Optimal Hedging of Basket Barrier Options with Additive Models and Its Application to Equity Value Separation Problem

At the heart of optimal hedging with additive models in Yamada (Recent advances in financial engineering: proceedings of the KIER-TMU international workshop on financial engineering, World Scientific, pp 225–245, 2010; Proceedings of the 2011 American control conference, pp 3856–3861, 2011; Asia-Pac Financ Mark 19(2):149–179, 2012) is to replicate the payoff of European basket options using separate options as close as possible. In this paper, we extend their technique for the case of path-dependent barrier options, where the mean square error of the payoffs between the basket barrier option and the sum of options on the individual assets is minimized over any smooth payoff functions. To this end, we propose to represent the underlying assets using the Brownian bride decomposition and show that computations involving conditional expectations of basket barrier options boil down to those of unconditional expectations. This procedure enables us to provide an algorithm to compute the necessary and sufficient condition for the optimal hedging problem based on the Monte Carlo method. Then, we consider to apply our methodology to the Black–Cox type first passage time structural model, where a defaultable company possesses/runs multiple assets/projects and the default may occur the first time the asset value hits a certain lower threshold before the maturity. We formulate the equity value separation problem using additive models, in which individual equity values are introduced so that their sum approximates the total equity value as close as possible. It is also shown that any portion of total equity value may be assigned as an initial value of each individual equity when using the optimal smooth functions. Finally, we examine the contributions of individual equity values to default or survival by applying a certain normalization for conditional expectations via numerical experiments to illustrate our proposed methodology.     

套期保值与金融衍生品风险管理研究

套期保值是企业经营的重要工具,能够锁定企业的经营成本,规避企业的经营风险。但是,如果套期保值运用不当,则会使企业遭受巨额的损失。本文首先对套期保值的原理及其作用进行基本的介绍,然后,结合我国央企巨亏事件,对套期保值巨亏动因进行深入的分析,以揭示套期保值的潜在风险及其认识误区。最后,对我国企业的套期保值风险控制提出若干建议。     

Deriving Optimal Portfolios for Hedging Housing Risk

Households that contemplate moving to different cities or trading up/down in the future are exposed to substantial housing risk. In order to mitigate this risk, we derive optimal portfolios using CME housing futures. Housing investment risk is hedged by selling housing futures amounting to the full value of the home. Housing consumption risk is hedged by buying housing futures in each city where the household might move. The size of the hedges depends on the probability of moving, on home values, and on labor income in each region. The hedging demands offset each other when the household intends to live in the same home indefinitely.     

Evidence on Hedging Effectiveness in Indian Derivatives Market

The hedging effectiveness for bank futures and CNX nifty are evaluated in this study. The study is based on 9,569 observations of the daily data for these index futures. For evaluation ordinary least square, co-integrated ordinary least square, generalized auto-regressive conditional heteroscedasticity (1, 1), and constant correlation generalized auto-regressive conditional heteroscedasticity (1, 1) hedging methods are estimated and compared. Result shows that constant correlation generalized auto-regressive conditional heteroscedasticity (1, 1) is an efficient hedging method that maximizes investors’ utility function considering transaction costs. Therefore, investors can rely on this constant correlation generalized auto-regressive conditional heteroscedasticity (1, 1) hedging method.     

Multivariate Shrinkage for Optimal Portfolio Weights

Abstract

This paper proposes a multivariate shrinkage estimator for the optimal portfolio weights. The estimated classical Markowitz weights are shrunk to the deterministic target portfolio weights. Assuming log asset returns to be i.i.d. Gaussian, explicit solutions are derived for the optimal shrinkage factors. The properties of the estimated shrinkage weights are investigated both analytically and using Monte Carlo simulations. The empirical study compares the competing portfolio selection approaches. Both simulation and empirical studies show that the proposed shrinkage estimator is robust and provides significant gains to the investor compared to benchmark procedures.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced byan expected-utility maximizing investor who, over a given timehorizon, is constrained to hold an asset which cannot be replicatedby dynamic trading and which therefore does not have a uniqueno-arbitrage price. We first derive the private valuation whichthe investor assigns to the nontraded asset in order to determinehis optimal investment in the traded assets. We thereby showthat, as part of this portfolio, the investor hedges the privatevaluation process of the nontraded asset, rather than its marketprice process. We also study the price at which the investorwould be willing to sell the nontraded asset if he were subsequentlyprohibited from trading in it, as well as the amount the investorwould be willing to pay to remove the trading restriction. Allthree values are shown to depend in an intuitive manner on theinvestor’s risk aversion, the residual risk of the nontradedasset unhedged by the traded assets, the difference betweenthe constrained holding and optimal unconstrained holding ofthe asset and the length of the time horizon over which theasset cannot be traded. JEL Classification: G11     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.     

