Optimal Hedging Strategy Research Articles

Hedging and pricing illiquid options with market impacts

In this paper, we consider hedging and pricing of illiquid options on an untradable underlying asset, where an alternative asset is used as a hedging instrument. Particularly, we consider the situation where the trade price of the hedging instrument is subject to market impacts caused by the hedger and the liquidity costs paid as a spread from the mid price. Pricing illiquid options, which often appears in trading of structured products, is a critical issue in practice because of its difficulties in hedging mainly due to untradability of the underlying asset as well as the liquidity costs and market impacts of the hedging instrument. First, by setting the problem under a discrete time model, where the optimal hedging strategy is defined by the local risk-minimization, we present algorithms to obtain the option price along with the hedging strategy by an asymptotic expansion. Moreover, we provide numerical examples. This model enables the estimation of the effect of both the market impacts and the liquidity costs on option prices, which is important in practice.

Analysis of Optimal Hedging Ratio of Copper Futures Based on ECM Model

In this paper, on the one hand, we need to prove that there is a cointegration relationship between copper futures price and spot price. Then, using the ECM model to estimate the optimal hedging resale value of copper futures contract in our country, it is based on the frequency statistics method, the optimal hedging strategy, the approach does not consider the existence of risk estimation, and the most natural way to solve this problem is the bayesian method. So, on the other hand, we are under the bayesian framework, Gibbs sampling method is used to the Chinese copper futures market, the optimal hedging strategy has carried on the empirical analysis. By comparing the hedging efficiency, the result of hedging based on Bayesian statistics is better than that based on frequency statistics.

Optimal hedging with basis risk under mean–variance criterion

Basis risk occurs naturally in a number of financial and insurance risk management problems. A notable example is in the context of hedging a derivative where the underlying security is either non-tradable or not sufficiently liquid. Other examples include hedging longevity risk using index-based longevity instrument and hedging crop yields using weather derivatives. These applications give rise to basis risk and it is imperative that such a risk needs to be taken into consideration for the adopted hedging strategy. In this paper, we consider the problem of hedging a European option using another correlated and liquidly traded asset and we investigate an optimal construction of hedging portfolio involving such an asset. The mean–variance criterion is adopted to evaluate the hedging performance, and a subgame Nash equilibrium is used to define the optimal solution. The problem is solved by resorting to a dynamic programming procedure and a change-of-measure technique. A closed-form optimal control process is obtained under a diffusion model setup. The solution we obtain is highly tractable and to the best of our knowledge, this is the first time the analytical solution exists for dynamic hedging of general European options with basis risk under the mean–variance criterion. Examples on hedging European call options are presented to foster the feasibility and importance of our optimal hedging strategy in the presence of basis risk.

ЭВОЛЮЦИЯ ФУНКЦИИ ЦЕНЫ АМЕРИКАНСКОГО ОПЦИОНА НА АКЦИИ С ВЫПЛАТОЙ ДИВИДЕНДОВ В МОДЕЛИ ДИФФУЗИИ СО СКАЧКАМИ

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

Hedging strategies for European contingent claims with the minimum shortfall risk criterion

This paper studied the optimal self-financing hedging strategies under the minimum shortfall risk criterion. By virtue of the Monte Carlo simulation, thousands of the underlying asset’s price paths are generated and the expected shortfall is estimated with the averaged terminal shortfall on all simulated price paths. Then, the Particle swarm optimization method is adopted to approximate the hedging positions. Compared with present researches, our numerical computing method can overcome the shortcomings that no explicit expressions about hedging strategies exist under the minimum shortfall risk criterion, And the empirically researching results show that, the higher strategy-adjusting-frequency may more excellently resist the financial market’s fluctuating risk and there is a reverse relationship between European call option’s strike prices and the hedging positions.

Optimal Hedging with Basis Risk under Mean-Variance Criterion

Basis risk occurs naturally in a number of financial and insurance risk management problems. A notable example is in the context of hedging a derivative where the underlying security is either non-tradable or not sufficiently liquid. Other examples include hedging longevity risk using index-based longevity instrument and hedging crop yields using weather derivatives. These applications give rise to basis risk and it is imperative that such a risk needs to be taken into consideration for the adopted hedging strategy. In this paper, we consider the problem of hedging a European option using another correlated and liquidly traded asset and we investigate an optimal construction of hedging portfolio involving such an asset. The mean-variance criterion is adopted to evaluate the hedging performance, and a subgame Nash equilibrium is used to define the optimal solution. The problem is solved by resorting to a dynamic programming procedure and a change-of-measure technique. A closed-form optimal control process is obtained under a diffusion model setup. The solution we obtain is highly tractable and to the best of our knowledge, this is the first time the analytical solution exists for dynamic hedging of general European options with basis risk under the mean-variance criterion. Examples on hedging European call options are presented to foster the feasibility and importance of our optimal hedging strategy in the presence of basis risk.

