New method for insurance valuation combining hedging and risk minimization.
problem Current insurance valuation methods do not reflect regulatory risk measures.
method Two-step hedging procedure using generalised regression.
result The method produces portfolios neutral to risk measures like VaR or expectiles.
Deep Hedging learns risk-neutral vol dynamics for option pricing.
problem Statistical arbitrage in market dynamics without transaction costs.
method Numerical approach to train market simulator and find risk-neutral density.
result Risk-neutral model for stochastic implied volatility can be used for pricing or Deep Hedging.
The paper extends two-step homogeneous geodesics to homogeneous Finsler spaces.
problem Extending two-step homogeneous geodesics to Finsler spaces.
method Providing sufficient conditions for (α,β) spaces and decomposable cubic spaces to have two-step Finsler geodesic orbit spaces. result Presented examples of two-step Finsler geodesic orbit spaces.
Classifies two-step solvable Lie groups with SKT structures.
problem Classifying Lie groups with SKT structures.
method Shear construction and analysis of SKT shear data on Abelian Lie algebras.
result Large part of the classification for two-step solvable SKT algebras of dimension six.
We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the graphs from which they arise are isomorphic.
Paper introduces new actuarial-consistent valuations for insurance liabilities.
problem Valuation of insurance liabilities considering both financial and actuarial risks.
method Proposes two-step actuarial valuations and actuarial-consistent procedures.
result Actuarial-consistent valuations are equivalent to two-step actuarial valuations under coherence.
Paper uses RL for dynamic swaption hedging, outperforming traditional methods.
problem Dynamic hedging of swaptions using reinforcement learning.
method Design agents with three objective functions to adapt hedging strategies dynamically.
result Deep hedging strategies using two swaps outperform traditional methods, even with model misspecification.
Study develops efficient nested deep hedging method for derivatives pricing.
problem Hedging derivatives in market frictions using multiple options.
method Nested deep hedging approach with efficient learning techniques.
result Reduces arbitrage opportunities and improves hedging risks.
Neural-SDE models improve option hedging with lower errors and robustness.
problem Improving option hedging strategies using machine learning.
method Derive sensitivity-based and minimum-variance-based hedging strategies using neural-SDE market models.
result Neural-SDE models achieve lower hedging errors and are more robust than traditional models.
Study tests if deep hedging differs from delta hedging in a GARCH market model.
problem Whether deep hedging includes speculative components in a GARCH market.
method Tested in a GARCH-based market model, comparing deep hedging and delta hedging.
result The difference between deep hedging and delta hedging is speculative if risk measure does not prioritize adverse outcomes.
Paper proposes a natural hedging framework with graphical assessment for longevity risk management.
problem Lack of a unified framework for natural hedging and graphical risk assessment.
method Structured natural hedging framework integrated with a graphical risk metric.
result Demonstrates flexibility, interpretability, and practical value for longevity risk management.
This article analyzes the relationship between co-persistence and hedging which indicates co-persistence ratio is just the long-term hedging ratio. The new method of exhaustive search algorithm for deriving co-persistence ratio is derived in the article. And we also develop a new hedging strategy of combining co-persis…
This paper examines the volatility and covariance dynamics of cash and futures contracts that underlie the Optimal Hedge Ratio (OHR) across different hedging time horizons. We examine whether hedge ratios calculated over a short term hedging horizon can be scaled and successfully applied to longer term horizons. We als…
Deep learning enhances options hedging performance.
problem Improving delta hedging for options using neural networks.
method Learning residuals between hedging function and implied Black-Scholes delta using neural networks.
result Deep learning significantly improves hedging performance, often by more than 100%.
Adversarial deep hedging learns to hedge without specifying asset price models.
problem Lack of effective underlying asset models for deep hedging.
method Adversarial learning framework where a hedger and a generator compete to improve hedging performance.
result Adversarial deep hedging achieves competitive performance without explicit asset process modeling.
New method reduces training time for deep hedging networks.
problem Challenges in training deep hedging networks with large batch sizes.
method Integrates topological features to reduce batch sizes.
result Practical training of deep hedging models without sacrificing performance.