Optimal Hedging of Prediction Errors Using Prediction Errors

Wind power energy has been paid much attention recently for various reasons, and the production of electricity with wind energy has been increasing rapidly for a few decades. One of the most difficult issues for using wind power in practice is that the power output largely depends on the wind condition, and as a result, the future output may be volatile or uncertain. Therefore, the prediction of power output in the future is considered important and is key to electric power generating industries making the wind power electricity market work properly. However, the use of predictions may cause other problems due to “prediction errors.” In this work, we will propose a new type of weather derivatives based on the prediction errors for wind speeds, and estimate their hedge effect on wind power energy businesses. At first, we will investigate the correlation of prediction errors between the power output and the wind speed in a Japanese wind farm, which is a collection of wind turbines that generate electricity in the same location. Then we will develop a methodology that will optimally construct a wind derivative based on the prediction errors using nonparametric regressions. A simultaneous optimization technique of the loss and payoff functions for wind derivatives is demonstrated based on the empirical data.     

Equilibrium Pricing and Optimal Hedging in Electricity Forward Markets

Spot power prices are volatile and since electricity cannot be economically stored, familiar arbitrage-based methods are not applicable for pricing power derivative contracts. This paper presents an equilibrium model implying that the forward power price is a downward biased predictor of the future spot price if expected power demand is low and demand risk is moderate. However, the equilibrium forward premium increases when either expected demand or demand variance is high, because of positive skewness in the spot power price distribution. Preliminary empirical evidence indicates that the premium in forward power prices is greatest during the summer months.     

Optimal Hedging in Futures Markets with Multiple Delivery Specifications

Nearly all futures contracts allow delivery of any of several qualities of the underlying asset. Consequently, the price of the futures contract is associated more with the price of the expected cheapest deliverable variety than with the price of the par-delivery variety. The delivery specifications introduce a delivery risk for every hedger in the market. We derive the optimal hedging strategies in these markets. Their hedging effectiveness is evaluated for wheat futures contracts in Chicago. Hedging optimally would have significantly reduced the variance of the rates of return on hedges while yielding similar mean returns.     

中国能源期货的对冲模型比较研究

本文以中国燃料油期货及现货数据为例,介绍了中国能源市场中对冲实践的一系列流程:从理论框架、模型选择、数据检验、对冲期限到对冲有效性检验。本文遵循该流程,对比了基于最小方差和效用最大化两类理论框架下的四类模型(OLS、VAR和两类不同的误差修正向量GARCH模型)。实证研究发现:(1)对冲效果与对冲期限呈现先上升后下降的倒U型关系;(2)在效用最大化理论框架下,采用基于向量的GARCH模型和15天动态对冲策略的投资组合对冲后修正夏普比率高达2.95,提升风险收益比的效果十分显著。     

Multivariate Models of Equity Returns for Investment Guarantees Valuation

Abstract

In this paper we investigate the valuation of investment guarantees in a multivariate (discrete-time) framework. We present how to build multivariate models in general, and we survey the most important multivariate GARCH models. A direct multivariate application of regime-switching models is also discussed, as is the estimation of these models using maximum likelihood and their comparison in a multivariate setting. The computation of the CTE provision is further presented. We have estimated the models with a multivariate dataset (Canada, United States, United Kingdom, and Japan), and we compared the quality of their fit using multiple criteria and tests. We observe that multivariate GARCH models provide a better overall fit than regime-switching models. However, regime-switching models appropriately represent the fat tails of the returns distribution, which is where most GARCH models fail. This leads to significant differences in the value of the CTE provisions, and, in general, provisions computed with regime-switching models are higher. Thus, the results from this multivariate analysis are in line with what was obtained in the literature of univariate models.     

