Optimal Hedging Research Articles

A New Approach to Minimal Variance Hedging of European Options

This paper addresses the following question: How can a financial institution, which has issued a European option, optimally hedge the payoff of this option by investing into the underlying stock and into the option itself? Here, optimality is measured in terms of minimal variance and the associated optimal hedging portfolio is derived by a sufficient stochastic maximum principle. We further obtain a pricing formula for general European options by an application of Fourier transform methods and deduce the time dynamics of the stochastic option price process. We finally apply our theoretical results to several practical examples.

Optimal foreign exchange hedge tenor with liquidity risk

We develop an optimal currency hedging strategy that allows fund managers who own foreign assets to choose the hedge tenors that will maximize their foreign exchange (FX) carry returns within a liquidity risk constraint. The strategy assumes that the offshore assets are fully hedged with FX forwards. The chosen liquidity risk metric is cashflow at risk (CFaR). The strategy involves time-dispersing the total nominal hedge value into future time buckets to maximize (minimize) the expected FX carry benefit (cost), given the constraint that the CFaRs in all the future time buckets are well managed within a liquidity budget. We show by Monte Carlo simulation and by backtesting that our hedging strategy successfully delivers good carry trade returns with little liquidity risk. We also provide practical insights on when and why fund managers should choose short-dated or long-dated tenors.

Robust Portfolio Choice With Sticky Wages

We present a robust version of the life-cycle optimal portfolio choice problem in the presence of labor income, as introduced in Biffis, Gozzi and Prosdocimi (Optimal portfolio choice with path dependent labor income: the infinite horizon case, SIAM Journal on Control and Optimization, 58(4), 1906-1938.) and Dybvig and Liu (Lifetime consumption and investment: retirement and constrained borrowing, Journal of Economic Theory, 145, pp. 885-907). In particular, in Biffis, Gozzi and Prosdocimi the influence of past wages on the future ones is modelled linearly in the evolution equation of labor income, through a given weight function. The optimization relies on the resolution of an infinite dimensional HJB equation. We improve the state of art in three ways. First, we allow the weight to be a Radon measure. This accommodates for more realistic weighting of the sticky wages, like e.g. on a discrete temporal grid according to some periodic income. Second, there is a general correlation structure between labor income and stocks market. This naturally affects the optimal hedging demand, which may increase or decrease according to the correlation sign. Third, we allow the weight to change with time, possibly lacking perfect identification. The uncertainty is specified by a given set of Radon measures $K$, in which the weight process takes values. This renders the inevitable uncertainty on how the past affects the future, and includes the standard case of error bounds on a specific estimate for the weight. Under uncertainty averse preferences, the decision maker takes a maxmin approach to the problem. Our analysis confirms the intuition: in the infinite dimensional setting, the optimal policy remains the best investment strategy under the worst case weight.

No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging

Deep hedging (Buehler et al. 2019) is a versatile framework to compute the optimal hedging strategy of derivatives in incomplete markets. However, this optimal strategy is hard to train due to action dependence, that is, the appropriate hedging action at the next step depends on the current action. To overcome this issue, we leverage the idea of a no-transaction band strategy, which is an existing technique that gives optimal hedging strategies for European options and the exponential utility. We theoretically prove that this strategy is also optimal for a wider class of utilities and derivatives including exotics. Based on this result, we propose a no-transaction band network, a neural network architecture that facilitates fast training and precise evaluation of the optimal hedging strategy. We experimentally demonstrate that for European and lookback options, our architecture quickly attains a better hedging strategy in comparison to a standard feed-forward network.

Scalarized utility-based multi-asset risk measures

Financial institutions have to satisfy capital adequacy tests required, e.g., by the Basel Accords for banks or by Solvency II for insurers. If the financial situation of an institution is tight, then it can happen that no reallocation of the initial endowment would pass the capital adequacy test. The classical portfolio optimization approach breaks down and a capital increase is needed. We introduce the scalarized utility-based multi-asset (SUBMA) risk measure which optimizes the hedging costs and the expected utility of an agent simultaneously subject to the capital adequacy test. We find that the SUBMA risk measure is coherent if the utility function has constant relative risk aversion and the capital adequacy test leads to a coherent acceptance set. In a one-period financial market model we present a sufficient condition for the SUBMA risk measure to be finite-valued and continuous. Under further assumptions on the utility function we obtain existence and uniqueness results for the optimal hedging strategies. Finally, we calculate the SUBMA risk measure in a continuous-time financial market model for two benchmark capital adequacy tests.

