Partial hedging and cash requirements in discrete time

This paper develops a discrete time version of the continuous time model of Bouchard et al. [J. Control Optim., 2009, 48, 3123–3150], for the problem of finding the minimal initial data for a controlled process to guarantee reaching a controlled target with probability one. An efficient numerical algorithm, based on dynamic programming, is proposed for the quantile hedging of standard call and put options, exotic options and quantile hedging with portfolio constraints. The method is then extended to solve utility indifference pricing, good-deal bounds and expected shortfall problems.     

A new computational tool for analysing dynamic hedging under transaction costs

This paper highlights a framework for analysing dynamic hedging strategies under transaction costs. First, self-financing portfolio dynamics under transaction costs are modelled as being portfolio affine. An algorithm for computing the moments of the hedging error on a lattice under portfolio affine dynamics is then presented. In a number of circumstances, this provides an efficient approach to analysing the performance of hedging strategies under transaction costs through moments. As an example, this approach is applied to the hedging of a European call option with a Black–Scholes delta hedge and Leland's adjustment for transaction costs. Results are presented that demonstrate the range of analysis possible within the presented framework.     

Learning minimum variance discrete hedging directly from the market

Option hedging is a critical risk management problem in finance. In the Black–Scholes model, it has been recognized that computing a hedging position from the sensitivity of the calibrated model option value function is inadequate in minimizing variance of the option hedge risk, as it fails to capture the model parameter dependence on the underlying price (see e.g. Coleman et al., J. Risk, 2001, 5(6), 63–89; Hull and White, J. Bank. Finance, 2017, 82, 180–190). In this paper, we demonstrate that this issue can exist generally when determining hedging position from the sensitivity of the option function, either calibrated from a parametric model from current option prices or estimated nonparametricaly from historical option prices. Consequently, the sensitivity of the estimated model option function typically does not minimize variance of the hedge risk, even instantaneously. We propose a data-driven approach to directly learn a hedging function from the market data by minimizing variance of the local hedge risk. Using the S&P 500 index daily option data for more than a decade ending in August 2015, we show that the proposed method outperforms the parametric minimum variance hedging method proposed in Hull and White [J. Bank. Finance, 2017, 82, 180–190], as well as minimum variance hedging corrective techniques based on stochastic volatility or local volatility models. Furthermore, we show that the proposed approach achieves significant gain over the implied BS delta hedging for weekly and monthly hedging.     

Optimal dynamic hedging in incomplete futures markets

This article derives optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of either a CARA or a logarithmic utility function. Existing futures contracts are not numerous enough to complete the market. In addition, in the case of CARA, the nonnegativity constraint on wealth is binding, and the optimal hedging demands are not identical to those that would be derived if the constraint were ignored. Fictitiously completing the market, we can characterize the optimal hedging demands for futures contracts. Closed-form solutions exist in the logarithmic case but not in the CARA case, since then a put (insurance) written on his wealth is implicitly bought by the investor. Although solutions are formally similar to those that obtain under complete markets, incompleteness leads in fact to second-best optima.     

Basis risk in static versus dynamic longevity-risk hedging

This paper provides a tractable, parsimonious model for assessing basis risk in longevity and its effect on the hedging strategies of Pension Funds and annuity providers. Basis risk is captured by a single parameter, that measures the co-movement between the portfolio and the reference population’s longevity. The paper sets out the static, full and customized swap-hedge for an annuity, and compares it with a dynamic, partial, and index-based hedge. We calibrate our model to the UK and Scottish populations. The effectiveness of static versus dynamic strategies depends on the rebalancing frequency of the second, on the relative costs, and on basis risk, which does not affect fully-customized, static hedges. We show that appropriately calibrated dynamic hedging strategies can still be reasonably effective, even at low rebalancing frequencies.     

Cutting the hedge: Exporters' dynamic currency hedging behaviour

We use a dataset that includes all New Zealand merchandise export transactions to analyse exporters' dynamic currency hedging behaviour. We focus on whether exporters change their hedging behaviour (“selectively hedge”) when the exchange rate and/or forward points depart from historical norms. We find that hedging ratios for exporters' Australian dollar exposures vary systematically as the exchange rate departs from historical averages; this behaviour is more marked for larger relative to smaller exporters. Consistent with efficient markets theory, there is no evidence that selective hedging is a profitable strategy for exporters.     

Minimizing CVaR in global dynamic hedging with transaction costs

This study develops a global derivatives hedging methodology which takes into account the presence of transaction costs. It extends the Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239] framework in two ways. First, to reduce the occurrence of extreme losses, the expected utility is replaced by the conditional Value-at-Risk (CVaR) coherent risk measure as the objective function. Second, the normality assumption for the underlying asset returns is relaxed: general distributions are considered to improve the realism of the model and to be consistent with fat tails observed empirically. Dynamic programming is used to solve the hedging problem. The CVaR minimization objective is shown to be part of a time-consistent framework. Simulations with parameters estimated from the S&P 500 financial time series show the superiority of the proposed hedging method over multiple benchmarks from the literature in terms of tail risk reduction.     

Arbitrage-free interval and dynamic hedging in an illiquid market

This paper derives two pricing PDEs for a general European option under liquidity risk. We provide two modified hedges: one hedge replicates a short option and the other replicates a long option inclusive of liquidity costs under continuous rebalancing. We identify an arbitrage-free interval by calculating the costs of the two hedges. Unlike in a setting with infinite overall transaction costs, the overall liquidity cost in our model is proved to be finite even under continuous rebalancing. Numerical results on option pricing and the moments of hedge errors of Black–Scholes and our modified hedges are also presented.     

