April 20, 2014

3C Risk Forum
The First 3-C Risk Forum & 2011 International Conference on Engineering and Risk Management (ERM)

October 28–30, 2011
RiskLab Global

hosted by the Fields Institute, Map to Fields
222 College Street, Toronto

Fields Institute

Professional Risk Managers’
International Association

Keynote Abstracts

John Birge (University of Chicago, Booth School of Business)
Managing risk with operational and financial instruments

Due to various market imperfections, firms have an incentive to manage idiosyncratic risk. Operational flexibility and financial tools offer complementary mechanisms for this process. This talk will discuss the motivation for different forms of risk management, relative advantages of operational and financial approaches, and a model for constructing an optimal risk management portfolio.

Endre Boros (Rutgers University)
How to mitigate the risk of blowing up and the cost of being too cautious?

Finding ways to intercept illicit nuclear materials and weapons destined for the U.S. via the maritime transportation system is an exceedingly difficult task. Today, only a small percentage of containers arriving to U.S. ports are inspected. Current technology provides highly uncertain detection, with a high risk of both unnoticing hidden nuclear material and raising costly false alarms. We present a new mathematical model for creating an optimal inspection policy based on a set of noisy and possibly stochastically dependent sensor technologies.

Matt Davison (University of Western Ontario)
Energy Storage: A problem at the intersection of quant finance, optimization, and energy policy

New renewable energy technologies are a major part of "green shift" plans to decrease humanity's carbon footprint. While wind and solar power hold the promise of clean energy, they pose a challenge to the operation of modern electricity networks because their output fluctuates both dramatically and unpredictably. Energy storage represents one solution to these fluctuations. As for wind turbines and solar panels, the economics of storage require careful thought.

This talk begins with a survey of the technological, economic, and regulatory framework for renewable energies and storage technologies. Next an instructive toy problem illustrating the interaction of finance, optimization, and energy policy advertised in the title is developed and analyzed. With our intuition firmly established, we discuss more sophisticated extensions to this model in the realms of pump storage hydro and natural gas storage. The talk concludes with some remarks about the policy impact of this research and its extensions.

John Hull
(Rotman School of Management, University of Toronto)
CVA and wrong way risk

This paper proposes a simple model for incorporating wrong-way and right-way risk into CVA (credit value adjustment) calculations. These are the calculations made by a dealer to determine the reduction in the value of its derivatives portfolio because of the possibility of a counterparty default. The model relates the hazard rate of the counterparty to the value of the transactions outstanding between the dealer and the counterparty. Numerical results for portfolios of 25 instruments dependent on five underlying market variables are presented. The paper finds that wrong-way and right-way risk have a significant effect on the Greek letters of CVA as well as on CVA itself. It also finds that the nature of the effect depends on the collateral arrangements.

David Olson (University of Nebraska-Lincoln)
Broader Perspectives of Risk Management

The 21st Century has seen tremendous investment uncertainty, with at least three major disruptive episodes in the 2001 bubble, the 2008 banking crisis, and now the current debt crises from Iceland, Portugal-Ireland-Greece-Spain, Italy, and the United States. Investors seek to be scientific, and base their decisions on data. But the only data we have is the past, and these three episodes have led to radically different data regimes. Value-at-risk calculations in the past decade have been based upon historical data, which demonstrated apparent normality. Past data also was used to identify correlations, allowing generation of combined portfolios with expected compensating risks. These assumptions have proven to be problematic. This study briefly discusses economic philosophies of risk management, reviews portfolio models reflecting tradeoffs between expected return and risk, and discusses the risk of basing decisions based solely upon historical data.

This is a joint work with Desheng Wu (University of Toronto)

Thomas Salisbury
Planning for retirement: sustainability versus legacy

When planning for retirement, individuals face the risk of living longer than expected, and therefore running out of the capital needed to sustain their income. There are ways to ensure against this, eg by purchasing annuities. But these have a downside; a true annuity offers mortality credits but leaves no legacy behind for one's heirs. In other words, retirees confront trading off their interests (ie sustainability) versus their kids' interests (ie legacy). I will discuss a pair of risk metrics that are useful in making decisions about this tradeoff: the Retirement Sustainability Quotient (RSQ) and Expected Financial Legacy (EFL). These are expectations, one focused on the current generation and the other one on the next. They can be analyzed in simple models via PDEs. This allows retirement decisions to be viewed as selecting a point on an RSQ/EFL efficient frontier. This talk reports on joint work with Huaxiong Huang, Moshe Milevsky, and Faisal Habib.

