Réunion d'hiver SMC 2025
Toronto, 5 - 8 decembre 2025
- ALEXANDRU BADESCU, University of Calgary
- FRANÇOIS-MICHEL BOIRE, University of Ottawa
- TAHIR CHOULLI, University of Alberta
Pricing formulas for vulnerable claims and death derivatives [PDF]
- FRANÇOIS-MICHEL BOIRE, University of Ottawa
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We consider the discrete-time market model described by the triplet $(S, \mathbb{F},\tau)$. Herein $\mathbb{F}$ is the ``public" flow of information which is available to all agents overtime, $S$ is the discounted price process of $d$-tradable assets, and $\tau$ is an arbitrary random time whose occurrence might not be observable via $\mathbb{F}$. This framework covers the credit risk theory where $\tau$ represents the default time, the life insurance setting where $\tau$ models the death time, and other areas of finance. For various vulnerable claims in credit risk and death derivatives in life insurance, we address the super-hedging pricing valuation problem in many aspects. First of all, we discuss how the Immediate-Profit arbitrage (IP for short), which is the economical assumption that guarantees the existence of the ``minimal" super-hedging price ${\widehat{{P}}}^{\mathbb{G}}$, is affected by $\tau$. Then we show, as explicit as possible, how the set of all super-hedging prices expands under the stochasticity of $\tau$ and its various risks. Afterwards, we elaborate, as explicit as possible, the pricing formulas for vulnerable claims and death derivatives. Finally, we single out explicitly the various informational risks in the dynamics of the price process ${\widehat{{P}}}^{\mathbb{G}}$ and quantify them. This latter fact is highly important for the mortality and longevity securitizations.
This talk is based on the following joint work with Emmanuel Lepinette (Paris-Dauphine, France):
T. Choulli and Emmanuel: Super-hedging-pricing formulas and Immediate-Profit arbitrage for market models under random horizon. to appear in Finance and Stochastics. A version of the paper is available at: arXiv:2401.05713.
- MATT DAVISON, Western University
- DENA FIROOZI, University of Toronto
Ranking Quantilized Mean-Field Games and Early-Stage Venture Investments [PDF]
- DENA FIROOZI, University of Toronto
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We study a class of quantilized mean-field game models with a capacity for ranking games, where the performance of each agent is evaluated based on its terminal state relative to the population's $\alpha$-quantile value, $\alpha \in (0,1)$. This evaluation criterion is designed to select the top $(1-\alpha)\%$ performing agents. We provide two formulations for this competition: a target-based formulation and a threshold-based formulation. In the former and latter formulations, to satisfy the selection condition, each agent aims for its terminal state to be exactly equal and at least equal to the population's $\alpha$-quantile value, respectively.
For the target-based formulation, we obtain an analytic solution and demonstrate the $\epsilon$-Nash property for the asymptotic best-response strategies in the $N$-player game. Specifically, the quantilized mean-field consistency condition is expressed as a set of forward-backward ordinary differential equations, characterizing the $\alpha$-quantile value at equilibrium. For the threshold-based formulation, we obtain a semi-explicit solution and numerically solve the resulting quantilized mean-field consistency condition.
Subsequently, we propose a new application in the context of early-stage venture investments, where a venture capital firm financially supports a group of start-up companies engaged in a competition over a finite time horizon, with the goal of selecting a percentage of top-ranking ones to receive the next round of funding at the end of the time horizon. We present the results and interpretations of numerical experiments for both formulations discussed in this context and show that the target-based formulation provides a very good approximation for the threshold-based formulation.
- CHRISTOPH FREI, University of Alberta
A Doubly Continuous Model for Equilibrium Trading Dynamics [PDF]
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Analysis of financial markets is usually based on rational expectations, where investors use all available information to trade in order to maximize their expected utility. In equilibrium models, prices are determined so that the market clears, meaning that demand equals supply. Typically, diverging information among homogeneous agents is not enough to generate trade in
equilibrium. To address this issue, we introduce and analyze a doubly continuous model with continuous time and continuous agent space. In this setting, each agent is infinitesimally small, contributing zero to trade, while collective trade emerges from the aggregation over non-negligible sets of agents. Our approach leverages tools from Brownian sheets and multiparametric stochastic calculus, providing insights into the interplay of information, behaviour, and equilibrium in financial markets.
This talk is based on joint work with Efstathios Avdis (University of Alberta), Sergei Glebkin (INSEAD), and Raphael Huwyler (University of Alberta).
