Hedging Of Options Research Articles

Foreign Exchange Risk Analysis and The Futures Hedging Strategy Construction--- The Case Study of Amazon

This paper explores the foreign exchange risk encountered by Amazon.com Inc. and proposes corresponding futures hedging strategies. With global market uncertainties, foreign exchange risk significantly impacts the financial performance of multinational companies like Amazon. The paper analyzes Amazon's foreign exchange risk factors, highlighting that the primary risks stem from international business revenues and holdings of foreign currency cash equivalents and marketable securities. Based on these risk factors, the study proposes several potential hedging strategies, including forward market hedging, futures hedging, and exchange rate options hedging. Forward market hedging mitigates risk by agreeing to exchange currencies at a predetermined rate in the future; futures hedging avoids counterparty default risk through standardized contracts; and exchange rate options hedging offers flexibility by allowing the exercise to be abandoned if the exchange rate moves favorably. The paper further develops a specific futures hedging strategy based on several key assumptions, including efficient market hypothesis, zero transaction costs, unlimited liquidity, and the absence of risk-free arbitrage opportunities. The strategy involves shorting futures contracts; if the exchange rate declines at maturity, the hedge is successful and profitable; if the exchange rate rises, the hedge is unsuccessful, resulting in a loss. The findings suggest that using futures contracts for hedging enables Amazon to stabilize its financial performance in case of market uncertainties, protecting it from adverse impacts of foreign exchange risk. Despite discrepancies between actual sales data and forecasts, the hedging strategy still demonstrates its effectiveness in maintaining financial stability.

Valuation and hedging of cryptocurrency inverse options

Currently, the most liquidly traded options on the crypto underlying are the so-called inverse options. An inverse option contract is quoted and traded in the units of the underlying cryptocurrency. The main economic reason for the popularity of inverse contracts in the crypto exchanges (such as Deribit) is that inverse contracts enable traders to operate without maintaining fiat cash accounts. For the theoretical part, we show that inverse options are just regular vanilla options considered under the martingale measure using the forward of the underlying as the numéraire. This measure requires an adjustment to option delta. For the empirical part, we use Deribit options data of past five years to backtest delta-hedged option strategies. We introduce USD and Coin accounting of trading Profit&Loss (P&L) which is important for designing strategies in crypto options. We show empirically that USD and Coin accounting rules are equivalent when performance is measured is Coin and USD units, respectively. We establish that the risk-premia observed in options on Deribit is negative and significant so that strategies selling volatility are expected to generate positive risk-adjusted performance in the long-term.

A Deterministic Policy Gradient Method for Order Execution and Option Hedging in the Presence of Market Impact

A Deterministic Policy Gradient Method for Order Execution and Option Hedging in the Presence of Market Impact

Research on the Strategy of Using Option Hedging by China Eastern Airlines

Research on the Strategy of Using Option Hedging by China Eastern Airlines

Contingent Claims and Hedging of Credit Risk with Equity Options

Abstract Using contingent-claims valuation, we introduce novel hedge ratios for credit exposures using put options. Option hedge ratios are generally in line with the empirical sensitivities of credit spread changes to put option returns and, relative to stock hedge ratios, produce further reductions in volatility for a portfolio of North American firms. We show that option hedge ratios capture option-specific credit exposure related to the VIX index and the default spread, which is unaccounted for by Merton’s (1974) equity hedge ratios alone. Combining stocks and put options for credit risk hedging can be done effectively using the volatility smirk. (JEL E43, E44, G10)

Hedging lookback-barrier option by Malliavin calculus in a mixed fractional Brownian motion environment

We present a Malliavin calculus approach to a mixed fractional Brownian motion option hedging model, that adequately describes, e.g., the hedging of a lookback-barrier option with the floating strike price. The Markovian setup and smooth stochastic differentials are necessary components in the payoff function for classical Δ-hedging of a contingent claim. This is in contrast to the Malliavin calculus approach, which may be used to any type of path-dependent options. Based on the fractional Clark–Ocone formula, an entirely probabilistic computation is developed to obtain the closed-form solution of the hedging portfolio for a lookback-barrier option with the floating strike price. Numerical experiments are performed to demonstrate the performance of our proposed hedging model, and we also conduct sensitivity analysis to investigate the correlation between model parameters and the hedging portfolio.

Static hedging of vanilla and exotic options in a South African context

In this paper, we test the performance of a static hedging strategy for a long-dated European call option and European spread call option in South Africa. The stochastic volatility double jump (SVJJ) model is calibrated to historical FTSE/JSE Top40 returns to generate real-world FTSE/JSE Top40 prices at future dates. The SVJJ model is also calibrated to the FTSE/JSE (Top40) implied volatility surface in order to value the options under the risk-neutral measure. Two static hedging programs are then implemented to test their effectiveness when replicating a long-dated European call option and European spread call option. Our results indicate that static hedging is a simple, yet effective, solution when hedging non-exchange-traded options with vanilla exchange-traded options.