David Simchi-Levi (Massachusetts Institute of Technology)
Mitigating Business Risks from the Known-Unknown to the Unknown-Unknown

In the last few years we have seen an increase in the levels of risk and volatility faced by enterprises. Some recent examples include the unrest in the Middle East, inflation in China, the Japanese tsunami disruption, the Iceland volcano eruption, oil price volatility, product recalls and huge fluctuations in financial markets.This requires business executives to systematically address business risks both the know-unknown operational risks as well as the unknown-unknown extreme risks. Unfortunately, there is very little that can be done after a disaster has occurred. Companies therefore need to devote more attention to planning their operations so they can better respond to mega disasters as well as more mundane operational problems. Luckily, there are proven ways to analyze the different sources of risks, assess the impact on the business and build various mitigation measures into the business strategy.

Rudi Zagst
(TUM, Germany)
The Crash-NIG Copula Model - Pricing of CDOs under changing market conditions

It is well known that the one-factor copula models are very useful for risk management and measurement applications involving the generation of scenarios for the complete universe of risk factors and the inclusion of CDO structures in a portfolio context. For this objective, it is necessary to have a simple and fast model that is also consistent with the scenario simulation framework. We present three extensions of the NIG one-factor copula model which jointly have not been considered so far: (i) tranches with different maturities modeled in a consistent way, (ii) a portfolio with different rating buckets, relaxing the assumption of a large homogeneous portfolio, and (iii) different correlation regimes. The regime-switching component of the proposed Crash-NIG copula model is especially important in view of the last credit crisis. We also introduce liquidity premiums into the Crash-NIG copula model and show that the credit crisis was substantially driven by liquidity effects.

Talk Abstracts

Yuri Lawryshyn (University of Toronto)
Valuing Risky Projects Based on Managerial Cash Flow Estimates: A Real Options Approach

Standard methods for valuing project alternatives are based on the Discounted Cash Flow (DCF) approach, where the weighted average cost of capital (WACC) is most commonly used as the discount factor. The DCF approach, by its nature, assumes that there is no managerial flexibility / optionality imbedded in the project, and that the financial risk profile of the cash-flows matches that of the average project, or investment, of the company. Real options analysis (ROA) has been recognized as a superior method for valuing managerial flexibility and can be utilized to estimate the value associated with managerial flexibility and to account for the risk profiles associated with cash-flow estimates. However, survey literature has shown that the adoption of ROA as a practitioner's tool has stagnated at a usage rate of approximately 10%, mostly because of the difficulty associated in practical implementation. We propose an approach which utilizes cash-flow estimates from managers as key inputs and results in project value cash-flows that exactly match arbitrary estimates. We achieve this through the introduction of an observable, but not tradable, market sector indicator process which drives the project's cash-flow, rather than modeling the project value directly. Our framework can be used to value managerial flexibilities and obtain hedges in an easy to implement manner for a variety of real options such as entry/exit, multistage, abandonment, etc. As well, our approach to ROA provides a co-dependence between cash-flows, is consistent with financial theory, requires minimal subjective input of model parameters, and bridges the gap between theoretical ROA frameworks and practice.

This is a joint work with Sebastian Jaimungal (University of Toronto)

Alexander Melnikov (University of Alberta)
Quantile risk management of equity-linked life insurance contracts with stochastic interest rate

The talk studies the problem of pricing equity-linked life insurance contracts in a two factor jump-diffusion financial market with stochastic interest rate, and focuses on the valuation of insurance contracts with stochastic guarantee. The contracts under consideration are based on two risky assets satisfying a two-factor jump-diffusion model: one asset is responsible for future gains, another one is a stochastic guarantee. As most life insurance products are long-term contracts, it is more practical to consider them in a stochastic interest rate environment instead of a constant interest rate. In our setting, stochastic interest rate is described by a jump-diffusion model too. Quantile hedging technique is exploited to price such finance/insurance contracts with initial capital constraints. Explicit formulas for both the price of the contracts and the survival probability are obtained. Our results are illustrated by numerical example based on financial indexes Russell 2000 and S&P 500.