Option hedging of stock indices: Benefits of signals of fundamental and technical analysis

The paper identifies country specific features of hedging strategies for stock indices. We propose the methodology of the optimization hedging parameters (the time of entering and exit, the type of an option strategy) based on the synthesis of technical (TA) and fundamental analysis (FA) indicators. Country differences in the design of the authors’ strategies are demonstrated on the tests for 20 stock indices in the period from 1980 to 2020. The research methodology is to optimize the parameters of hedging strategies for the each country on the training sample with checking the effect on the test sample. The Sharpe ratio is maximized. The originality of our paper is in the model constructions for missing data series (index futures and put options) and testing both on historical data and on simulated data under two different assumptions about the behavior of the underlying asset price: the random walk model and the Markov-switching volatility model. For each country index, more than 18,000 combinations of parameters are analyzed. Our research shows that the synthesis of fundamental (FA) and technical analysis (TA) gives the best option hedging result. We reveal country peculiarities both in the preferences of FA and TA indicators and in the use of option strategies. The estimates on historical and simulated data allow us to draw a conclusion about the patterns in the dynamics of the stock index. The random walk hypothesis receives additional support for the US market. In the coronavirus situation, the proposed methodology allows investors to effectively hedge the risks of drawdown.

Hedging with financial innovations in the Asia-Pacific markets during the COVID-19 pandemic: the role of precious metals

<abstract> In this study, we exploit the information contained in financial innovations in precious metals for hedging the risks associated with the Asia-Pacific equities during the current pandemic. We measure financial innovations as exchange traded funds (ETFs) for gold, silver, platinum and palladium which contrast with investment in the physical precious metals since the former tracks well the prices of the latter and as well provides cost-effective alternative to invest in the markets without storage costs. Based on the optimal portfolio weights and optimal hedge ratios, we find that gold offers the best hedge (followed by silver, platinum, and palladium) against the risk associated with the Asia-Pacific equities during the COVID-19 pandemic albeit with a lower hedging effectiveness during the pandemic. Overall, including gold ETFs in an Asia-Pacific equity portfolio would provide both a valuable portfolio combination that could improve the risk-adjusted performance of the market in addition to serving as an effective hedge for equity-related risks. </abstract>

THE ROLES OF ECONOMIC POLICY UNCERTAINTY AND THE COVID-19 PANDEMIC IN THE CORRELATION BETWEEN CRYPTOCURRENCY AND STOCK MARKETS

We are the first to explore the effect of economic policy uncertainty (EPU) and the COVID-19 pandemic on the correlation between the cryptocurrency index CRIX and the world stock market portfolio, as well as the hedging properties of CRIX. To this end, we mainly apply the dynamic conditional correlation model with mixed data sampling regressions, a threshold vector autoregressive model and the generalized impulse response function. We demonstrate that the correlation is influenced by the uncertainty stance of the economy and behaves differently in low-, medium- and high-uncertainty periods. Most of the abnormal market relations exist in high levels of EPU or during the COVID-19 period, and the impact of global EPU is greater than that of EPU originating in the United States, Europe, Russia and China. Moreover, the CRIX can serve as a hedge asset against the world stock market. The high (low) level of EPU has a significantly positive (negative) effect on the optimal hedge ratio of CRIX, which increases significantly during the COVID-19 period. Our findings have implications for risk management, portfolio allocations and hedging strategies.

SOME NOTES ABOUT THE MARTINGALE REPRESENTATION THEOREM AND THEIR APPLICATIONS

An important theorem in stochastic finance field is the martingale representation theorem. It is useful in the stage of making hedging strategies (such as cross hedging and replicating hedge) in the presence of different assets with different stochastic dynamics models. In the current paper, some new theoretical results about this theorem including derivation of serial correlation function of a martingale process and its conditional expectations approximation are proposed. Applications in optimal hedge ratio and financial derivative pricing are presented and sensitivity analyses are studied. Throughout theoretical results, simulation-based results are also proposed. Two real data sets are analyzed and concluding remarks are given. Finally, a conclusion section is given.

Deep Hedging of Derivatives Using Reinforcement Learning

This article shows how reinforcement learning can be used to derive optimal hedging strategies for derivatives when there are transaction costs. The article illustrates the approach by showing the difference between using delta hedging and optimal hedging for a short position in a call option when the objective is to minimize a function equal to the mean hedging cost plus a constant times the standard deviation of the hedging cost. Two situations are considered. In the first, the asset price follows a geometric Brownian motion. In the second, the asset price follows a stochastic volatility process. The article extends the basic reinforcement learning approach in several ways. First, it uses two different Q-functions to track both the expected value of the cost and the expected value of the square of the cost. This approach increases the range of objective functions that can be used. Second, it uses a learning algorithm that allows for continuous state and action space. Third, it compares the accounting profit and loss (P&amp;L) approach and the cash flow approach. The authors find that a hybrid approach involving the use of an accounting P&amp;L approach that incorporates a relatively simple valuation model works well. <b>TOPICS:</b>Big data/machine learning, derivatives, simulations <b>Key Findings</b> ▪ The authors show how reinforcement learning can be used to derive optimal hedging strategies for derivatives in the presence of transaction costs. ▪ They extend the standard reinforcement learning approach by using multiple Q-functions to increase the range of objective functions that can be used and by using algorithms that allow the state space and action space to be continuous. ▪ For valuing the hedging position at each step, the authors compare three approaches: the accounting P&amp;L, cash flow, and a hybrid involving the use of an accounting P&amp;L approach that incorporates a relatively simple valuation model.

