4 Presentations

• 
  10:30 AM - 10:55 AM

  Deep Hedging with Market Impact

  • Andrei Neagu, presenter, Concordia University
  • Frédéric Godin, Concordia University
  • Clarence Simard, Université du Québec à Montréal
  • Leila Kosseim, Concordia University

  This work explores the optimization of hedging strategies for financial options in the presence of imperfect liquidity for the underlying asset. A deep reinforcement learning approach is used to obtain the solution to the problem of minimizing global hedging losses risk under a given illiquidity market impact model. Numerical investigations reveal that the discrepancies between the optimal policy and delta hedging benchmarks are complex and materially driven by various interacting (and sometimes competing) parameters and state variables, such as market depth and impact resilience parameters, the underlying asset drift, the hedging portfolio value, time-to-maturity and past hedging positions. Such complexity highlights the need to rely on sophisticated optimization schemes such as deep reinforcement learning to uncover the optimal policy.

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  10:55 AM - 11:20 AM

  Portfolio Optimization Driven By Quantum-Inspired Techniques

  • Ethan Wang, presenter, InfinityQ Technology Inc.

  The two primary objectives of portfolio optimization are to maximize expected return and minimize risk. Optimizing both objectives simultaneously is an NP-hard problem known as Mean-Variance Optimization (MVO). To reduce its complexity, a strategy is to first select a subset of weakly correlated assets before MVO, which reduces the problem size and promotes a lower risk portfolio. The problem of selecting such a subset can be mapped to the classic Maximum Weighted Independent Set (MWIS) problem, which we then formulate as a Quadratic Unconstrained Binary Optimization (QUBO) problem. In this study, we test this strategy on various market indices using TitanQ, a quantum-inspired optimization solver developed by InfinityQ Technology. In a fast-paced industry such as quantitative finance, the speed and scalability that quantum-inspired computing offers is crucial in creating a competitive edge, especially in high frequency trading where large markets need to be analyzed in milliseconds. We analyze methods of mapping the MWIS problem to the QUBO model and compare the performance of portfolios with their respective MWIS sub-portfolio. Backtesting with historical data from the Python library yfinance, the strategy provides a 3.32% greater expected return and a 1.17% lower risk on average across portfolios of sizes 29 to 467.

• 
  11:20 AM - 11:45 AM

  Risk-Averse Policy Gradient for Tail Risk Optimization Using Extreme Value Theorem

  • Parisa Davar, presenter, Concordia University

  In this work, our focus is on the risk-averse Policy Gradient algorithm in a tail risk optimization problem. Our objective is to find the optimal policy that minimizes tail risk, given a risk measure such as CVaR. We employed Extreme Value Theory (EVT), along with the automated threshold method to manage risks associated with extreme events. This paper is the first to integrate EVT within RL algorithms for sequential decision making. To evaluate our approach, we initially tested it on simulated data generated from the Generalized Pareto Distribution (GPD) and the Burr distribution. Subsequently, we applied our method to address a hedging problem, aiming to mitigate exceedingly high risks and finding optimal gamma hedging strategies within a highly volatile market where options are notably expensive. This involved identifying the optimal proportion of gamma to utilize for hedging, while minimizing costs and risk associated with gamma hedging errors. We utilize the finite difference method to approximate the gradient of the estimated CVaR. The experimental results indicate convergence in the policy, CVaR estimation, and the gradient approximation of estimated CVaR. Moreover, integrating EVT into risk-averse policy gradient methods significantly improves performance, especially in markets following a Normal Inverse Gaussian distribution (NIG).

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  11:45 AM - 12:10 PM

  Valuation of syndicated revolving credit line in the presence of covenants

  • Michèle Breton, GERAD, HEC Montréal
  • Tiguene Nabassaga, presenter, GERAD, HEC Montréal

  Revolving loan commitments are not generally traded in the secondary market; hence, it is not possible to use market-to-market valuation for this type of facility. In the literature, two families of approaches have been proposed to value revolving loan commitment: contingent claims (Hawkins 1982, Chateau 1990), and game theory (Boot, Thakor, and Udell 1987, T. S. Campbell 1978). We seek to contribute to the methodology as well as the application point of view. We introduce a valuation model approach based on a dynamic stochastic game. The model accounts for the lender’s right to change the spread or to refuse a drawn from the facility in certain circumstances, and for the first time, the borrower’s flexibility in changing their risk-taking strategy (possibility of asset substitution). This is formalized as a stochastic dynamic game with a leader (the lender) and a follower (the borrower) using feedback strategies.

  We use the model to value a syndicated facility package that includes a term loan and a revolving credit line. We consider various facility management options, including full or partial take-down for the borrower, with and without the right to freeze the facility for the leader. The presence of revolving credit adds value to the facility when the borrower’s leverage is relatively low. The lender can optimally allow the draw from the facility even when the borrower is in technical default.