Study delta-vega hedging for recalibrated options under model uncertainty.
problem Uncertainty in Black-Scholes model and recalibration to market prices.
method Dynamic recalibration of a Black-Scholes model to a liquid vanilla option, delta-vega hedging analysis.
result Delta-vega hedging is asymptotically optimal for small uncertainty aversion.
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.
We consider model-free pricing of digital options, which pay out if the underlying asset has crossed both upper and lower barriers. We make only weak assumptions about the underlying process (typically continuity), but assume that the initial prices of call options with the same maturity and all strikes are known. Unde…
Study the hedging of cryptocurrency options in a volatile market.
problem Hedging options in a volatile, non-stationary cryptocurrency market.
method Calibrated to SVI-implied volatility surfaces, Monte Carlo price paths generated using SVCJ, GARCH, and historical data. Delta, Delta-Gamma, Delta-Vega, and Minimum Variance strategies applied. Wide range of market models tested.
result Calibration results indicate stochastic volatility, low jump frequency, and infinite activity. Short-dated options less sensitive to volatility or Gamma hedges; longer-dated options benefit from multiple-instrument hedges.
Derivative-informed models improve financial surrogates for accurate hedging and risk management.
problem Developing fast surrogate models for financial derivatives and risk quantities.
method Derivative-informed operator learning framework combining neural operators, random features, and tangent sensitivity equations.
result The framework reduces hedging and risk errors by 40-76% compared to standard surrogates.
Unified pricing method for FX options with barriers.
problem Calculating the value and sensitivities of FX options with barriers.
method Unified Vanna-Volga pricing technique for single and double barrier FX options.
result Derivation of closed formulas for Delta, Vega, Vanna, and Volga.
Study computes option sensitivities using Malliavin calculus for hybrid stochastic models.
problem Computing option sensitivities (Greeks) under hybrid stochastic volatility and interest rate models.
method Integrates Malliavin calculus for Delta, Vega, and Rho computation; extends to non-differentiable payoffs.
result Malliavin calculus enables effective numerical implementations for various option types.
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.
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…
The paper redefines semi-static hedging as derivatives and calculates hedging errors.
problem The costs of maintaining hedging portfolios and the limitations of semi-static hedging.
method New integral representations, approximations, and efficient numerical methods for calculating Wiener-Hopf factors and Laplace-Fourier inversion.
result The hedging error of static hedging portfolios can be larger than variance-minimizing portfolios.
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.
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.
Optimal hedging strategies identified for markets with fast-varying volatility.
problem No perfect hedge in markets with fast-varying stochastic volatility.
method Analyzes various delta-type hedging strategies and their performance in a specific asymptotic regime of rapid mean reversion.
result Identifies the `practitioners' delta hedging scheme as optimal in the considered regime of rapid mean reversion.
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.
Optimizes hedging strategy using Fourier-integration for variance-optimality.
problem Finding optimal hedging strategy under variance-optimality criterion.
method General representations and Fourier-integration for Heston model; sparse hedging selection.
result Sparse semi-static hedging strategy using Fourier-integration.
The paper develops a Fourier-based method for optimal hedging in stochastic volatility models.
problem Optimal hedging in financial markets with stochastic volatility.
method Fourier representation in a semimartingale factor model.
result A tractable formula for expected squared hedging error and optimal strategy.
Paper mathematically extends timing risk hedging for barrier options.
problem Timing risk in barrier options under multi-dimensional models.
method Semi-static hedge using barrier options and asymptotic expansions.
result Higher order semi-static hedges can reduce hedging cost by over 90%.
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.
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…
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.
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.
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.
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…
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.
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.
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.
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.
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.
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.
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.
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.
Develops hedging formula in fractional model with costs.
problem Hedging in fractional Black-Scholes model with transaction costs.
method Explicit formula for hedging portfolio using fractional Brownian motion.
result Explicit formula for conditional-mean hedging portfolio.
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.
The paper addresses hedging Asian options with transaction costs using asymptotic hedging.
problem Hedging Asian options in markets with transaction costs.
method Asymptotic hedging approach.
result Probability convergence of investment portfolio value to payment function as revision count approaches infinity.