Hedging Parameters Research Articles

INSTRUMEN LINDUNG NILAI MENURUT PERSPEKTIF ISLAM: ANALISIS PELAKSANAANNYA DALAM SEKTOR KEWANGAN DI MALAYSIA

The concept of hedging that is understood in the conventional financial system and the Islamic financial system has the same purpose, which is to manage risk. Islamic scholars agree that the law of hedging is a must in the syariah because it brings maslahah and fulfills the objective principles of the syariah. Even so, this concept that leads to the protection of property is accepted by Sharia scholars in accordance with the general principles in Islam that celebrate the welfare of the community. However, the application of the concept of hedging in the Islamic financial system needs to be different from the conventional financial system so that it does not conflict with the guidance contained in the Qur'an and the Sunnah which reject harm. Therefore, this writing aims to evaluate the actual position of the hedging concept according to the Sharia and then propose hedging parameters that are in line with the principles of the Sharia. The results of the study found that Islam recognizes the concept of hedging as one of the risk management methods, but its acceptance is bound by the condition of compliance with the guidelines that have been set. This study is expected to provide useful input especially to the Islamic finance industry in an effort to create more Sharia-compliant hedging instruments.

Research on Trend Investing Strategy and Hedging Strategy

An investment method based on traditional subjective judgments faces huge challenges, while the strategy of quantitative investment is to find the optimal alpha model to judge the best timing of selling and buying and designing the most effective investment portfolio. Therefore, compared with traditional investment methods, quantitative investment breaks through the limitations of subjective judgment with its qualitative and quantitative advantages. The futures market attracts many investors with its low transaction costs and the two-way nature of transactions. However, most of the investment strategies that are frequently used in the market have low stability and do not guarantee correlation with the general market trend. This makes the investments risky, particularly for individual investors. Therefore, this paper will explore both futures investment and risk hedging strategies, aiming to ensure that every buy and sell is the correct choice as much as possible, such that futures investment is relatively stable and has high returns. This article focuses on using the moving average cross strategy through the python programming language to achieve the judgment of buying and selling in the process of futures trading and drawing the net worth curve of the real-time futures market data and perform a correlation analysis to determine which commodity sector is the most suitable using the trend strategy. For risk hedging, the article mainly uses the correlation analysis to study the relation between the prices of different types of futures. Furthermore, the futures and options market price fluctuations are discussed in depth, and also analysed is how to use and balance hedge parameters for risk hedging.

An accurate and stable numerical method for option hedge parameters

We propose an unconditionally stable numerical algorithm, which uses the Feynman-Kac formula of the Black-Scholes equation to obtain accurate option prices and hedge parameters. We discretize the asset and time using uniform grid points. We approximate the option values by piecewise quadratic polynomials for each time step and integrate them analytically over the log-normal distribution. The piecewise quadratic approximation gives the third-order convergence in the asset direction, and the analytic integration reduces truncation error in the time direction. The estimation errors are propagated backward in time following the convection and diffusion characteristics of the Black-Scholes equation, which assures the unconditional stability of our method. The vectorized code implementation reduces the time complexity. The convergence test shows that our approach outperforms the Crank-Nicolson scheme of the finite difference method in both time and asset directions, and the stability test verifies that our method is stable as the Crank-Nicolson. Furthermore, we show that our algorithm reduces the price errors and hedge parameter errors by more than 50% from the benchmark.

Reducing transaction costs for interest rate risk hedging with stochastic programming

Traditional methods for hedging interest rate risk do not take transaction costs into account as they aim to eliminate all risk. We propose a two-stage stochastic programming model for hedging interest rate risk where transaction costs are weighed against portfolio variance. High-quality measurements of term structures enable us to extract the systematic risk factors and make precise estimates of the perceived transaction costs. The hedging cost is weighed against the reduction in portfolio variance by using an adjustable hedging parameter. The hedging procedure is simulated on a daily basis in a realistic setting over an out-of-sample period from 2002 to 2018, and the results are compared to traditional hedging methods through detailed performance attribution. Using second-order stochastic dominance, we show that the proposed method is preferred by all risk-averse investors.

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.