Proves conjecture about compatible SKT and balanced metrics on compact solvmanifolds.
problem Compact complex manifolds with both SKT and balanced metrics.
method Shear construction and classification of two-step solvable Lie algebras.
result Proves conjecture for compact two-step solvmanifolds with invariant complex structures.
Deep Hedging learns optimal strategies for various risk levels.
problem Finding optimal hedging policies for diverse risk aversions.
method Continuous Reinforcement Learning with actor-critic algorithm.
result Demonstrated effectiveness in a stochastic volatility model.
Geometric structure reveals optimal investment and hedging products.
problem Optimal design of investment and hedging products.
method Investigation of geometric structure in risks and returns using a simple formula.
result Duality between hedging and investment with geometric interpretation of rationality.
The paper compares traditional regression with modern neural network methods for financial hedging and risk compression.
problem Finding optimal hedge ratios and managing portfolio risk using traditional regression methods has limitations.
method The paper introduces regularization techniques and common factor analyses using neural networks to improve upon regression methods.
result Neural network methods provide better performance in hedge ratio estimation and risk compression compared to traditional regression.
Paper presents a machine learning algorithm for hedging ETF options, outperforming static hedging methods.
problem Semi-static hedging of ETF options with transaction costs and varying market conditions.
method Data-driven machine learning algorithm considering transaction costs, automated portfolio management, and PnL attribution analysis.
result The static hedging approach outperforms dynamic hedging methods in terms of profit and loss.
We prove that two-step analytic sub-Riemannian structures on a compact analytic manifold equipped with a smooth measure and Lipschitz Carnot groups satisfy measure contraction properties.
Risk aversion is a key element of utility maximizing hedge strategies; however, it has typically been assigned an arbitrary value in the literature. This paper instead applies a GARCH-in-Mean (GARCH-M) model to estimate a time-varying measure of risk aversion that is based on the observed risk preferences of energy hed…
Proposes deep hedging for index options using implied volatility surface.
problem Managing risk in index option portfolios with complex dynamics.
method Integrates surface-informed decisions with multiple hedging instruments, accounting for transaction costs and variance risk premium.
result Consistently outperforms traditional hedging strategies across various market conditions.
This report was originally written as an industry white paper on Hedge Funds. This paper gives an overview to Hedge Funds, with a focus on risk management issues. We define and explain the general characteristics of Hedge Funds, their main investment strategies and the risk models employed. We address the problems in H…
Study on hedging with delayed strategies for exponential utility maximization.
problem Maximizing exponential utility in semistatic hedging.
method Explicit computations for delayed semistatic hedging.
result Developed methods for hedging with delayed strategies.
A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial pr…
Proposes a deep hedging method for robust pricing and hedging under parameter uncertainty.
problem Pricing and hedging under parameter uncertainty for generalized affine processes.
method Deep learning approach linked to variational form of Kolmogorov equation.
result Robust deep hedging outperforms existing methods in volatile periods.
We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge in…
Forward hedging reshapes incentive provision in firms.
problem How does forward hedging affect incentive provision in firms?
method We consider a CARA framework to jointly characterize optimal production, compensation, and static hedging in equilibrium.
result Delegation and external hedging are partial substitutes, and delegation can increase firm value even when the agent is more risk averse.
Paper proposes a deep hedging method for Bermudan swaptions to manage residual profit and loss.
problem Real-world market conditions differ from ideal assumptions in traditional hedging methods, leading to residual profit and loss.
method Deep hedging framework applied to Bermudan swaptions, allowing flexible risk measures and hedge strategies.
result Effective residual profit and loss management demonstrated through numerical analysis.
Optimal hedging strategy found in markets with incomplete pricing kernels.
problem Finding optimal hedging in markets with incomplete pricing kernels.
method Demonstrated existence of an optimal hedge portfolio using an expected least squared-error criterion.
result Existence of an optimal hedge portfolio in Lévy-Ito markets.
Study optimal hedging for claims with random weights in discrete time.
problem Optimal hedging for claims with random weights in discrete time.
method Explicit recursive representation of optimal hedging strategy, without ND condition.
result Obtained explicit optimal hedging strategy in a recursive form.