- NIUSHAN GAO, Toronto Metropolitan University
- GENEVIÈVE GAUTHIER, HEC Montréal
Beyond volatility of volatility: Decomposing the informational content of VVIX [PDF]
- GENEVIÈVE GAUTHIER, HEC Montréal
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This study investigates the informational content of the VVIX, traditionally viewed as a proxy for the S\&P 500 index's volatility of the volatility (VOV). We show that this interpretation is incomplete: the VVIX also embeds a long-run variance (LRV) component. To establish this result, we first demonstrate that regressions of squared VVIX on VOV proxies gain substantial explanatory power once LRV measures are incorporated. We then develop a tractable theoretical framework linking VVIX to three risk drivers---instantaneous variance, LRV, and VOV---and show that the VVIX loads on both VOV and LRV. Our empirical analysis reveals that VVIX dynamics are dominated by LRV in calm markets, but by VOV during financial stress. We further show that these variance components explain option returns in distinct markets: S\&P 500 index option straddles load on the instantaneous variance and LRV, while VIX option straddles load on the VOV. Taken together, our results redefine the role of the VVIX, establishing it as a measure of both VOV and LRV uncertainty, with important implications for how it should be read and used by finance practitioners.
- FRÉDÉRIC GODIN, Concordia University
Deep Hedging with Options Using the Implied Volatility Surface [PDF]
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We propose a deep hedging framework for index option portfolios, grounded in a realistic market simulator that captures the joint dynamics of S\&P 500 returns and the full implied volatility surface. Our approach integrates surface-informed decisions with multiple hedging instruments and explicitly accounts for transaction costs. The hedging strategy also considers the variance risk premium embedded in the hedging instruments, enabling more informed and adaptive risk management. Tested on a historical out-of-sample set of straddles from 2020 to 2023, our method consistently outperforms traditional delta-gamma hedging strategies across a range of market conditions.
- MATHEUS GRASSELLI, McMaster University
- CODY HYNDMAN, Concordia University
- ANASTASIS KRATSIOS, McMaster University
- ANNE MACKAY, Université de Sherbrooke
Pricing lookback options on quantum computers [PDF]
- CODY HYNDMAN, Concordia University
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Quantum computing promises computational speed up that could have a significant impact across industries. In this presentation, we explore the application of VarQITE, a quantum time evolution algorithm, to option pricing. Extending the work of Fontanela et al. (2021), we consider discretely monitored lookback options and use VarQITE to solve a partial differential equation associated to its price. To address the jump condition in the PDE, which poses a significant challenge in the quantum implementation, we re-write it in terms of multiple continuous equations, thus improving the accuracy of the results. A brief introduction to quantum computing will also be presented.
- ROMAN MAKAROV, Wilfrid Laurier University
- ALEXANDER MELNIKOV, University of Alberta
On Market Completions Approach to Option Pricing and Related Questions [PDF]
- ALEXANDER MELNIKOV, University of Alberta
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We consider a financial market with a reducible incompleteness. It means that the market can be embedded to a complete market by adding new risky assets. We call such embedding as a market completion. In the framework of such a market one can give a dual characterization of upper and lower option prices via maximization/minimization of expectations of discounted payoffs over market completions instead of martingale measures. Moreover, the method also works for the so-called indifference option pricing. To improve option price approximations, we explore a combination of the market completion method and machine learning technique in an incomplete jump-diffusion market model. Finally, we show how this approach work in life insurance applications.
- ADAM METZLER, Wilfrid Laurier University
- JINNIAO QIU, University of Calgary
Some recent progress on stochastic HJB equations [PDF]
- JINNIAO QIU, University of Calgary
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In this talk, we shall present some recent progress in the study of stochastic Hamilton-Jacobi-Bellman (HJB) equations, which arise naturally in the context of non-Markovian control problems, particularly within the field of mathematical finance. The non-Markovian nature of these problems may also involve path dependence or mean-field interactions, in addition to general randomness in the coefficients. The discussion will cover various aspects, including the well-posedness of such stochastic HJB equations, numerical approximations, and their applications.
- MARK REESOR, Wilfrid Laurier University
- ALEXANDRE ROCH, Université du Québec à Montréal
- DAVID SAUNDERS, University of Waterloo
- ALEXANDER SCHIED, University of Waterloo
- XIAOFEI SHI, University of Toronto
- KRISTINA STANKOVA, University of Western Ontario
Applying ruin theory to retirement savings: A case study [PDF]
- ALEXANDRE ROCH, Université du Québec à Montréal
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In this talk, we will discuss how an advanced ruin theory model can be applied to retirement savings of individuals aiming at evaluating long-term risks related to their portfolios. To illustrate our approach, we fit the model to transactional data provided by a registered investment provider to the Financial Wellness Lab at Western University. We split the clients by gender and risk tolerance and examine how investment portfolios evolve over time in each group of clients.
- LARS STENTOFT, Western University
- ANTONY WARE, University of Calgary
- TING-KAM LEONARD WONG, University of Toronto
- FOIVOS XANTHOS, Toronto Metropolitan University
- ANTONY WARE, University of Calgary