schumpeterian Waste" is inherent in the process. Further, while deployment of new infrastructure may be efficiently planned and executed, it has often been characterized by redundant and unremunerative projects, whether undertaken by the private or the public sectors. Thus, the process of innovation is critically dependent upon sources of funding relatively unconcerned with visible economic return.The two principle sources of funding for the upstream phase of discovery and invention have been the rents earned by monopoly corporations and state programs of non-economic investment, often motivated by issues of national security. The downstream phase of economic exploration has repeatedly been financed through speculative bubbles in the financial markets. From the canal and railway manias of the first and second industrial revolutions through electrification and the internet in the twentieth century, infrastructure investments have also been funded by financial speculation. While transformational innovation on the supply side of the economy transcends the normative goal of efficient resource allocation, too great a concern with efficient resource allocation can also encourage toleration of macroeconomic waste: unemployed human and physical resources. In turn, toleration of such "Keynesian Waste" can feed back to inhibit development of the Innovation Economy.

Wed. Sept. 28, 2011
5:00 p.m.

Vadim Linetsky, McCormick School of Engineering and Applied Sciences, Northwestern University

Unified Credit-Equity Modeling: From Single-Name to Multi-Name
This talk surveys our work on unified credit-equity models that view the stock price as the fundamental observable state variable that jumps to zero in the event of the firm's default on its debt and treat both credit derivatives and equity derivatives in a unified fashion as contingent claims on the defaultable stock price process. After surveying single-name models, we present
multi-name unified credit equity model.