Dual and single hedging strategy: a novel comparison from the direct and cross hedging perspective

PurposeThe purpose of this paper is to deeply study and compare the dual and single hedging strategy, from the direct and cross hedging perspective.Design/methodology/approachThe authors not only first consider the dual hedge of integrated risks in this oil prices and foreign exchange rates setting but also make a novel comparison between the dual and single hedging strategy from a direct and cross hedging perspective. In total, six econometric models (to conduct one-step-ahead out-of-sample rolling estimation of the optimal hedge ratio) and two hedging performance criteria are employed in two different hedging backgrounds (direct and cross hedging).FindingsResults show that in the direct hedging background, a dual hedge cannot outperform the single hedge. But in the cross dual hedging setting, a dual hedge performs much better, possibly because the dual hedge brings different levels of advantages and disadvantages in the two different settings and the superiority of the dual hedge is more obvious in the cross dual hedging setting.Originality/valueThe existing literature that deals with oil prices and foreign exchange rates mostly concentrates on their relationship and comovements, while the dual hedge of integrated risks in this setting remains underresearched. Besides, the existing literature that deals with dual hedge gets its conclusions only based on a single specific background (direct or cross hedging) and lacks deeper investigation. In this paper, the authors expand the width and depth of the existing literature. Results and implications are revealing.

Persistence as an Optimal Hedging Strategy

Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new, to our knowledge, theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest new opportunities for experimental investigation and design. Overall, we provide a new, to our knowledge, way of conceptualizing and modeling cellular decision making in volatile environments by explicitly unifying theory from mathematical biology and finance.

Volatility Connectedness between Clean Energy Firms and Crude Oil in the COVID-19 Era

The work investigates the volatility connectedness between oil price and clean energy firms over the period 2011–2020 (including the COVID-19 outbreak). Using the volatility spillover models, and dynamic conditional correlation, we are able to identify the volatility spillover effect between these financial markets and its implications for portfolio diversification. The results indicate a significant change in both static and dynamic volatility connectedness around the COVID-19 outbreak. For instance, total connectedness index changes from 21.36% (pre-COVID-19) to 61.23% (COVID-19). This finding shows the strong effect of the COVID-19 pandemic on these financial markets. Furthermore, we show how the WTI oil from the volatility transmitter (before the outbreak of the pandemic) becomes a risk receiver after the start of the global pandemic COVID-19. Our findings indicate that recent pandemic intensified volatility spillovers, supporting the financial contagion effects. Finally, we determine the optimal hedge ratios and portfolio weights. The estimates provided suggest the need for active portfolio management, taking into account the distinct characteristics of each sector and thus, the firm. For example, the optimal weight analysis shows how the clean sector has become important in optimal diversification strategies. Our results can be used for portfolio decisions and regulatory policymaking, particularly in the current context of high uncertainty.

Sample average approximation of CVaR-based hedging problem with a deep-learning solution

Conditional Value-at-Risk (CVaR) is an extremely popular risk measure in finance and is usually optimized to reduce the risk of large losses. This paper considers the CVaR optimization problem for hedging a portfolio of derivatives with bounded constraints. We focus on minimizing the CVaR of the loss of the hedging portfolio by a deep learning solution because of its promising application to classic portfolio optimization. As the cost objective function in the deep learning framework, the CVaR does not have a closed-form expression, but it can be estimated by using the i.i.d samples average approximation method. While many works have adopted minimizing the estimated CVaR to obtain the optimal solution, they lack theoretical performance guarantees for sample-based solutions. This paper attempts to bridge this gap. On the one hand, we introduce a typical deep neural network architecture for training the optimal hedging strategies, which helps us to analyze the properties of function set for this neural network. On the other hand, we offer a sufficient condition to guarantee that the optimal strategies obtained by using the estimated CVaR can be assured in practical applications. In particular, we prove that the uniform convergence in probability of the estimated CVaR to CVaR over a set of functions, which are generated by the proposed deep neural network. Numerical experiments verify the proposed sufficient condition and demonstrate the feasibility and superiority of this approach.