Deep Reinforcement Learning for Dynamic Stock Option Hedging: A Review

This paper reviews 17 studies addressing dynamic option hedging in frictional markets through Deep Reinforcement Learning (DRL). Specifically, this work analyzes the DRL models, state and action spaces, reward formulations, data generation processes and results for each study. It is found that policy methods such as DDPG are more commonly employed due to their suitability for continuous action spaces. Despite diverse state space definitions, a lack of consensus exists on variable inclusion, prompting a call for thorough sensitivity analyses. Mean-variance metrics prevail in reward formulations, with episodic return, VaR and CvaR also yielding comparable results. Geometric Brownian motion is the primary data generation process, supplemented by stochastic volatility models like SABR (stochastic alpha, beta, rho) and the Heston model. RL agents, particularly those monitoring transaction costs, consistently outperform the Black–Scholes Delta method in frictional environments. Although consistent results emerge under constant and stochastic volatility scenarios, variations arise when employing real data. The lack of a standardized testing dataset or universal benchmark in the RL hedging space makes it difficult to compare results across different studies. A recommended future direction for this work is an implementation of DRL for hedging American options and an investigation of how DRL performs compared to other numerical American option hedging methods.

Hedging goals

Goal-based investing is concerned with reaching a monetary investment goal by a given finite deadline, which differs from mean-variance optimization in modern portfolio theory. In this article, we expand the close connection between goal-based investing and option hedging that was originally discovered in Browne (Adv Appl Probab 31(2):551–577, 1999) by allowing for varying degrees of investor risk aversion using lower partial moments of different orders. Moreover, we show that maximizing the probability of reaching the goal (quantile hedging, cf. Föllmer and Leukert in Finance Stoch 3:251–273, 1999) and minimizing the expected shortfall (efficient hedging, cf. Föllmer and Leukert in Finance Stoch 4:117–146, 2000) yield, in fact, the same optimal investment policy. We furthermore present an innovative and model-free approach to goal-based investing using methods of reinforcement learning. To the best of our knowledge, we offer the first algorithmic approach to goal-based investing that can find optimal solutions in the presence of transaction costs.

Options trading strategies for the price coverage of the algerian oil barrel sahara blend

This paper focuses on the problem of hedging the risk of financial loss generated by the fall in the price of the Algerian oil barrel Sahara Blend, with the aim of proposing an approach allowing the reduction of financial losses, following unfavorable movements in oil prices. After a reminder on the strategic importance of the energy sector for the Algerian economy, we will evaluate the derivative products using different models. We present some option hedging strategies. Our results indicate that the use of options would effectively cushion a possible drop in the price of Sahara Blend, provided that the choice of the option exchange strategy is optimal. The study covers the period from 12/31/2019 to 06/30/2021, and the data is available on the websites www.oilprice.com and www.fred.stlouisfed.org. Finally, the results indicate that taking into account the cost of hedging and gains at maturity, bear spread and traddle strategies remain the most optimal.

Analysis on Hedging and Risk Management of Options and Futures

Options play an irreplaceable role in today's financial markets This article begins with an introduction to the meaning and rules of use of options, where a party who owns an option has the right, but not the obligation, to buy or try to sell an asset at a particular price on or before a specific date. As the price of the underlying changes, the option price changes along with it, providing an opportunity to hedge risk and speculate. In the face of different market conditions, this article proposes different options strategies that enable investors to choose the right combination of options to mitigate risk and get more returns under different circumstances. Maximize gains or minimize losses by taking advantage of the different properties of call and put options and the effects of the combination. Finally, this article draws conclusions on the characteristics of futures in risk management and the implications for investors or companies.

Data-driven hedging of stock index options via deep learning

We develop deep learning models to learn the hedge ratio for S&P500 index options from options data. We compare different combinations of features and show that with sufficient training data, a feedforward neural network model with time to maturity, the Black-Scholes delta and market sentiment as inputs performs the best in the out-of-sample test under daily hedging. This model significantly outperforms delta hedging and a data-driven hedging model. Our results also demonstrate the importance of market sentiment for hedging.

