A new hedging strategy uses deep reinforcement learning to manage gamma and vega risks.
problem Managing gamma and vega risks in derivatives trading with stochastic underlying.
method Deep distributional reinforcement learning (D4PG) combined with quantile regression.
result Optimal hedging strategy depends on objective function, transaction costs, and option maturity.
We study option pricing and hedging with uncertainty about a Black-Scholes reference model which is dynamically recalibrated to the market price of a liquidly traded vanilla option. For dynamic trading in the underlying asset and this vanilla option, delta-vega hedging is asymptotically optimal in the limit for small u…
Optimal hedging strategies for exotic options using vanilla options.
problem Hedging exotic options with illiquid vanilla options.
method Simple approximations and variational techniques in a market model and stochastic volatility model framework.
result Optimal Delta and Vega hedging strategies can be computed easily.
ANADDH uses deep learning to improve volatility risk management.
problem Traditional Vega hedging strategies are inadequate for rapidly changing markets.
method Combines distributional reinforcement learning with adaptive Nesterov acceleration.
result Significant performance gains over existing hedging techniques.
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.
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.
In a market with a rough or Markovian mean-reverting stochastic volatility there is no perfect hedge. Here it is shown how various delta-type hedging strategies perform and can be evaluated in such markets in the case of European options. A precise characterization of the hedging cost, the replication cost caused by th…
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.
We investigate the pricing of cliquet options in a jump-diffusion model. The considered option is of monthly sum cap style while the underlying stock price model is driven by a drifted Lévy process entailing a Brownian diffusion component as well as compound Poisson jumps. We also derive representations for the density…
We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum…
Inspired by the results in a recent paper by G. Galloway and C. Vega (see arXiv:1712.00785), we investigate a number of geometric consequences of the existence of a timelike conformal Killing vector field on a globally hyperbolic spacetime with compact Cauchy hypersurfaces, especially in connection with the so-called B…
We analyze 27 house price indexes of Las Vegas from Jun. 1983 to Mar. 2005, corresponding to 27 different zip codes. These analyses confirm the existence of a real-estate bubble, defined as a price acceleration faster than exponential, which is found however to be confined to a rather limited time interval in the recen…
This article prices OTC derivatives with either an exogenously determined initial margin profile or endogenously approximated initial margin. In the former case, margin valuation adjustment (MVA) is defined as the liability-side discounted expected margin profile, while in the latter, an extended partial differential e…
PIVOT bridges Black-Scholes price and implied volatility spaces via a differentiable layer.
problem Lack of a differentiable interface between price and implied volatility spaces.
method Develops PIVOT, a differentiable layer that preserves LBR's forward pass and avoids backpropagation through branch logic, addressing singularity issues.
result PIVOT achieves high performance and accuracy, reducing price and implied volatility errors by up to 43.4% and 21.3% respectively.
The aim of this paper is to present a dual-term structure model of interest rate derivatives in order to solve the two hardest problems in financial modeling: the exact volatility calibration of the entire swaption matrix, and the calculation of bucket vegas for structured products. The model takes a series of long-ter…
Paper uses neural networks to compress large portfolios of options, reducing risk and capital requirements.
problem Managing risk and capital requirements for large portfolios of financial options.
method Artificial neural network framework for portfolio compression, static hedging, and risk management.
result The compressed portfolio's risk profiles align closely with the target portfolio's, reducing capital requirements.
Principal component analysis (PCA) is a useful tool when trying to construct factor models from historical asset returns. For the implied volatilities of U.S. equities there is a PCA-based model with a principal eigenportfolio whose return time series lies close to that of an overarching market factor. The authors show…
We consider the problem of learning a general graph G=(V,E) using edge-detecting queries, where the number of vertices ∣V∣=n is given to the learner. The information theoretic lower bound gives mlogn for the number of queries, where m=∣E∣ is the number of edges. In case the number of edges m is also given t…
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.
Recent networking research has identified that data-driven congestion control (CC) can be more efficient than traditional CC in TCP. Deep reinforcement learning (RL), in particular, has the potential to learn optimal network policies. However, RL suffers from instability and over-fitting, deficiencies which so far rend…
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…
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.
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.
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.
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.