Pablo Oliveres (Ryerson University)
Computing OR-risk measures: recent techniques and open problems

We discuss some recent advances and open problems in a Loss Distribution Approach under the context of operational risk and credit risk. Among those topics we review the modeling of severity, frequency and dependence between different business lines and type of events. We discuss asymptotic methods to compute probabilities far in the tail, therefore Value-at-Risk and expected shortfall. Also we address to the use of an Extreme Value approach in modeling the loss distribution and how to combine external and internal data.

Liayn Yang (Rotman School of Business, University of Toronto)
Differential Access to Price Information in Financial Markets

Recently exchanges have been supplementing their tape revenue by directly selling trade and quote data to some traders. We analyze how this practice affects the cost of capital, market liquidity and welfare by studying a two-period economy in which rational traders can purchase information about past transactions from the exchanges. In an economy in which traders are endowed with private signals about asset value, allowing the exchange to sell price data increases the cost of capital and worsens market liquidity relative to a world in which all traders freely observe previous prices. However, selling price data reduces the cost of capital and increases liquidity relative to an economy in which no traders can observe price information. If traders have to decide whether to purchase private signals, as well as whether to purchase price data, selling price data can cause traders to reduce their effort to gather information on the underlying asset. This secondary effect may increase the equilibrium cost of capital, but paradoxically it results in greater liquidity. Our welfare analysis also shows that as more previous price information is present in the market, noise traders are made better-off and speculative rational traders are made worse-off. In our view, allowing exchanges to sell price information is undesirable because it generally reduces efficiency and market quality. We believe that the practice should be restricted.


Session Abstracts

Nabeel Butt (University of Western Ontario)
A tree-based approximation for a multidimensional transaction cost model

The problem of optimizing portfolios in the presence of transaction costs has attracted significant interest. In this talk we consider a discrete-time formulation of a fixed cost transaction cost model. We examine applicability of numerical tree approximation as an alternative simplistic approach to solve transaction cost problems .The approach is able to solve a model in arbitrary dimensions and non-standard geometries. Using the exact probability model in context of dynamic programming could be computationally intensive for it might involve root finding or optimization of complicated integrals. We provide a computational study of tree-based method on a simple fixed transaction cost model and highlight its many advantages.

This is a joint work with Matt Davison (University of Western Ontario)

Ryan Donnelly (University of Toronto)
A Branch-and-Price Algorithm for Solving an Order Cutoff Assignment Problem

We investigate a particular class of guaranteed withdrawal benefit products where the underlying fund is a mixed fund and driven by two classes of diffusive processes: local volatility and stochastic volatility. By rewriting the guarantee as an Asian option, and through dimensional reduction techniques the problem is written in terms of a two dimensional PDE. We then provide an efficient ADI algorithm, whereby the correlation terms are treated explicitly while other operators are split, to solve the PDE and demonstrate how the various model parameters affect the valuation of this complex product. Finally, since these guarantees of very long termed, we demonstrate how stochastic interest rates can be easily incorporated.

This is a joint work with Sebastian Jaimungal (University of Toronto) and Dmitri Rubisov (BMO Capital Markets).

Kevin D. Ferreira (University of Toronto)
The Marketing of Innovative Products with Adoption Network Effects

Throughout history there have been many examples of innovations that "for-some-reason" were incredibly successful. On the flip-side, there are also numerous examples of innovations that may be deemed as incredible failures. New products are an important source of sales and profit for a firm; furthermore, new product developments typically involve large financial commitments. As a result, forecasting the acceptance of a new product would be a significant advantage to any firm. However, this task can often be difficult which is evident from the number of failed products that have been introduced to market. We present a word of mouth diffusion model that aims to shed some light on these conditions, and provide a tool to aid in the planning of the launch of a new innovation. It is able to capture the process by which customers become aware of a new technology via a diffusion function, and the adoption decision at the micro-level.

