Study good-deal hedging under uncertain market prices, reducing speculative components.
problem Good-deal valuation under model uncertainty and speculative risk.
method Robust approach using backward stochastic differential equations.
result Reduction or elimination of speculative components in good-deal hedging.
Study robust hedging and valuation under combined uncertainty about asset price drifts and volatilities.
problem Robust hedging and valuation under uncertainty about asset price drifts and volatilities.
method Non-dominated multiple priors approach to model uncertainty, worst-case good-deal bounds, coherent risk measures, second-order backward stochastic differential equations.
result Characterization of hedging strategies and good-deal bounds via solutions to backward stochastic differential equations.
We propose a pricing technique based on coherent risk measures, which enables one to get finer price intervals than in the No Good Deals pricing. The main idea consists in splitting a liability into several parts and selling these parts to different agents. The technique is closely connected with the convolution of coh…
We study convex risk measures describing the upper and lower bounds of a good deal bound, which is a subinterval of a no-arbitrage pricing bound. We call such a convex risk measure a good deal valuation and give a set of equivalent conditions for its existence in terms of market. A good deal valuation is characterized …
Investigates good deal bounds for financial markets with convex constraints.
problem Financial market models with convex constraints.
method Study of good deal valuation as a convex risk measure.
result Properties of good deal valuation and its relation to superhedging cost and FTA.
We shall provide in this paper good deal pricing bounds for contingent claims induced by the shortfall risk with some loss function. Assumptions we impose on loss functions and contingent claims are very mild. We prove that the upper and lower bounds of good deal pricing bounds are expressed by convex risk measures on …
We study hedging and pricing of unattainable contingent claims in a non-Markovian regime-switching financial model. Our financial market consists of a bank account and a risky asset whose dynamics are driven by a Brownian motion and a multivariate counting process with stochastic intensities. The interest rate, drift, …
We consider option pricing in a regime-switching diffusion market. As the market is incomplete, there is no unique price for a derivative. We apply the good-deal pricing bounds idea to obtain ranges for the price of a derivative. As an illustration, we calculate the good-deal pricing bounds for a European call option a…
Study financial contracts pricing in markets with nonproportional costs and constraints.
problem Financial contract pricing in markets with nonproportional transaction costs and portfolio constraints.
method Direct and dual characterization of market-consistent prices with acceptable risk thresholds.
result Extension of the Fundamental Theorem of Asset Pricing to include good deals and scalable good deals.
This paper deals with applications of coherent risk measures to pricing in incomplete markets. Namely, we study the No Good Deals pricing technique based on coherent risk. Two forms of this technique are presented: one defines a good deal as a trade with negative risk; the other one defines a good deal as a trade with …
In an L∞-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures…
Extends classical model of transaction costs to convex costs and multivariate positions.
problem Risk arbitrage and hedging under transaction costs with convex costs and multivariate positions.
method Extends classical model to convex transaction costs and multivariate acceptable positions, using results for unbounded and non-closed random sets.
result Formulates no arbitrage conditions and explores their connections, leading to a decrease in superhedging prices.
CDS (credit default swap) contracts that were initiated some time ago frequently have spreads and/or maturities that are not available on the current market of CDSs, and are thus illiquid. This article introduces an incomplete-market approach to valuing illiquid CDSs that, in contrast to the risk-neutral approach of cu…
Survey on algebraic minimal cones and nonassociative algebras.
problem Exploring algebraic minimal cones and nonassociative algebras.
method Recollections and recent developments in the field.
result Dedication to Vladimir Miklyukov's memory.
Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show tha…
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 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…
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…
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.
Flexible framework for optimal static hedging using vanilla options.
problem Minimizing squared hedging error with cost constraints.
method Model-free expression for optimal strategy, analytical approximations for expectations.
result General method for approximating hedging expectations in Markov diffusion markets.
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.
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…
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.