2022 Optimization Days

HEC Montréal, Québec, Canada, 16 — 18 May 2022

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TB1 - Recent advances in numerical methods for financial engineering

May 17, 2022 03:30 PM – 05:10 PM

Location: Walter Capital (blue) Previously BDC

Chaired by David Ardia

5 Presentations

  • 03:30 PM - 03:50 PM

    Multiperiod portfolio allocation: a study of volatility clustering, non-normalities and predictable returns

    • Michel Denault, presenter, GERAD - HEC Montréal
    • Jean-Guy Simonato, HEC Montréal

    We examine a dynamic, multiperiod portfolio facing predictable returns with GARCH volatilities and Johnson-distributed errors. Allocations are obtained by quadrature. Accounting for volatility clustering strongly reduces the large hedging demands typically seen. Out-of-sample tests reveal mixed but interesting evidence about the benefits for the returns of using a multiperiod approach with volatility clustering.

  • 03:50 PM - 04:10 PM

    Equal Risk Pricing of Derivatives with Reinforcement Learning

    • Frédéric Godin, presenter, Concordia

    The equal risk pricing methodology for derivatives pricing is introduced. The deep reinforcement learning associated implementation is discussed. Numerical experiments results are presented, along with an analysis of the choice of the objective function and of the hedging instruments. The approach is also benchmarked against traditional pricing methods.
    The talk is based among others on the following papers:
    Carbonneau, A., & Godin, F. (2021). Equal risk pricing of derivatives with deep hedging. Quantitative Finance, 21(4), 593-608.
    Carbonneau, A., & Godin, F. (2021). Deep equal risk pricing of financial derivatives with multiple hedging instruments. arXiv preprint arXiv:2102.12694.
    Carbonneau, A., & Godin, F. (2021). Deep equal risk pricing of financial derivatives with non-translation invariant risk measures. arXiv preprint arXiv:2107.11340.

  • 04:10 PM - 04:30 PM

    Optimal quadratic hedging in discrete-time under basis risk

    • Ismael Assani, presenter, Université de Montréal

    Basis risk arises whenever one hedges a derivative using an instrument different from the underlying asset. Recent literature has shown that this risk can significantly impair hedging effectiveness. This article derives new semi-explicit expressions for optimal discrete-time quadratic hedging strategies under basis risk when the dynamics of the underlying asset and of the hedging instrument are driven by correlated processes with stationary and independent increments. The solutions are derived under the physical measure in terms of inverse Laplace (or Fourier) transforms and can be computed accurately in a fraction of a second. Several numerical experiments are conducted to evaluate the performance of optimal quadratic hedges for different levels of basis risk. Overall, we find that these hedges can significantly reduce the risk of hedging options with long-term maturities. Moreover, we observe that the relative gains achieved over a benchmark delta hedge are larger when the hedging strategy is exposed to basis risk than if it is not.

  • 04:30 PM - 04:50 PM

    Computationally-efficient Variance Filtering in Multidimensional Affine Models

    • Gabrielle Trudeau, presenter, HEC Montréal
    • Geneviève Gauthier, HEC Montréal
    • Christian Dorion, HEC Montreal

    Estimating multidimensional stochastic volatility (SV) models can rapidly become challenging. As the number of latent variables increases, obtaining unbiased estimates of the parameters and latent variables is increasingly challenging with existing filters. Building on the informativeness of intraday statistics, we develop an analytical filter that achieves unbiasedness while remaining highly tractable even as the number of volatility components, or assets, or both increase.

  • 04:50 PM - 05:10 PM

    The impact of safety covenants in syndicated loan agreements

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

    We propose a stochastic dynamic game model of syndicated loan contract
    adjustments in the presence of a safety covenant. The model accounts for the
    lender's right to punish (increase the interest payments or the collateral)
    or tolerate any breach of the covenant, and for the borrower's flexibility
    in adjusting its investment and risk-taking strategy. We consider a
    Stackelberg setting under two possible information structures; in the first
    case, the lender uses a feedback strategy (variable spread), while in the
    second case, the lender's strategy is open-loop (performance pricing). Our
    numerical experiments show that, while a safety covenant improves the loan
    value in most states, it can have an adverse effect when bankruptcy risk
    becomes important. Additional investigation shows that the lender can
    optimally tolerate some technical default to prevent this adverse effect.