Equal Risk Pricing of Derivatives with Deep Hedging

Carbonneau, Alexandre; Godin, Frédéric

doi:10.48550/arxiv.2002.08492

Cited by 1 publication

(6 citation statements)

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“…It is important to note that the choice of dynamics for the financial market could imply that relevant necessary information to compute the time-t n trading strategy should be added to feature vectors. For instance, Carbonneau and Godin (2020) apply the deep hedging algorithm with GARCH models which entails adding the volatility process to feature vectors. In the current paper, the models considered for the underlying imply that {S…”

Section: Methodsmentioning

confidence: 99%

“…The numerical scheme to optimize the trainable parameters θ is now described. For convenience, a similar notation as in the work of Carbonneau and Godin (2020) is used. For a given loss function and an initial portfolio value, the objective is to find θ such that the risk exposure of a short position in Φ is minimized (i.e.…”

Section: Training Of Neural Networkmentioning

confidence: 99%

“…While the MSE and SMSE are the only penalties considered in numerical experiments of Section 4, the optimization procedure for global hedging policies presented in Section 3 is flexible to any well-behaved penalties (see e.g. Carbonneau and Godin (2020) for an implementation with the Conditional Value-at-Risk measure).…”

Section: Optimal Hedging Problemmentioning

confidence: 99%

“…Li et al (2009), Becker et al (2019) and Carbonneau and Godin (2020)). Hedging has also received some attention: Halperin (2020) and Kolm and Ritter (2019) propose TD-learning approaches to the hedging problem and Hongkai et al (2020) and Carbonneau and Godin (2020) deep hedge European options under respectively the quadratic penalty and the Conditional Value-at-Risk measure. The deep hedging algorithm trains an agent to learn how to approximate optimal hedging decisions by neural networks through many simulations of a synthetic market.…”

Section: Introductionmentioning

confidence: 97%

“…Jiang et al (2017) and Almahdi and Yang (2017)) and option pricing (e.g. Li et al (2009), Becker et al (2019) and Carbonneau and Godin (2020)). Hedging has also received some attention: Halperin (2020) and Kolm and Ritter (2019) propose TD-learning approaches to the hedging problem and Hongkai et al (2020) and Carbonneau and Godin (2020) deep hedge European options under respectively the quadratic penalty and the Conditional Value-at-Risk measure.…”

Section: Introductionmentioning

confidence: 99%

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Deep Hedging of Long-Term Financial Derivatives

Carbonneau¹

2020

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This study presents a deep reinforcement learning approach for global hedging of longterm financial derivatives. A similar setup as in Coleman et al. ( 2007) is considered with the risk management of lookback options embedded in guarantees of variable annuities with ratchet features. The deep hedging algorithm of Buehler et al. (2019a) is applied to optimize neural networks representing global hedging policies with both quadratic and non-quadratic penalties. To the best of the author's knowledge, this is the first paper that presents an extensive benchmarking of global policies for long-term contingent claims with the use of various hedging instruments (e.g. underlying and standard options) and with the presence of jump risk for equity. Monte Carlo experiments demonstrate the vast superiority of non-quadratic global hedging as it results simultaneously in downside risk metrics two to three times smaller than best benchmarks and in significant hedging gains. Analyses show that the neural networks are able to effectively adapt their hedging decisions to different penalties and stylized facts of risky asset dynamics only by experiencing simulations of the financial market exhibiting these features. Numerical results also indicate that non-quadratic global policies are significantly more geared towards being long equity risk which entails earning the equity risk premium.

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Section: Methodsmentioning

confidence: 99%

Section: Training Of Neural Networkmentioning

confidence: 99%

Section: Optimal Hedging Problemmentioning

confidence: 99%