Hybrid Power Generation Supply Chain Financing and Purchasing Strategies with Option Hedging against Disruption

Environmental pollution has stimulated cleaner and sustainable energy (CSE) resource consumption which fuels low-carbon electric-power growth. This consumption is particularly affected by two factors. One of them is the power grid’s capital size in the electricity supply chain (ESC) and the other is the carbon emission reduction level elasticity of electricity consumption. Further, the financial strategy directly exerts quantifiable influence on one of the factors of capital size, while the procurement strategy plays a role in another factor. However, the impact of strategic behavior on all participants in the ESC remains unexplored. Thus, we construct a game model for the ESC consisting of two heterogeneous power plants and a strategic power grid with financial constraints, in order to analyze the purchasing and financing strategies for low-carbon electric-power consumption and examine the profit scenario from the credit and option hedging. We find that for the power grid, high self-owned funds level or affluent credit line encourages procurement. And when considering the power grid funds are uniformly distributed on or are constant, this funds property variation surely imposes influence on the wind electricity purchases. We find price elasticity of demand shows monotonic on the purchase when the power grid funds are constant but not necessarily when funds are uniformly distributed. The two power plants pursue the most favorable scenario for profit-maximizing by means of credit interest rate. Whether the power plants increase the financial credit interest is contingent upon option portfolios, the grid’s fund property, and wind yield conditions. We also find whether the relations between the two power plants are competitive or complementary depending on the wind yield rate. Numerical study shows that when the power grid funds are uniformly distributed, executing the double option seems to be the most profitable choice for the power grid and the traditional energy power plant, whereas with the uniform distribution of the grid’s funds, executing the call option but abandoning put is the most profitable to the traditional energy power plant. Moreover, under the grid’s fund of uniform distribution, it can both motivate power user consumption for clean energy generation and expand the power grid’s capital size.

Robust Risk-Aware Option Hedging

The objectives of option hedging/trading extend beyond mere protection against downside risks, with a desire to seek gains also driving agent's strategies. In this study, we showcase the potential of robust risk-aware reinforcement learning (RL) in mitigating the risks associated with path-dependent financial derivatives. We accomplish this by leveraging a policy gradient approach that optimizes robust risk-aware performance criteria. We specifically apply this methodology to the hedging of barrier options, and highlight how the optimal hedging strategy undergoes distortions as the agent moves from being risk-averse to risk-seeking. As well as how the agent robustifies their strategy. We further investigate the performance of the hedge when the data generating process (DGP) varies from the training DGP, and demonstrate that the robust strategies outperform the non-robust ones.

The pricing and static hedging of multi-step double barrier options

As a sequel to Lee et al. (2022b), this paper explores the pricing of multi-step double barrier options with arbitrary European-type payoffs from a static hedging perspective. Using the reflection principle of Brownian motion, we develop how to construct an exact static hedging portfolio consisting of simple discrete barrier options under the Black–Scholes model. This equivalent conversion from continuous monitoring to discrete ones provides an efficient way of evaluating multi-step double barrier options, while overcoming the drawbacks of dynamic hedging. We illustrate our result with numerical examples, and extend it to other asset price dynamics such as jump diffusion.

Hedging cryptocurrency options

The cryptocurrency market is volatile, non-stationary and non-continuous. Together with liquid derivatives markets, this poses a unique opportunity to study risk management, especially the hedging of options, in a turbulent market. We study the hedge behaviour and effectiveness for the class of affine jump diffusion models and infinite activity Lévy processes. First, market data is calibrated to stochastic volatility inspired-implied volatility surfaces to price options. To cover a wide range of market dynamics, we generate Monte Carlo price paths using an stochastic volatility with correlated jumps model, a close-to-actual-market GARCH-filtered kernel density estimation as well as a historical backtest. In all three settings, options are dynamically hedged with Delta, Delta–Gamma, Delta–Vega and Minimum Variance strategies. Including a wide range of market models allows to understand the trade-off in the hedge performance between complete, but overly parsimonious models, and more complex, but incomplete models. The calibration results reveal a strong indication for stochastic volatility, low jump frequency and evidence of infinite activity. Short-dated options are less sensitive to volatility or Gamma hedges. For longer-dated options, tail risk is consistently reduced by multiple-instrument hedges, in particular by employing complete market models with stochastic volatility.

Multi-period Static Hedging of European Options

Multi-period Static Hedging of European Options

Valuation and hedging of cryptocurrency inverse options: with backtest simulations using Deribit options data

Valuation and hedging of cryptocurrency inverse options: with backtest simulations using Deribit options data

Reconstructing volatility: Pricing of index options under rough volatility

AbstractAvellaneda et al. (2002, 2003) pioneered the pricing and hedging of index options – products highly sensitive to implied volatility and correlation assumptions – with large deviations methods, assuming local volatility dynamics for all components of the index. We present an extension applicable to non‐Markovian dynamics and in particular the case of rough volatility dynamics.

The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching

Abstract It is more difficult to give Laplace transform directly in a defined form or derive it by Fourier transform in mathematics teaching. The article gives a solution for solving high exponential series sum by using Laplace transform. With the help of Laplace transform, calculus operations can be transformed into complex plane algebra operations. The application of the algorithm to the option hedging strategy verifies the applicability of the algorithm proposed in this article.