The Föllmer–Schweizer decomposition under incomplete information

In this paper we study the Föllmer–Schweizer decomposition of a square integrable random variable with respect to a given semimartingale S under restricted information. Thanks to the relationship between this decomposition and that of the projection of with respect to the given information flow, we characterize the integrand appearing in the Föllmer–Schweizer decomposition under partial information in the general case where is not necessarily adapted to the available information level. For partially observable Markovian models where the dynamics of S depends on an unobservable stochastic factor X, we show how to compute the decomposition by means of filtering problems involving functions defined on an infinite-dimensional space. Moreover, in the case of a partially observed jump-diffusion model where X is described by a pure jump process taking values in a finite dimensional space, we compute explicitly the integrand in the Föllmer–Schweizer decomposition by working with finite dimensional filters. Finally, we use our achievements in a financial application where we compute the optimal hedging strategy under restricted information for a European put option and provide a comparison with that under complete information.

ЭВОЛЮЦИЯ ФУНКЦИИ ЦЕНЫ АМЕРИКАНСКОГО ОПЦИОНА НА АКЦИИ С ВЫПЛАТОЙ ДИВИДЕНДОВ В МОДЕЛИ ДИФФУЗИИ СО СКАЧКАМИ

This work is devoted to the analysis and evolution of the value function of American type options on a dividend paying stock under jump diffusion processes. An equivalent form of the value function is obtained and analyzed. Moreover, variational inequalities satisfied by this function are investigated. These results can be used to investigate the optimal hedging strategies and optimal exercise boundaries of the corresponding options.

Is hedging the crack spread no longer all it's cracked up to be?

The traditional approach to hedging the crude oil refining margin (crack spread) adopts a fixed 3:2:1 ratio between the futures positions of crude oil, gasoline, and heating oil. However, hedging the latter in arbitrary proportions might be more effective under some conditions. The paper constructs optimal hedging strategies for both scenarios during the periods of relatively stable and volatile oil prices observed in recent years. Minimization of downside risk (LPM2) and variance are used as alternative hedging objectives. The joint distribution of spot and futures price log returns is modeled using a kernel copula method. The hedging performance of the constructed strategies is compared using hedging effectiveness, expected profit, and expected shortfall. The results show that allowing for arbitrary proportions in the sizes of futures positions generally achieves a better hedging performance. The advantage becomes particularly important during periods characterized by greater variation of the cross-dependence between the price log returns of individual commodities. In addition, using LPM2 as a hedging criterion can help hedgers to better track downside risk as well as lead to higher expected profit and lower expected shortfall.

Optimal Hedging with Options and Futures against Price Risk and Background Risk

On the condition that both futures and options exist in the markets for hedging, this paper examines the optimal hedging strategy under price risk and background risk. Compared with the previous research, which has studied options hedging against basis risk and production risk being extended to options and futures hedging against price risk and background risk, we proposed a model and have taken the budget of buying options into consideration. The model is fairly general and some existing models are special cases of it. We firstly derive the necessary and sufficient conditions that guarantee the optimality of an under-hedge, a full-hedge and an over-hedge of futures for the risk-averse utility. Then, sufficient conditions are stipulated under which an over-hedge is optimal. Furthermore, we propose a program minimizing of tail conditional expectation (TCE), which is inherently equivalent to the risk measure of expected shortfall risk (ES) or the conditional VaR (CVaR) under the continuous-time framework. Finally, we find that ES, in our proposed model, is significantly smaller than the one in the model of options hedging only. Therefore, the results emphasize the need for combining futures hedging and options hedging, and it also shows that imposing background risk, whether it be additive or multiplicative, always has a great impact on the hedging efficiency. We also present some sensitivities of the relevant parameters to provide some suggestions for the investors.

Optimal hedging using both regular and weather derivatives

This paper analyses how to achieve optimal hedging of a cash flow to be received at a future date T, when facing price risk, cost and quantity uncertainty. We explore and compare the case where the only instrument available to hedge is a regular forward contract (to hedge the price uncertainty), the case where we only have access to a linear-type weather derivative to hedge quantity, and the case where both types of contracts are available. A closed form solution for both the optimal hedging strategies and the quality of the hedging under each scenario are identified. We show how to obtain the optimal hedging strategies through linear regressions. Then, by using simulations, we explore how the results critically depend on some key factors such as the volatility of some stochastic variables considered and the degree of correlation among some of the variables considered.

