Journées de l'optimisation 2022
HEC Montréal, Québec, Canada, 16 — 18 mai 2022
TB1  Recent advances in numerical methods for financial engineering
17 mai 2022 15h30 – 17h10
Salle: Walter Capital (bleu) Anciennement BDC
Présidée par David Ardia
5 présentations

15h30  15h50
Multiperiod portfolio allocation: a study of volatility clustering, nonnormalities and predictable returns
We examine a dynamic, multiperiod portfolio facing predictable returns with GARCH volatilities and Johnsondistributed errors. Allocations are obtained by quadrature. Accounting for volatility clustering strongly reduces the large hedging demands typically seen. Outofsample tests reveal mixed but interesting evidence about the beneﬁts for the returns of using a multiperiod approach with volatility clustering.

15h50  16h10
Equal Risk Pricing of Derivatives with Reinforcement Learning
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), 593608.
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 nontranslation invariant risk measures. arXiv preprint arXiv:2107.11340. 
16h10  16h30
Optimal quadratic hedging in discretetime under basis risk
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 semiexplicit expressions for optimal discretetime 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 longterm 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.

16h30  16h50
Computationallyefficient Variance Filtering in Multidimensional Affine Models
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.

16h50  17h10
The impact of safety covenants in syndicated loan agreements
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 risktaking 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 openloop (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.