Discrete-time Variance-optimal Deep Hedging in Affine GARCH Models

Cao, Hongkai; Cui, Zhenyu; Liu, Yanchu

doi:10.2139/ssrn.3659275

Cited by 3 publications

(4 citation statements)

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“…Conversely, Carbonneau andGodin (2021a, 2021b) use the deep reinforcement learning approach of Buehler et al (2019) coined as deep hedging. Other papers have relied on the deep hedging methodology for the hedging of financial derivatives: Cao et al (2020), Carbonneau (2021), Horvath et al (2021 and Lütkebohmert et al (2022). Deep reinforcement learning is a very convenient technique for multistage optimization and decision making in financial contexts: it allows tackling high-dimensional settings with multiple state variables, underlying asset dynamics and trading instruments.…”

Section: Literature Reviewmentioning

confidence: 99%

Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures

Carbonneau

Godin

2023

Risks

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The objective is to study the use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives. The ability to move beyond the class of convex risk measures considered in several prior studies provides more flexibility within the pricing scheme. In particular, suitable choices for the risk measure embedded in the ERP framework, such as the semi-mean-square-error (SMSE), are shown herein to alleviate the price inflation phenomenon observed under the tail value at risk-based ERP as documented in previous work. The numerical implementation of non-translation invariant ERP is performed through deep reinforcement learning, where a slight modification is applied to the conventional deep hedging training algorithm so as to enable obtaining a price through a single training run for the two neural networks associated with the respective long and short hedging strategies. The accuracy of the neural network training procedure is shown in simulation experiments not to be materially impacted by such modification of the training algorithm.

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Section: Literature Reviewmentioning

confidence: 99%

Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures

Carbonneau

Godin

2023

Risks

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“…The periodic computation of long short-term memory neural networks is done with so-called LSTM cells, which are similar to but more complex than the typical hidden layer of RNNs. LSTMs have recently been applied with success to approximate global hedging policies in several studies: Buehler et al (2019a), Cao et al (2020) and Carbonneau (2020). Additional remarks are made in subsequent sections to motivate this choice of neural networks for the specific setup of this paper.…”

Section: Deep Equal Risk Pricingmentioning

confidence: 99%

“…Carbonneau and Godin (2020) also introduce novel -completeness metrics to quantify the level of market incompleteness which will be used throughout this current study. Several papers have studied different aspects of the class of deep hedging algorithms: Buehler et al (2019a) extend upon the work of Buehler et al (2019b) by hedging path-dependent contingent claims with neural networks, Carbonneau (2020) presents an extensive benchmarking of global policies parameterized with neural networks to mitigate the risk exposure of very long-term contingent claims, Cao et al (2020) show that the deep hedging algorithm provides good approximations of optimal initial capital investments for variance-optimal hedging problems and Horvath et al (2021) deep hedge in a non-Markovian framework with rough volatility models for risky assets.…”

Section: Introductionmentioning

confidence: 99%

Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments

Carbonneau,

Godin

2021

Preprint

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This paper studies the equal risk pricing (ERP) framework for the valuation of European financial derivatives. This option pricing approach is consistent with global trading strategies by setting the premium as the value such that the residual hedging risk of the long and short positions in the option are equal under optimal hedging. The ERP setup of Marzban et al.(2020) is considered where residual hedging risk is quantified with convex risk measures.The main objective of this paper is to assess through extensive numerical experiments the impact of including options as hedging instruments within the ERP framework. The reinforcement learning procedure developed in Carbonneau and Godin (2020), which relies on the deep hedging algorithm of Buehler et al. (2019b), is applied to numerically solve the global hedging problems by representing trading policies with neural networks. Among other findings, numerical results indicate that in the presence of jump risk, hedging long-term puts with shorter-term options entails a significant decrease of both equal risk prices and market incompleteness as compared to trading only the stock. Monte Carlo experiments demonstrate the potential of ERP as a fair valuation approach providing prices consistent with observable market prices. Analyses exhibit the ability of ERP to span a large interval of prices through the choice of convex risk measures which is close to encompass the variance-optimal premium.

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“…Conversely, Carbonneau and Godin (2021b) and Carbonneau and Godin (2021a) use the deep reinforcement learning approach of Buehler et al (2019) coined as deep hedging. Other papers have relied on the deep hedging methodology for the hedging of financial derivatives: Cao et al (2020), Carbonneau (2021), Horvath et al (2021) and Lütkebohmert et al (2021). Deep reinforcement learning is a very favorable technique for multistage optimization and decision-making in financial contexts: it allows tackling high-dimensional settings with multiple state variables, underlying asset dynamics and trading instruments.…”

Section: Literature Reviewmentioning

confidence: 99%

Deep equal risk pricing of financial derivatives with non-translation invariant risk measures

Carbonneau¹,

Godin²

2021

Preprint

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The use of non-translation invariant risk measures within the equal risk pricing (ERP) methodology for the valuation of financial derivatives is investigated. The ability to move beyond the class of convex risk measures considered in several prior studies provides more flexibility within the pricing scheme. In particular, suitable choices for the risk measure embedded in the ERP framework such as the semi-mean-square-error (SMSE) are shown herein to alleviate the price inflation phenomenon observed under Tail Value-at-Risk based ERP as documented for instance in Carbonneau and Godin (2021b). The numerical implementation of non-translation invariant ERP is performed through deep reinforcement learning, where a slight modification is applied to the conventional deep hedging training algorithm (see Buehler et al., 2019) so as to enable obtaining a price through a single training run for the two neural networks associated with the respective long and short hedging strategies. The accuracy of the neural network training procedure is shown in simulation experiments not to be materially impacted by such modification of the training algorithm.

show abstract

Discrete-time Variance-optimal Deep Hedging in Affine GARCH Models

Cited by 3 publications

References 0 publications

Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures

Deep Equal Risk Pricing of Financial Derivatives with Non-Translation Invariant Risk Measures

Deep Equal Risk Pricing of Financial Derivatives with Multiple Hedging Instruments

Deep equal risk pricing of financial derivatives with non-translation invariant risk measures

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