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.
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.
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.
Model-free approach to hedge path-dependent options using min-max optimization.
problem Hedging path-dependent options with maturity T using a static portfolio of vanilla options.
method Model-free approach based on primal-dual Martingale Optimal Transport (MOT) problem, solving a min-max optimization problem.
result Provides theoretical bounds on hedging error at maturity T.
QLBS and RLOP methods improve option pricing and hedging performance.
problem Improving option pricing and hedging performance under market frictions.
method Incorporates risk aversion and trading costs into QLBS, proposes RLOP approach.
result RLOP outperforms in dynamic hedging by reducing shortfall probability.
It turns out that in the bivariate Black-Scholes economy Margrabe type options exhibit symmetry properties leading to semi-static hedges of rather general barrier options. Some of the results are extended to variants obtained by means of Brownian subordination. In order to increase the liquidity of the hedging instrume…
Deep learning models predict S&P500 option hedge ratios.
problem Optimizing hedging strategies for S&P500 index options.
method Feedforward neural network with time to maturity, delta, and sentiment variables.
result Deep learning model outperforms traditional hedging methods.
Optimizes credit index option hedging with reinforcement learning.
problem Finding the best strategy for hedging credit index options.
method Applied reinforcement learning with TRVO algorithm in a realistic setting.
result The derived hedging strategy outperforms traditional methods.
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.
We price and hedge American options robustly in continuous time.
problem Pricing and hedging American options in continuous time with model uncertainty.
method Assumes continuous semimartingale asset prices and closed convex constraints on volatility. Proves robust pricing-hedging duality and identifies American options as European options on an enlarged space.
result We prove robust pricing-hedging duality and show it holds against richer models with dynamic trading of European options.
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.
This paper analyzes hedge errors in Black-Scholes models using finite difference techniques.
problem Accurate hedging strategies in dynamic market environments.
method Asymptotic approach and finite difference techniques.
result Reduction of hedge errors and enhancement of option pricing model robustness.
Risk-averse reinforcement learning optimizes option hedging.
problem Optimizing option hedging under risk aversion and realistic market conditions.
method Applied Trust Region Volatility Optimization (TRVO) to a vanilla option hedging environment.
result The derived hedging strategy outperforms Black & Scholes and is robust to market variations.
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.
The paper introduces and studies hedging for game (Israeli) style extension of swing options considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions we derive a formula for valuation of multiple exercise options via classical hedging arguments. Introducing t…
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.
Perfect hedging of options with a dynamic portfolio in rough volatility models.
problem Hedging options in rough volatility models.
method Presented a simple but general result showing perfect hedging with a dynamic portfolio of underlying and variance swap.
result Rough volatility models significantly reduce hedging error compared to diffusion-based models.
Second-order optimization speeds up deep hedging for complex options.
problem Hedging exotic options with market frictions in realistic markets.
method Second-order optimization scheme leveraging pathwise differentiability and Kronecker-factoring.
result Our method optimizes the policy in 1/4 the steps of standard optimization.
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.
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%.
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.
We create a robust hedging method for American options.
problem Hedging American options in uncertain financial markets.
method Aggregated Snell envelopes in a semi-martingale setting.
result Existence of a minimal hedging strategy in general settings.
This paper extends static hedging for European options over multiple maturities.
problem Hedging European options over multiple time periods.
method Developed a spanning relation for multiple shorter-term options using a Markovian framework.
result Demonstrated a practical implementation using Gaussian Quadrature for finite sets of shorter-term options.
New dual approach for hedging Bermudan options efficiently.
problem Computing efficient hedging portfolios for Bermudan options.
method Pure dual approach, rewriting dual pricing formula as excess reward representation, strict convexification, Monte Carlo method.
result Convergence and effectiveness of the new algorithm tested on various Bermudan options.
Study calculates liquidity costs for delta hedging of European options.
problem Determining expected liquidity costs in delta hedging.
method Derives an integration formula for liquidity costs, including option prices and delta process.
result Expected liquidity costs can be calculated faster than Monte Carlo simulations.
The aim of this paper is to provide a mathematical contribution on the semi-static hedge of timing risk associated to positions in American-style options under a multi-dimensional market model. Barrier options are considered in the paper and semi-static hedges are studied and discussed for a fairly large class of under…
Paper uses deep learning to price and hedge options in incomplete markets.
problem Incomplete markets lack unique no-arbitrage solutions for pricing and hedging European options.
method Constrained deep learning approach with a single neural network representing option prices and hedging strategies.
result Constrained networks produce superior P&L distributions compared to unconstrained networks.
Reinforcement learning improves option pricing and hedging accuracy.
problem Improving financial instrument pricing and hedging accuracy.
method Q-Learning Black Scholes approach applied to option pricing and hedging.
result The reinforcement learning model accurately estimates option prices and hedging strategies under various volatility and moneyness levels.