The application of nonlinear fuzzy parameters PDE method in pricing and hedging European options

In recent years, fuzzy sets theory has been introduced as a means of modeling the uncertainties of the input parameters of the Black–Scholes–Merton European options pricing formula. However, some standard assumptions underlying the Black–Scholes–Merton model including those of constant interest rate and volatility no longer hold in fuzzy environments. Therefore, it is inappropriate to price options with uncertain parameters based on the Black–Scholes–Merton formula. In this paper, we propose a methodology for option pricing under fuzzy environments which is essentially different from the Black–Scholes–Merton option pricing framework. We build a nonlinear fuzzy-parameter PDE model for obtaining the fuzzy option prices and we develop dominating optimal hedging strategies under fuzzy environments which provide valuable insights for risk management and trading in financial markets.

Production Planning with Shortfall Hedging, under Partial Information and Budget Constraint

We study production planning integrated with risk hedging by considering shortfall as the risk measure. In addition to the one-time production quantity decision, there is a real-time hedging strategy throughout the horizon; and the goal is to minimize the gap between a pre-specified target and the total terminal wealth achieved by both production and hedging. We assume partial information --- hedging is executed based on information from the financial market only, and impose a budget constraint to cap any loss from hedging. To find the optimal hedging strategy, we construct a dual problem, which provides a lower bound to the original problem. Solving the lower-bound problem yields the optimal terminal wealth from hedging; the real-time hedging strategy is then mapped out via martingale representation theorem. Interestingly, the optimal hedging strategy takes the form of a portfolio of two options, a digital option and a put option. With the hedging strategy optimized, we show that optimizing production quantity is a convex minimization problem. With both production and hedging optimized, we provide a complete characterization of the efficient frontier: the minimized shortfall as an increasing function of the target. We also derive an explicit quantification of the shortfall reduction achieved by hedging. Asymptotic analysis on several key parameters (such as the target, the budget, and the production quantity) generates additional insights to the hedging strategy and its impact.

Dependence between oil price volatility, Islamic and conventional Dow Jones indexes: Implication for portfolio management and hedging effectiveness

The purpose behind this paper is twofold. Firstly, it aims at discussing the relationship between oil price and Islamic as well as conventional Dow Jones indexes. Secondly, it focuses on determining the optimal portfolio hedging strategy. In broader terms, it helps analyze the extreme dependence structure lying between oil price and Islamic as well as conventional Dow Jones indexes, using Kendall Tau estimation through copula approach. More importantly, it is designed to determine the most appropriate hedging strategy fit for oil stock portfolio against the negative variation risk predominating stock market prices. The variables involved in our research are WTI and Brent Oil Price, Islamic Dow Jones index, and conventional Dow Jones index. Using daily data relevant to the period ranging from January 1, 1996 to March 17, 2014, the study applies the FIEGARCH-EVT-Copula and Hedge ratios analysis. The reached findings have revealed that the dependence structure proves to differ noticeably among the Islamic Dow Jones – oil price and the conventional Dow Jones one. Indeed, the Islamic Dow Jones indexes appear to be more dependent on the WTI and Brent oil price than the conventional Dow Jones index. Based on the Hedging ratio and mean–variance approach, investment in Islamic index–oil portfolio has been discovered to be more beneficial as compared to investing in conventional index–oil portfolio.

PRICING AND HEDGING GAME OPTIONS IN CURRENCY MODELS WITH PROPORTIONAL TRANSACTION COSTS

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 probabilistic dual representations for the bid and ask price of a game option.

Dependence between oil and commodities markets using time-varying Archimedean copulas and effectiveness of hedging strategies

ABSTRACTThe aim of this work is to study in a first step the dependence between oil and some commodity prices (cotton, rice, wheat, sucre, coffee, and silver) using copula theory, and then in a second step to determine the optimal hedging strategy for oil–commodity portfolio against the risk of negative variation in commodity markets prices. The model is implemented with an AR-GARCH model with innovations that follow t distribution for the marginal distribution and the extreme value copula for the joint distribution and parameters and dependence indices are re-estimated in each new day which allow taking into account nonlinear dependence, tails behavior, and their development over time. Various copula functions are used to model the dependence structure between oil and commodity markets. Empirical results show an increase in the dependence during the last 6 years. Volatility for commodity prices registered record levels in the same time with the increase in uncertainty. Optimal hedging ratio varies over time as a consequence of the change in the dependence structure.