A Spectral Element Method for Option Pricing Under Regime-Switching with Jumps

In this paper, we propose the spectral element method to price European, digital, butterfly, American, discrete and continuous barrier options in a Markovian jump-diffusion regime-switching economy. The spectral element method discretisation is considered for the approximation of the spatial derivatives in a system of partial integro-differential equations and is chosen because it possesses spectral accuracy such that highly accurate option prices can be obtained using a small number of grid discretisation nodes. Essentially, the spectral element method consists of splitting the computational domain into as many elements as needed and approximating the basis functions by high-order orthogonal polynomials within each element. In order to sustain the high-order convergence in time, we also use an exponential time integration scheme to solve the semi-discrete system. Our numerical examples support our error analysis and indicate that the spectral element method converges exponentially for the values and the hedging parameters of the regime-dependent options. Therefore, the proposed scheme provides a viable alternative to the finite difference or finite element methods which usually converge only algebraically.

On the pricing of multi-asset options under jump-diffusion processes using meshfree moving least-squares approximation

The moving least-squares (MLS) approximation is a powerful numerical scheme widely used in the meshfree literature to construct local multivariate polynomial basis functions for expanding the solution of a given differential or integral equation. For partial integro-differential equations arising from the valuation of multi-asset options written on correlated Lévy-driven assets, we propose here an MLS-based collocation scheme in conjunction with implicit-explicit (IMEX) temporal discretization to numerically solve the problem. We apply the method to price both European and American options and compute the option hedge parameters. In the case of American options, we use an operator splitting approach to solve the linear complementarity formulation of the problem. Our numerical experiments show the efficiency of the proposed scheme in comparison with some competing approaches, specially finite difference methods.

On expansions for the Black-Scholes prices and hedge parameters

We derive new formulas for the price of the European call and put options in the Black-Scholes model, under the form of uniformly convergent series generalizing previously known approximations; these series are obtained by means of tools from multidimensional complex analysis. We also provide precise boundaries for the convergence speed and apply the results to the calculation of hedge parameters (Greeks).

The Credit Asset of Enterprise Accounts Receivable Pricing Model

Based on the thinking of holism and reductionism, this paper creatively constructed the credit asset pricing model of enterprises’ accounts receivable, namely, the BEST pricing model, and it was demonstrated effectively. The model gave an overall evaluation on the default probability of buyer and environment, as well as buyer loss given default resulting from the factors including Seller (S), Buyer (B), and Environment (E). The model is also utilized with the optimal control management Technology (T) to maximize the intrinsic value of the credit asset. The paper put forward the Duration of accounts receivable aging, measurement method of dynamic free interest rate, and amended the KMV model to solve the default probability of accounts receivable of listed and nonlisted companies. To evaluate the credit asset risk, the following were selected: three effective financial indicators, seven nonfinancial index clusters, and sixty-three specific nonfinancial index variables of the buyer; one index and eight specific indicators of the seller; and one index and fourteen specific indicators of nonsystematic risk of the environment. Five appropriate hedge parameters are used to control the risk.

Season-Dependent Hedging Policies for Reservoir Operation—A Comparison Study

During periods of significant water shortage or when drought is impending, it is customary to implement some kind of water supply reduction measures with a view to prevent the occurrence of severe shortages (vulnerability) in the near future. In the case of operation of a water supply reservoir, this reduction of water supply is affected by hedging schemes or hedging policies. This research work aims to compare the popular hedging policies: (i) linear two-point hedging; (ii) modified two-point hedging; and, (iii) discrete hedging based on time-varying and constant hedging parameters. A parameterization-simulation-optimization (PSO) framework is employed for the selection of the parameters of the compromising hedging policies. The multi-objective evolutionary search-based technique (Non-dominated Sorting based Genetic Algorithm-II) was used to identify the Pareto-optimal front of hedging policies that seek to obtain the trade-off between shortage ratio and vulnerability. The case example used for illustration is the Hemavathy reservoir in Karnataka, India. It is observed that the Pareto-optimal front that was obtained from time-varying hedging policies show significant improvement in reservoir performance when compared to constant hedging policies. The variation in the monthly parameters of the time-variant hedging policies shows a strong correlation with monthly inflows and available water.

Multi-Objective Simulation-Optimization Model for Long-term Reservoir Operation using Piecewise Linear Hedging Rule

An efficiently parameterized and appropriately structured piecewise linear hedging rule is formulated and included within a multi-objective simulation-optimization (S-O) framework that seeks to obtain Pareto-optimal solutions for the long-term hedged operation of a single water supply reservoir. Two conflicting objectives, namely, “minimize the total shortage ratio” and “minimize the maximum shortage” are considered in the S-O framework, while explicit specification of constraints is avoided in the optimization module. Evolutionary search based non-dominated sorting genetic algorithm is used as the driver, which is linked to the simulation engine that invokes the piecewise linear hedging rule within the S-O framework. Preconditioning of the multi-objective stochastic search of the time-varying piecewise linear hedging model is effected by feeding initial feasible solutions sampled from the Pareto-optimal front of a simple constant hedging parameter model, which has resulted in significant improvement of the Pareto-optimality and the computational efficiency.

Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates

This paper studies an outside-reset option with multiple strike resets and reset dates, in which the strike price is adjusted by an external process associated with the underlying risky asset. We obtain analytical pricing formula for this option and the hedging parameters Delta and Gamma. Furthermore, some numerical examples are provided to analyze some characteristics of the outside-reset option and to examine the impacts of the external parameters on option prices and Greeks. These results show that the external process can significantly affect option prices and Greeks.

Pricing and hedging barrier options under a Markov-modulated double exponential jump diffusion-CIR model

A semi-closed-form valuation model is presented for barrier options whose underlying asset follows a mean-reverting and regime-switching double exponential jump diffusion process, and the interest rate is modulated by a mean-reverting square root model. The proposed model captures the impact of regime-switching uncertainty on barrier option prices and their hedge parameters in long and short business cycles. The model provides richer economic insight and is more appropriate for valuing barrier options in commodity markets as well as in equity and foreign-exchange markets, when an economy faces regime-switching uncertainty.

Analysis of a jump-diffusion option pricing model with serially correlated jump sizes

ABSTRACTThis paper extends the classical jump-diffusion option pricing model to incorporate serially correlated jump sizes which have been documented in recent empirical studies. We model the series of jump sizes by an autoregressive process and provide an analysis on the underlying stock return process. Based on this analysis, the European option price and the hedging parameters under the extended model are derived analytically. Through numerical examples, we investigate how the autocorrelation of jump sizes influences stock returns, option prices and hedging parameters, and demonstrate its effects on hedging portfolios and implied volatility smiles. A calibration example based on real market data is provided to show the advantage of incorporating the autocorrelation of jump sizes.

A Dimension and Variance Reduction Monte-Carlo Method for Option Pricing under Jump-Diffusion Models

We develop a highly efficient MC method for computing plain vanilla European option prices and hedging parameters under a very general jump-diffusion option pricing model which includes stochastic variance and multi-factor Gaussian interest short rate(s). The focus of our MC approach is variance reduction via dimension reduction. More specifically, the option price is expressed as an expectation of a unique solution to a conditional Partial Integro-Differential Equation (PIDE), which is then solved using a Fourier transform technique. Important features of our approach are (i) the analytical tractability of the conditional PIDE is fully determined by that of the Black-Scholes-Merton model augmented with the same jump component as in our model, and (ii) the variances associated with all the interest rate factors are completely removed when evaluating the expectation via iterated conditioning applied to only the Brownian motion associated with the variance factor. For certain cases when numerical methods are either needed or preferred, we propose a discrete fast Fourier transform method to numerically solve the conditional PIDE efficiently. Our method can also effectively compute hedging parameters. Numerical results show that the proposed method is highly efficient.

A dimension and variance reduction Monte-Carlo method for option pricing under jump-diffusion models

ABSTRACTWe develop a highly efficient MC method for computing plain vanilla European option prices and hedging parameters under a very general jump-diffusion option pricing model which includes stochastic variance and multi-factor Gaussian interest short rate(s). The focus of our MC approach is variance reduction via dimension reduction. More specifically, the option price is expressed as an expectation of a unique solution to a conditional Partial Integro-Differential Equation (PIDE), which is then solved using a Fourier transform technique. Important features of our approach are (1) the analytical tractability of the conditional PIDE is fully determined by that of the Black–Scholes–Merton model augmented with the same jump component as in our model, and (2) the variances associated with all the interest rate factors are completely removed when evaluating the expectation via iterated conditioning applied to only the Brownian motion associated with the variance factor. For certain cases when numerical methods are either needed or preferred, we propose a discrete fast Fourier transform method to numerically solve the conditional PIDE efficiently. Our method can also effectively compute hedging parameters. Numerical results show that the proposed method is highly efficient.

