2018-19 Financial Mathematics Seminars

If you are interested in giving a talk at our seminar please contact Foivos Xanthos (foivos@ryerson.ca).

Upcoming Seminars

Monday, December 3 , 2018 at 2:00pm, Location: ENG-210
Dr. Michael Hasler , Rotman School of Management, University of Toronto
Title: The CAPM Holds.
Abstract: Under realistic conditions, the conditional risk premium of an asset is equal to its conditional market beta times the conditional risk premium of the market (Merton, 1972). We empirically test this CAPM relation using beta-sorted portfolios, size-and-book-to-market sorted portfolios, and industry portfolios. We show that regressing an asset excess return onto the product of its conditional beta and the market excess return yields an R2 of about 80%, an intercept of zero, and a slope of one. These results provide strong evidence that a single factor explains both the level and the variation in the cross-section of returns.

Recent Seminars

Thursday, November 15 , 2018 at 2:00pm, Location: ENG-210
Dr. Yisong S. Tian , Schulich School of Business York University
Title: A moving average design for stock option plans.
Abstract: Previous research suggests that Asian stock options provide stronger managerial incentives than traditional stock options do and ameliorate the problem of managerial gaming. We show that these options lose most of the initial advantage in managerial incentives in just six months after the grant date and then provide a similar level of incentives in the subsequent one to three years. Beyond that, they provide weaker incentives than traditional stock options do over the last five to seven years of the option grant’s life. o solve the problem of diminishing incentives, life-time averaging should be replaced with moving averages. Moving average options not only maintain the level of incentives over time but are also effective in protecting against managerial gaming.

Thursday, September 20 , 2018 at 2:00pm, Location: ENG-210
Dr. Tuan Quoc Tran , Ryerson University
Title: Asset fire sales and strategic trading by regulated banks.
Abstract: This paper aims to understand how regulatory constraints on liquidity and capital affect the behaviour of financial institutions participating in and impacting the open market for banking assets. Bank strategies that optimally account for the trading of other banks can replace the naive behaviour assumptions currently at the heart of financial systemic risk models. To this end, a multi-agent game is introduced, where each agent is a bank that trades a single risky asset to maximize its profi t while satisfying certain requirements set up by the regulator. Each bank's trading is assumed to have a signifi cant impact on the price, which is taken into account by all banks' strategies. We prove the existence of Nash equilibrium strategies for the game, provide algorithms to find these equilibrium strategies, and explore some of the implications of the model.

Thursday, September 6 , 2018 at 3:00pm, Location: ENG-210
Prof. Wei Xu, Tongji University, Shanghai, China
Title: Machine Learning Methods for Risk Management of Large Variable Annuity Portfolios
Abstract: Variable annuity (VA) embedded guarantees have rapidly grown in popularity around the world in recent years. Valuation of VAs has been studied extensively in past decades. However, most of these studies focus on a single contract. These methods cannot be extended to value a large variable annuity portfolio due to the computational complexity. We propose an efficient moment matching machine learning method to compute the annual dollar deltas, VaRs and CVaRs for a large variable annuity portfolio whose contracts are over a period of 25 years. There are two stages for our method. First, we select a small number of contracts and propose a moment matching Monte Carlo method based on the Johnson curve, rather than the well known nested simulations, to compute the annual dollar deltas, VaRs and CVaRs for each selected contract. Then, these computed results are used as a training set for well known machine learning methods, such as regression tree, neural networks, and so on. Afterwards, the annual dollar deltas, VaRs and CVaRs for the entire portfolio are predicted through the trained machine learning method. Compared to other existing methods, our method is very efficient and accurate, especially for the first 10 years from the initial time. Finally, our test results support our claims.

Thursday, March 29, 2018 at 2:00pm, Location: ENG-210
Anastasis Kratsios, Concordia University
Title: Arbitrage - Free Regularization
Abstract: We introduce a novel framework that generalizes the HJM modeling approach to a wide variety of asset classes. This framework allows us to remove arbitrage - opportunities from a model within a given class using a new regularization procedure that minimally deforms the model subject to an arbitrage penalty. This technique extends classical financial modeling methods by first using interpretable factor - models that fit the data well, and subsequently applying the arbitrage - free regularization procedure. We illustrate the approach through implementations for forward - rate curves and stochastic local volatility surfaces. This talk is based on joint work with Cody Hyndman (Concordia University).