Meng Han (University of Toronto)
Approximations to Loss Probabilities in Credit Portfolios

Credit risk analysis and management at the portfolio level are challenging problems for financial institutions due to their portfolios' large size, heterogeneity and complex correlation structure. The conditional-independence framework is widely used to calculate loss probabilities for credit portfolios. The existing computational approaches within this framework fall into two categories: (1) simulation-based approximations and (2) asymptotic approximations. The simulation-based approximations often involve a two-level Monte Carlo method, which is extremely time-consuming, while the asymptotic approximations, which are typically based on the Law of Large Numbers (LLN), are not accurate enough for tail probabilities, especially for heterogeneous portfolios. We give a more accurate asymptotic approximation based on the Central Limit Theorem (CLT), and we discuss when it can be applied. To further increase accuracy, we also propose a hybrid approximation, which combines the simulation-based approximation and the asymptotic approximation. We test our approximations with some artificial and real portfolios. Numerical examples show that, for a similar computational cost, the CLT approximation is more accurate than the LLN approximation for both homogeneous and heterogeneous portfolios, while the hybrid approximation is even more accurate than the CLT approximation. Moreover, the hybrid approximation significantly reduces the computing time for comparable accuracy compared to simulation-based approximations.

This is a joint work with Alex Kreinin (Algorithmics) and Ken Jackson (University of Toronto).

Sean Jewell (University of Toronto)
Stochastic Pairs Trading through cointegration

Historically, simple pairs trading strategies have been a prevalent contrarian indicator, and many have practiced both fundamental and basic statistical approaches. Due to the utter inadequacy in using correlation as a stable indicator we borrow the notion of conintegration from econometrics to assemble stable baskets of securities. We retain pairs trading's essential concept--mean reversion-- and rebuild a strategy suggested by Kim: from a basket of cointegrated securities we fit a stochastic mean-reverting Ornstein-Uhlenbeck process, and implement dynamic-allocation methods to maximize an expected utility function. [1]

[1] Kim, S.-J., Primbs, J., and Boyd, S. Dynamic spread trading. Stanford University, June 2008.

Michael Jong Kim
(University of Toronto)
A Two-State Regime Switching Model with General Sojourn Time Distributions

Regime-switching models in financial time series typically follow an underlying Markov process. As a result, the sojourn times in each regime follows an exponential (in continuous time) or geometric (in discrete time) distribution. In real financial time series, this restrictive class of distributions may be unrealistic. In this paper we propose a two-state, continuous-time regime switching model with general sojourn time distribution. Multivariate return data that is stochastically related to the regime process is available at discrete time points. Using the EM algorithm, it is shown that maximizers of pseudo likelihood function have explicit closed form expressions. Furthermore, forecasting and value at risk (VaR) evaluation can be done analytically. The results developed in the paper are illustrated on real carbon emission financial data.

This is a joint work with Desheng Dash Wu (University of Toronto) and Luis Seco (University of Toronto).

Zheng Li (University of Toronto)
On Estimating Large Covariance Matrices

In statistical finance, data sets are becoming much larger, with more parameters. Old statistical methods
of handling data sets are no longer reasonable in many cases, as the increased
number of parameters make the standard covariance estimates converge far too slowly. This
talk will concern itself with certain methods of estimating the covariance matrix more efficiently, and the finance applications of these methods.

Melissa Mielkie (University of Western Ontario)
Dynamic Hedging in a Market Driven by Regime-Switching Volatility

Much work on pricing and hedging options has used either simple constant volatility stock price models or stochastic volatility models where volatility can take any positive value. Observation of real market data suggests that volatility, while stochastic, is well modeled by moves between a finite number (often just two) states. We propose that the transitional probabilities of volatility are given by an N-state Markov model, and that the actual jumps between volatility regimes are driven by independent Poisson jump processes. Heston's stochastic volatility technique of using an additional "hedging" derivative is employed. Practical problems with this approach for the two volatility state case lead us to examine several different hedging strategies to determine their profitability. We consider the effects of an option going too far in- or out-of the money on our hedging strategies, and show how the market price of volatility risk is necessary to price an option in a market driven by regime-switching volatility.

This is a joint work with Matt Davison (University of Western Ontario).

Mike Pavlin (University of Toronto)
Corporate Payout Policy, Cash Savings, and The Cost of Consistency: Evidence from a Structural Estimation

We develop a dynamic model in which firms choose their optimal financing, investment, dividends, and cash holdings while facing costly equity issuance, debt and capital adjustments costs and taxed interest on cash balances. We extend this base-case model to capture the effect of a manager, who perceives a cost to cutting payout. Applying simulated method of moments (SMM) to the dynamic model we infer that the magnitude of this downward adjustment cost accounts for an equity value loss of approximately 7% in US firms. Results include payout smoothing leading to increased accumulation of excess cash and larger estimated payout consistency cost for firms which have more dispersed analyst forecasts, compensate their CEOs with low pay-performance packages and have larger institutional holdings.