THE VALUATION OF SELF-FUNDING INSTALMENT WARRANTS

We present two models for the fair value of a self-funding instalment warrant. In both models we assume the underlying stock process follows a geometric Brownian motion. In the first model, we assume that the underlying stock pays a continuous dividend yield and in the second we assume that it pays a series of discrete dividend yields. We show that both models admit similarity reductions and use these to obtain simple finite-difference and Monte Carlo solutions. We use the method of multiple scales to connect these two models and establish the first-order correction term to be applied to the first model in order to obtain the second, thereby establishing that the former model is justified when many dividends are paid during the life of the warrant. Further, we show that the functional form of this correction may be expressed in terms of the hedging parameters for the first model and is, from this point of view, independent of the particular payoff in the first model. In two appendices we present approximate solutions for the first model which are valid in the small volatility and the short time-to-expiry limits, respectively, by using singular perturbation techniques. The small volatility solutions are used to check our finite-difference solutions and the small time-to-expiry solutions are used as a means of systematically smoothing the payoffs so we may use pathwise sensitivities for our Monte Carlo methods.

A multi-level dimension reduction Monte-Carlo method for jump–diffusion models

This paper develops and analyses convergence properties of a novel multi-level Monte-Carlo (mlMC) method for computing prices and hedging parameters of plain-vanilla European options under a very general b -dimensional jump–diffusion model, where b is arbitrary. The model includes stochastic variance and multi-factor Gaussian interest short rate(s). The proposed mlMC method is built upon (i) the powerful dimension and variance reduction approach developed in Dang et al. (2017) for jump–diffusion models, which, for certain jump distributions, reduces the dimensions of the problem from b to 1 , namely the variance factor, and (ii) the highly effective multi-level MC approach of Giles (2008) applied to that factor. Using the first-order strong convergence Lamperti–Backward-Euler scheme, we develop a multi-level estimator with variance convergence rate O ( h 2 ) , resulting in an overall complexity O ( ϵ − 2 ) to achieve a root-mean-square error of ϵ . The proposed mlMC can also avoid potential difficulties associated with the standard multi-level approach in effectively handling simultaneously both multi-dimensionality and jumps, especially in computing hedging parameters. Furthermore, it is considerably more effective than existing mlMC methods, thanks to a significant variance reduction associated with the dimension reduction. Numerical results illustrating the convergence properties and efficiency of the method with jump sizes following normal and double-exponential distributions are presented.

Pricing American-style Parisian down-and-out call options

We propose an integral equation approach for pricing American-style Parisian down-and-out call options under the Black–Scholes framework. For this type of options, the knock-out feature is activated only if the underlying asset price continuously remains below a pre-determined barrier for a sufficiently long period of time. As such, the corresponding pricing problem becomes a three-dimensional (3-D) free boundary problem, instead of a two-dimensional (2-D) one as is the case of “one-touch” barrier options, and this poses a computational challenge. In our approach , we first reduce the 3-D problem to a 2-D one, and then, by applying the Fourier sine transform to the resulting 2-D problem, we can derive a pair of coupled integral equations governing the option price at any given time in terms of (i) the option price at the barrier and (ii) the optimal exercise boundary at that time. This pair of coupled integral equations can be solved using the Newton–Raphson iterative procedure, after which, the option price, the optimal exercise boundary, and the hedging parameters can be obtained in a straightforward manner. A complexity analysis of the method, together with numerical results, show that the proposed approach is robust and significantly more efficient than existing uniform finite difference methods with Crank–Nicolson timestepping, especially in dealing with spot prices near the barrier. Numerical results are also examined in order to provide new insight into several interesting properties of the option price and the optimal exercise boundary.

Pricing American-style Parisian up-and-out call options

In this paper, we propose an integral equation approach for pricing an American-style Parisian up-and-out call option under the Black–Scholes framework. The main difficulty of pricing this option lies in the determination of its optimal exercise price, which is a three-dimensional surface, instead of a two-dimensional (2-D) curve as is the case for a “one-touch” barrier option. In our approach, we first reduce the 3-D pricing problem to a 2-D one by using the “moving window” technique developed by Zhu and Chen (2013, Pricing Parisian and Parasian options analytically. Journal of Economic Dynamics and Control, 37(4): 875-896), then apply the Fourier sine transform to the 2-D problem to obtain two coupled integral equations in terms of two unknown quantities: the option price at the asset barrier and the optimal exercise price. Once the integral equations are solved numerically by using an iterative procedure, the calculation of the option price and the hedging parameters is straightforward from their integral representations. Our approach is validated by a comparison between our results and those of the trusted finite difference method. Numerical results are also provided to show some interesting features of the prices of American-style Parisian up-and-out call options and the behaviour of the associated optimal exercise boundaries.