Smooth Extremal Models in Finance and Insurance

This article describes smooth nonstationary generalized additive modeling for sample extremes, in which spline smoothers are incorporated into models for exceedances over high thresholds. We summarize the smoothing methodology as a new tool for practical extreme value exploration in finance and insurance.     

Jump-Dependent Model for Optimal Index Futures Hedging in Five Major Asian Stock Markets

This article develops a jump-dependent model to capture the dependences between spot and futures returns and their jumps simultaneously, named JD model. We examine hedging performance of the presenting JD model for the futures contracts of Hong Kong, Japan, Korea, Singapore, and Taiwan. The results have shown that the JD model has better out-of-sample performance than the OLS for Korea, Singapore, and Taiwan. Since these three markets have higher jump dependence between spot and futures, we consider that jump dependence plays an important role in hedging performance. The higher jump dependence means spot and futures markets move more closely when unusual news reveals itself and thus futures could hedge the spot more effectively when extreme unusual news arrives.     

最优动态汇率风险套期保值模型研究

构建一个最优动态汇率风险套期保值理论模型,并将其套期保值效率与静态策略进行实证对比.采用对角BEKK模型来捕捉货币现货与期货市场的交互影响,从而刻画风险最小化套期比率的动态特征,结果表明,套期保值能减少汇率风险,但具体的套期保值策略的效率高低排序与避险频率相关.     

Determination of Optimal Hedging Strategy for Index Futures: Evidence from Turkey

This paper aims to determine optimal hedge strategy for the Istanbul Stock Exchange (ISE)-30 stock index futures in Turkey by comparing hedging performance of constant and time-varying hedge ratios under mean-variance utility criteria. We employ standard regression and bivariate GARCH frameworks to estimate constant and time-varying hedge ratios respectively. The Turkish case is particularly challenging since Turkey has one of the most volatile stock markets among emerging economies and the turnover ratio as a measure of liquidity is very high for the market. These facts can be considered to highlight the great risk and, therefore, the extra need for hedging in the Istanbul Stock Exchange (ISE). The empirical results from the study reveal that the dynamic hedge strategy outperforms the static and the traditional strategies.     

Properties of Multinomial Lattices with Cumulants for Option Pricing and Hedging

In this paper, we analyze properties of multinomial lattices that model general stochastic dynamics of the underlying stock by taking into account any given cumulants (or moments). First, we provide a parameterization of multinomial lattices, and demonstrate that mean, variance, skewness, and kurtosis of the underlying may be matched using five branches. Then, we investigate the convergence of the multinomial lattice when the basic time period approaches zero, and prove that the limiting process of the multinomial lattice that matches annualized mean, variance, skewness and kurtosis is given by a compound Poisson process. Finally, we illustrate the effect of higher order moments in the underlying asset process on the price of derivative securities through numerical experiments using the multinomial lattice, and provide a comparison with jump-diffusion models.     

Fourth Moment Structure of Multivariate GARCH Models

This article derives conditions for the existence of fourthmoments of multivariate GARCH processes in the general vectorspecification and gives explicit results for the fourth momentsand autocovariances of the squares and cross products. Resultsare provided for the kurtosis and cokurtosis between components.Applications of the results include the definition of impulseresponse functions for kurtosis and cokurtosis, the derivationof the spectral density matrix of the squares and cross products,and a measure for causality in volatility. A bivariate exchangerate example illustrates the applications.     

Heavy-tailed Behavior of Commodity Price Distribution and Optimal Hedging Demand

This study explores the importance of imposing a correct distributional hypothesis in a risk management strategy, by comparing hedge ratios under the restrictive normality assumption to those under the generalized stable distribution. Concepts are illustrated for the case of a representative Pennsylvania dairy farm manager who purchases corn as a feed input. The results show that time processes of corn prices and basis risk in five Pennsylvania regions do not correspond to the normal distribution, and they more correctly correspond to one of the stable distribution set. The estimated hedge ratios under the stable distribution are typically larger than those under the normal distribution. The difference would be a bias from imposing a wrong distributional assumption.