Jason Ricci
(University of Toronto)
Self-Exciting Marked Point Processes for Algorithmic Trading

Algorithmic Trading (AT) and High Frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data.
Recently, self-exciting processes have been used to model trading activity at high frequencies. Such processes can account for the clustering of intensity of trades and the feedback effect which trading induces. Here, we use a multi-factor Hawkes process to model the limit-order book dynamics and study the optimal control problem for a trader who places limit buy-and-sell orders in a limit order book with a stochastic fill rate function. Asymptotic expansions in the level of risk-aversion lead to closed form and intuitive results which are also adapted to the state of the market.

This is a joint work with Alvaro Cartea (University Carlos III) and Sebastian Jaimungal (University of Toronto)

Johnny Tam (University of Toronto)
A Branch-and-Price Algorithm for Solving an Order Cutoff Assignment Problem

We define an order cutoff for a retailer as a time in the day such that orders sent to the depot before this point will be delivered by tomorrow, and orders submitted after will be delivered by the day after tomorrow. The later a retailer's cutoff, the sooner it receives its orders which helps it to maintain ideal inventory levels. Given a choice of cutoffs, not all retailers in a supply chain can have the latest one since transportation takes a significant amount of time. This paper tries to assign optimal order cutoffs to retailers. We call this an order cutoff assignment problem and we solve it using a mathematical programming approach called branch-and-price. 60 sample problems were solved and results showed that branch-and-price becomes more effective as the number of vehicles increase but much less effective as the number of retailers increase.

Jue Wang (University of Toronto)
Prediction of fractal Physiological signals based on self-similarity

Abstract: Many physiological signals (e.g. heart rate, arterial blood pressure) exhibit complex fractal dynamics across multiple time scales, which can be difficult to model in traditional time series framework. A common feature of these fractal signals is statistical self-similarity: small parts of the signal resemble the whole in their statistical property. In this paper, we present a new prediction scheme by exploiting this self-similarity. The prediction is implemented in the wavelet domain: using Haar wavelet, the original prediction along the time axis is converted into the prediction of wavelet coefficients on a dyadic tree. We apply the new prediction methods to the mean arterial pressure (MAP) signals and found incorporating short-term variations can significantly improve the long-term prediction. The results suggest the self-similarity based prediction is an extremely promising tool for clinical practice.

Jean Xi (University of Western Ontario)
An inverse Stieltjes moment-based method in model parameter estimation under a Markov-modulated market

We consider a Markov-modulated Black-Scholes-type market consists of a riskless asset and a risky asset whose dynamics depend on an unobservable continuous-time Markov chain. The coupled system of Dupire-type partial differential equations satisfied by the option price in such a market is derived. Using an inverse Stieltjes moment approach, we recover the model parameters, which include the volatilities and the intensity rates of the Markov chain. We show the applicability and accuracy of our proposed method by proving numerical demonstrations. Sensitivity analyses are also carried out to examine the behaviour of the estimated results when model parameters are varied.

This is a joint work with Rogemar Mamon (University of Western Ontario) and Marianito Rodrigo (University of Wollongong).

Pei Jun Zhao
(University of Toronto)
Drug Development - A Tale of Financial Risks and Gains

Drug development is an expensive and risky process for every pharmaceutical company. From market research to laboratory experimentation, companies often face numerous failures before gaining an insightful or serendipitous drug discovery. This is then followed by years of testing and awaiting government approval. Currently, the price tag in releasing a new drug onto the market is, on average, anywhere from $300 to $800 million. Thus, to cover the cost of research, development, and accreditation, the drug must be stand the test of time, and sell successfully for years to come. With rapid advancement in biotechnology, cutting-edge pharmaceutical research may lead to novel drugs, but often at the expense of increased risk. So it is very important to take a balanced approach. First, companies should wait until more research has confirmed the safety and efficacy of recent biotechnology. Second, companies must not lose out on future market share. Finally, as the cost of genetic testing decreases, and as the technology attains popularity in society, the field of genetic screening offers a new frontier in the design of custom-made drugs that fit individual needs while minimizing side-effects - all in an attempt to lower risks and increase gains.

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