Neural nets replicate hedging payoffs for realistic discrete-time settings.
problem Hedging in realistic, discrete-time financial markets with transaction costs.
method Deep learning techniques to train neural networks to replicate modified payoff functions.
result Neural networks can better accommodate realistic hedging scenarios and transaction costs.
Proposes a neural network for efficient deep hedging strategies.
problem Hard training of optimal hedging strategies due to action dependence.
method Introduces no-transaction band network, a neural architecture.
result Demonstrates faster and more precise hedging strategies.
An investor faced with a contingent claim may eliminate risk by perfect hedging, but as it is often quite expensive, he seeks partial hedging (quantile hedging or efficient hedging) that requires less capital and reduces the risk. Efficient hedging for European call option was considered in the standard Black-Scholes m…
We derive variance-optimal hedging strategies for SABR and rough Bergomi models.
problem Finding efficient hedging strategies in lognormal SABR and rough Bergomi models.
method Analytic expressions for variance-optimal hedging strategies and mean-square hedging errors.
result The variance-optimal hedging strategy in SABR coincides with Delta adjustment.
HedgeNet uses neural networks to reduce hedging errors for financial options.
problem Reducing hedging errors for financial options.
method Designing HedgeNet to minimize hedging error, trained on S&P 500 and Euro Stoxx 50 options.
result HedgeNet significantly reduces hedging error compared to Black-Scholes benchmark.
Optimal transport reformulates multiple quantile hedging problem.
problem Multiple quantile hedging problem in incomplete markets.
method Reformulated as Monge optimal transport problem, introduced Kantorovitch version, proved no duality gap.
result Multiple quantile hedging problem can be seen as semi-discrete optimal transport problem.
A new DRL model optimizes hedging with market impact for low-liquidity stocks.
problem Optimizing hedging strategies for stocks with limited liquidity.
method Integrates Deep Reinforcement Learning with realistic market impact features.
result Optimal hedging policies learned from DRL model perform better in low-liquidity scenarios.
We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail specific metrics to compare the hedging effectiveness of short and long hedgers using crude oil futures contracts. The metrics used include Lower Partial Moments (LPM), Value at Risk (VaR) and Conditional Value…
New approach minimizes tail risk in option hedging.
problem Minimizing tail risk in option hedging strategies.
method Risk-sensitive reinforcement learning without parametric models.
result Significantly lower tail risk and higher mean P&L than delta hedging.
Paper proposes a deep RL method for hedging variable annuities, outperforming misspecified models.
problem Model miscalibration in variable annuity contracts with GMMB and GMDB riders.
method Two-phase deep reinforcement learning approach: training phase in a controlled environment, online learning phase in real market.
result Trained reinforcement learning agent hedges equally well as correct Delta in training phase and outperforms misspecified Deltas.
In a financial market model, we consider the variance-optimal semi-static hedging of a given contingent claim, a generalization of the classic variance-optimal hedging. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy, we use a Fourier approach in a general multidime…
RL and DTSOC for final quadratic hedging performance studied.
problem Optimal hedging of European call options with and without transaction costs.
method Reinforcement Learning and Deep Trajectory-based Stochastic Optimal Control.
result RL and DTSOC perform similarly to variance-optimal hedging in various market models.
Discrete time hedging in a complete diffusion market is considered. The hedge portfolio is rebalanced when the absolute difference between delta of the hedge portfolio and the derivative contract reaches a threshold level. The rate of convergence of the expected squared hedging error as the threshold level approaches z…
Algorithm for hedging American options with transaction costs.
problem Hedging American options considering transaction costs.
method Backward Hedging algorithm minimizing loss function.
result Optimal hedging strategy determined by minimizing loss function.
Develops a robust hedging valuation adjustment measure for dynamic hedging under liquidity-demand stress.
problem Dynamic hedging under liquidity-demand stress
method Define robust HVA as the worst-case expected loss over a relative-entropy neighborhood of the loss distribution generated by simulated rebalancing and maturity-unwind trades.
result Distinguishes fixed-radius convention from fixed benchmark-stress convention and shows wider no-trade bands lower rebalancing costs but raise hedge-error risk.