Thursday, November 23, 2017 at 10:30am, Location: ENG-210
Dr. Bin Zou, University of Connecticut
Title: Systemic Risk and Optimal Design of Central Clearing Counterparty (CCP)
Abstract: We propose a novel central clearing counterparty (CCP) design for a financial network with multilateral clearing, where the participation rate of individual banks depends on the volume-based fee charged by the CCP. We introduce a general demand function for the individual banks' participation rate, and seek the optimal fee that maximizes the net worth of the CCP. The optimal fee is explicitly solved for the case of a quadratic demand function. We show that partial participation of banks in the CCP at the optimal fee rate reduces banks' aggregate shortfall in the financial network and also reduces the overall systemic risk. This result justifies the alignment of interests of the profitable aspect and the regulatory aspect of the CCP. Furthermore, we carry out numerical examples to verify the theoretical results.

Thursday, November 16, 2017 at 10:30am, Location: ENG-210
Dr. Cosimo-Andrea Munari, University of Zurich
Title: Risk Measures in Mathematical Finance
Abstract: The aim of the talk is to provide a broad overview of the theory of risk measures and their applications to finance and insurance. We will assess what has been achieved so far and discuss a variety of recent, partly still open, research questions. In particular, we will pay special attention to the prominent class of cash-additive risk measures and argue why one should go beyond cash-additivity.

Thursday, April 6, 2017 at 3:00pm, Location: ENG-210
Dr. Ruodu Wang, University of Waterloo
Title: A theory for measures of tail risk
Abstract: The notion of “tail risk” has been a crucial consideration in modern risk management. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures which quantify the tail risk, that is, the behavior of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this talk. The two popular classes of regulatory risk measures in banking and insurance, the Value-at-Risk (VaR) and the Expected Shortfall (ES), are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs. The study on tail risk measures brings in new tools and insights for prudent risk management as highlighted in the recent Basel documents on financial regulation. This talk focuses on mathematical developments of the theory.

Thursday, November 17, 2016 at 2:00pm, Location: ENG-210
Dr. Sebastian Ferrando, Ryerson University
Title: Trajectorial Martingales, Null Sets, Integration and Convergence.
Abstract: Starting with a trajectory space, providing a non-stochastic analogue of a martingale process, we use the notion of super replication to introduce a definition for a null function and the associated notion of a property holding almost everywhere (a.e.). The latter providing what can be seen as the worst case analogue of sets of measure zero in a stochastic setting. The a.e. notion is used to prove the pointwise convergence, on a full set of the original trajectory space, of the limit of a trajectorial martingale transform sequence. The setting also allows to construct a natural integration operator.

Thursday, October 27, 2016 at 2:00pm, Location: ENG-210
Dr. Foivos Xanthos, Ryerson University
Title: Robust representations of risk measures on Orlicz spaces
Abstract: In 2002, Delbaen proved a robust representation theorem for risk measures on L via L1. It has since been an intriguing problem to extend this result to a more general class of underlying spaces. In this talk, we present a solution to this problem for Orlicz spaces.

Thursday, September 29, 2016 at 2:30pm, Location: ENG-210
Dr. Pablo Olivares, Ryerson University
Title: Pricing and Hedging some Crack and Spark Contracts in Energy Markets under Levy Processes
Abstract: We discuss the pricing of some derivative contracts in the Energy market whose payoff depends on the value of multiple assets. In particular, we focus on European and Barrier options having electricity, gasoline, natural gas and uranium as underlying assets. In order to capture their particular dynamic, we consider models with discontinuous jumps and mean reverting properties. Several ad-hoc approximations and numerical issues are analysed.

Thursday, January 28, 2016 from 12:00pm-1:00pm, Location: ENG288
Speaker: Michael Hasler, Rotman School of Management, University of Toronto
Dynamic Attention Behaviour Under Return Predictability

Thursday, January 21, 2016, 1-2pm, Location: VIC736
Speaker: Dr. Oleksandr Romanko, Research Analyst,
Risk Analytics - Business Analytics, IBM Canada
Adjunct Professor, University of Toronto
Scenario-Based Financial Value-at-Risk Optimization

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