Dynamic financing and hedging under model uncertainty

ABSTRACT We extend the classic framework to investigate a firm's optimal financing, investment, payout and hedging strategies under model uncertainty (or ambiguity). It shows that model uncertainty has essentially different effects on liquidity policies compared to traditional business risk. A firm facing model uncertainty prefers refinancing less and payout earlier, and the marginal value may be increased when the refinancing option is in the money. Moreover, our model demonstrates that hedging tools play an important role in mitigating the negative impacts on firm value caused by model uncertainty, which illustrates an interesting result that traditional risk management method works well not only on business risk but also on model uncertainty.

Diversifying investor's portfolio using bitcoin: An econometric analysis

Rational investors look into maximizing returns with minimal risk. Since this is highly unlikely, optimizing risk and return is a practical solution. Bitcoin is a new financial product that can be included in an investment portfolio. This paper looks at Bitcoins as a separate asset class and attempts to capture the volatility using the Exponential GARCH (E‐GARCH) as well as to check if Bitcoins can be used as an optimal tool to hedge using the Dynamic Conditional Correlation GARCH against four traditional asset classes in the U.S. economy which includes the stock market (S&amp;P 500 index), Bonds (U.S. Aggregate Bond Index), Gold and Crude Oil. The period of study is a little over 7 years. The results suggest that Bitcoin stands as a highly speculative class of asset with extremely high volatility and with respect to hedging, Bitcoin stands as a possible tool of hedge with the U.S. Aggregate Bond index and to a certain extent against Gold but fails to be an optimal hedge against the S&amp;P 500 and Crude Oil in the U.S. economy between April 29, 2013 and October 31, 2019 due to its highly volatile nature.

Multivariate continuous-time modeling of wind indexes and hedging of wind risk

With the introduction of the exchange-traded German wind power futures, opportunities for German wind power producers to hedge their volumetric risk are present. We propose two continuous-time multivariate models for wind power utilization at different wind sites, and discuss the properties and estimation procedures for the models. Applying the models to wind index data for wind sites in Germany and the underlying wind index of exchange-traded wind power futures contracts, the estimation results of both models suggest that they capture key statistical features of the data. We show how these models can be used to find optimal hedging strategies using exchange-traded wind power futures for the owner of a portfolio of so-called tailor-made wind power futures. Both in-sample and out-of-sample hedging scenarios are considered, and, in both cases, significant variance reductions are achieved. Additionally, the risk premium of the German wind power futures is analysed, leading to an indication of the risk premium of tailor-made wind power futures.

Methanol futures hedging with skewed normal distribution by copula method

As an environmental protection fuel, methanol is widely used in national economy. The tremendous price fluctuation of methanol makes risk avoidance an important issue. However, traditional normal hypothesis in the existing literature underestimates the potential risk and leads to an inefficient hedging strategy, so we studied hedging strategy with methanol futures contracts based on the skewed normal hypothesis. Considering that copula methods allow us to construct a flexible multivariate distribution when solving the problem of asymmetry and nonlinearity, the dependence structure between spot and futures return is modelled through copula functions in this paper. Since likelihood equations do not have explicit solutions in the context of skewed normal, Genetic Algorithm is used to estimate the parameters of a skew normal distribution. To deal with the complexity of the proposed model, the artificial bee colony algorithm is adopted to search for the optimal solutions. Empirical results show that skewed normal distribution can represent the distribution characteristics of return better and improve the hedging effectiveness. Gaussian copula describes the dependence structure of spot and futures quite well. The algorithms designed to obtain the parameters in the marginal distributions and to find the optimal hedge ratio are effective and feasible.

Currency hedging for single-currency equity portfolios: Does cross-asset risk matter?

Foreign investors who are fully invested in a single-currency domestic equity portfolio are exposed to domestic equity risk, but also to currency risk. The standard approach to hedging the currency risk optimally is to estimate a single optimal hedge ratio, but this approach hedges only exchange rate risk, not cross-asset risk. We provide an alternative approach that estimates two optimal hedge ratios to adjust the currency exposures—one associated with the domestic currency and one associated with the foreign currency—and hedges both exchange rate risk and cross-asset risk. This alternative approach can significantly reduce risk.

Risk management and optimal capital structure under ambiguity

This study examines how managers’ perceived ambiguity influences risk management policies and capital structure decisions. After deriving the optimal hedge ratio and leverage ratio under ambiguity, we show the relationship between our results and recent studies. Our result supports the empirical evidence of a negative relationship between ambiguity and leverage ratio. We also find that the efficiency of hedging is an important factor when examining the value of hedging under ambiguity. The literature shows that the value of hedging increases with ambiguity; however, this result holds only when the efficiency of hedging is large, as in a full-hedge strategy.