Study evaluates hedging strategies for S&P500 index options.
problem Improving returns and risk management in index option portfolios.
method Compared Black-Scholes-Merton and Variance-Gamma models for hedging strategies.
result Systematic option-writing strategies can yield superior returns compared to buy-and-hold benchmarks.
Pricing and hedging rainbow options using Bayesian MS-VAR process.
problem Pricing and hedging rainbow options under varying economic conditions.
method Bayesian Markov-Switching Vector Autoregressive (MS-VAR) process to model regime-switching economic variables.
result Model provides a simpler and more economic variable-dependent approach for rainbow options pricing and hedging.
Modeling option market making with hedging-induced price impact.
problem Tackles the challenge of market making in options markets with price impact.
method Models option order flow using Cox processes and studies the dynamics of inventory and price under hedging-induced impact.
result Establishes the well-posedness of the mixed control problem involving quoting and hedging.
We present a method of hedging Conditional Value at Risk of a position in stock using put options. The result leads to a linear programming problem that can be solved to optimise risk hedging.
The approach that allows find European option price on the assumption of hedging at discrete times is proposed. The routine allows find the option price not for lognormal distribution functions of underlying asset only but for wide enough classes of distribution functions too. It is shown that there exists a nonzero po…
Trains neural nets for gamma hedging with model uncertainty.
problem Gamma hedging with model mismatch.
method Trains neural networks using loss functions that reward model uncertainty.
result Networks can learn optimal gamma hedging even with model mismatch.
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise strategies are presented, together with numerical examples, as well as probabili…
This paper presents hedging strategies for European and exotic options in a Levy market. By applying Taylor's Theorem, dynamic hedging portfolios are con- structed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European optio…
Two neural network methods solve American-style option pricing and hedging.
problem Solving American-style option pricing and hedging problems efficiently.
method Two novel neural network methods: one series of networks and one global network.
result Simultaneous computation of upper and lower bounds with reduced complexity.
This work addresses the problem of optimal pricing and hedging of a European option on an illiquid asset Z using two proxies: a liquid asset S and a liquid European option on another liquid asset Y. We assume that the S-hedge is dynamic while the Y-hedge is static. Using the indifference pricing approach we derive a HJ…
We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We obtain the duality of results for the sub- and super-hedging prices. For the sub…
Enhanced hedging for S&P 500 options using volatility surface data.
problem Optimizing hedging strategies for S&P 500 options with transaction costs.
method Deep policy gradient reinforcement learning with volatility surface feedback.
result Outperforms conventional hedging methods in simulations and backtesting.
We consider the fundamental theorem of asset pricing (FTAP) and hedging prices of options under non-dominated model uncertainty and portfolio constrains in discrete time. We first show that no arbitrage holds if and only if there exists some family of probability measures such that any admissible portfolio value proces…
In this paper we introduce a deep learning method for pricing and hedging American-style options. It first computes a candidate optimal stopping policy. From there it derives a lower bound for the price. Then it calculates an upper bound, a point estimate and confidence intervals. Finally, it constructs an approximate …
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…
We analyze the errors arising from discrete readjustment of the hedging portfolio when hedging options in exponential Levy models, and establish the rate at which the expected squared error goes to zero when the readjustment frequency increases. We compare the quadratic hedging strategy with the common market practice …
This study examines the collateral choice option and its valuation and hedging.
problem Non-zero collateral basis spreads impact asset valuation and require complex modeling.
method Develops a stochastic valuation model for the collateral choice option and proposes hedging strategies.
result The stochastic model attributes risks to all involved collateral currencies, unlike the deterministic model.
KANHedge improves hedging of high-dimensional options using learnable B-spline activation functions.
problem Challenges in high-dimensional option pricing and hedging due to the curse of dimensionality.
method Introduces KANHedge, a novel BSDE-based hedger leveraging Kolmogorov-Arnold Networks with learnable B-spline activation functions.
result KANHedge provides improved hedging performance, achieving significant reductions in hedging cost metrics.
The problem of stock hedging is reconsidered in this paper, where a put option is chosen from a set of available put options to hedge the market risk of a stock. A formula is proposed to determine the probability that the potential loss exceeds a predetermined level of Value-at-Risk, which is used to find the optimal s…
Deep BSDE method for pricing and hedging complex financial portfolios.
problem Simultaneous pricing and delta-gamma hedging of large portfolios of multi-asset Bermudan options.
method Discretely reflected BSDEs, One Step Malliavin scheme, neural network regression Monte Carlo method.
result Efficient and accurate pricing and hedging strategies for high-dimensional portfolios.