Local risk minimization for vulnerable European contingent claims on nontradable assets under regime switching models

ABSTRACTThis article focuses on an optimal hedging problem of the vulnerable European contingent claims. The underlying asset of the vulnerable European contingent claims is assumed to be nontradable. The interest rate, the appreciation rate and the volatility of risky assets are modulated by a finite-state continuous-time Markov chain. By using the local risk minimization method, we obtain an explicit closed-form solution for the optimal hedging strategies of the vulnerable European contingent claims. Further, we consider a problem of hedging for a vulnerable European call option. Optimal hedging strategies are obtained. Finally, a numerical example for the optimal hedging strategies of the vulnerable European call option in a two-regime case is provided to illustrate the sensitivities of the hedging strategies.

Toward an optimal hedging strategy considering earnings volatility through fair value accounted financial derivatives

Purpose The purpose of this paper is to determine a financial institution's optimal hedging degree under consideration of costly earnings volatility induced by fair value accounted derivatives. The discussion on the adoption of fair value accounting in the financial industry has been rather controversial in recent years. Under this accounting regime, the change in market values of specific assets must be considered as profit or loss. Critics argue that fair value accounting induces higher earnings volatility compared to historical cost accounting and, therefore, may initiate a downward spiral during recessions. Thus, increased earnings volatility induces costs, which can be explained by disappointed capital market expectations. Consequently, in general, a lowering of earnings volatility will be rewarded. Consistent with this theoretical finding, empirical research provides strong evidence that companies pursue income smoothing to reduce earnings volatility. In contrast to industrial corporations, financial institutions may easily reduce their earnings volatility by engaging in additional hedging activities. However, more intense hedging usually reduces expected profits. Design/methodology/approach Based on a research project initiated by a large German bank, this study quantitatively models the trade-off between the (utility of) costs of earnings volatility and the reduction of profit potential through additional hedging. Findings By conducting sensitivity analyses and simulations of the crucial factors of the trade-off, we examine relevant causal relationships to obtain first indications about the economic benefits of income smoothing. Originality/value To the best of our knowledge, we are the first to develop an optimization model that supports decision-making by attempting to determine an optimal (additional) hedging degree considering the costs induced by earnings volatility.

Hedging crop yield with exchange-traded weather derivatives

Purpose – The application of weather derivatives in hedging crop yield risk is gaining more interest. However, the further development of weather derivatives – particularly exchange-traded – in the agricultural sector has been impeded by concerns over their hedging performance. The purpose of this paper is to develop a new framework to derive the optimal hedging strategy and evaluate hedging effectiveness. Design/methodology/approach – This framework incorporates a stochastic temperature model, a crop yield model, a risk-neutral pricing method and a profit optimization procedure. Based on a large number of simulated scenarios, the authors study crop yield hedge for a future year. The authors allow the hedger to choose from different types of exchange-traded weather derivatives, and examine the impact of various factors on the optimal hedging strategy. Findings – The analysis shows that hedging objective, pricing method and geographical location of the hedged exposure all play important roles in choosing the best hedging strategy and assessing hedging effectiveness. Originality/value – This framework is forward-looking, because it focusses on the crop yield hedge for a future year rather than on the historical hedging effectiveness often studied in literature. It utilizes the most up-to-date information related to temperature and crop yield, and hence produces a hedging strategy which is more relevant to the year under consideration.

CURRENCY HEDGING STRATEGIES USING MULTIVARIATE GARCH MODELS

Hedging on futures or forward markets is an important tool to reduce risk. Thus, in order to manage the currency risk, it is important to have a suitable hedging strategy. Hedging is a means to offset potential losses on investment by making the second investment, which is expected to move in the opposite way in the financial markets. Therefore, this study aims to identify the relationship between spot and futures contract exchange rates and spot and forwards contract exchange rates. Secondly, calculate the optimal hedge ratio in order for effective optimal portfolio design and hedging strategy using CCC, DCC and Diagonal-BEKK models. The data consist of daily closing prices of spot, futures and 3-month forwards contract for currencies within ASEAN and ASEAN+3 countries. The empirical results revealed that the best model for hedging effectiveness is found to be CCC and DCC. These two models are able to reduce the variance 59.64 percent for Japanese Yen, 97.42 percent for Malaysia Ringgit, 66.14 percent for Singapore Dollar and 93.42 for Philippine Peso. Hence, it can be suggested to investors to hedge Malaysia Ringgit since the currency has the highest reduction in risk.