A monotonically converging algorithm for the severity of ruin in a discrete semi-markov risk model

This paper deals with the severity of ruin in a discrete semi-Markov risk model. It is shown that the work of Reinhard and Snoussi (Stochastic Models, 18) can be extended to cover the case where the premium is an integer value and no restriction on the annual result is imposed. In particular, it is shown that the severity of ruin without initial surplus is solution of a system of equations. It can be obtained by a monotonically converging algorithm when the claims are bounded.     

State transformation of information spillover in asset markets and effective dynamic hedging strategies

This paper aims to develop a strategy to effectively and dynamically hedge risk by considering regime transitions of spillover effects between assets. We take six assets (stocks, bonds, real estate, currency exchange, crude oil, and gold) that are commonly used to construct investment portfolios as examples and analyze asset price data between September 2002 and January 2022. In doing so, we aim to examine the information spillover of different asset prices in both bear and bull market environments to determine whether state transformation affects dynamic hedging effectiveness. Using Markov-Switching Factor-Augmented Vector Autoregression (MS-FAVAR), we construct a regimen-switching model using variables from finance and economic conditions as endogenous variables to define the state transformations of the information spillover. Empirical results reveal that the MS-FAVAR model highlights changes in information spillover during a financial crisis/economic recession. Using dynamic-weighted hedging portfolios constructed with different indicators, we find that hedging effectiveness and volatility vary depending on the state of information spillover between different asset markets and that bear markets significantly impacted hedging effectiveness. Results also show that the panic sentiment (the fear index) explains the probability of a bear market. It is suggested that the state transformation of information spillovers should be monitored periodically, and hedging portfolios should be dynamically adjusted (bear or bull market) with shifting fear sentiment.     

A Markov regime switching approach for hedging energy commodities

This paper estimates constant and dynamic hedge ratios in the New York Mercantile Exchange oil futures markets and examines their hedging performance. We also introduce a Markov regime switching vector error correction model with GARCH error structure. This specification links the concept of disequilibrium with that of uncertainty (as measured by the conditional second moments) across high and low volatility regimes. Overall, in and out-of-sample tests indicate that state dependent hedge ratios are able to provide significant reduction in portfolio risk.     

播种等待杜鹃啼——如何通过投资达至财务健康

新世纪的第二个十年开始了,有人预测十年以后的2020年,中国GDP将会超越美国,重回180年前世界第一的位置。无论是十年还是十五年,我们这代人能够见到这一天或迟或早地到来,每个人都应该认真考虑在这个重归荣光的历史大潮中,取得自己应得的那一份。其中的方法无外“参与”二字,找个好工作是参与,创业是参与,投资也是参与。     

A regime-switching real-time copula GARCH model for optimal futures hedging

A regime-switching real-time copula GARCH (RSRTCG) model is suggested for optimal futures hedging. The specification of RSRTCG is to model the margins of asset returns with state-dependent real-time GARCH and the dependence structure of asset returns with regime switching copula functions. RSRTCG is faster in adjusting to the new level of volatility under different market regimes which is a regime-switching multivariate generalization of the state-independent univariate real-time GARCH. RSRTCG is applied to cross hedge the price risk of S&P 500 sector indices with crude oil futures. The empirical results show that RSRTCG possesses superior hedging performance compared to its nested non-real-time or state-independent copula GARCH models based on the criterion of percentage variance reduction, utility gain, model confidence set, model combination strategy, risk-adjusted return and reward-to-semivariance ratio.     

Hypothesis testing for diffusion processes with continuous observations: Direct computation of large deviation results for error probabilities

We propose statistical tests for deciding between two alternatives for diffusion processes observed continuously over a finite time interval. Our tests emphasize the large deviation aspects, or equivalently, the asymptotic behavior of probabilities of type I and type II errors and the rate at which these probabilities go to zero as the observation time increases. We obtain these rates using direct methods of calculation. We provide specific computational examples for diffusion processes commonly used in finance and show that the error probabilities for these cases go to zero exponentially fast. Applications in finance and economics are discussed.     

Quantitative error estimates for a least-squares Monte Carlo algorithm for American option pricing

We prove new error estimates for the Longstaff–Schwartz algorithm. We establish an $O(\log^{\frac{1}{2}}(N)N^{-\frac{1}{2}})$ convergence rate for the expected L ² sample error of this algorithm (where N is the number of Monte Carlo sample paths), whenever the approximation architecture of the algorithm is an arbitrary set of L ² functions with finite Vapnik–Chervonenkis dimension. Incorporating bounds on the approximation error as well, we then apply these results to the case of approximation schemes defined by finite-dimensional vector spaces of polynomials as well as that of certain nonlinear sets of neural networks. We obtain corresponding estimates even when the underlying and payoff processes are not necessarily almost surely bounded. These results extend and strengthen those of Egloff (Ann. Appl. Probab. 15, 1396–1432, 2005), Egloff et al. (Ann. Appl. Probab. 17, 1138–1171, 2007), Kohler et al. (Math. Finance 20, 383–410, 2010), Glasserman and Yu (Ann. Appl. Probab. 14, 2090–2119, 2004), Clément et al. (Finance Stoch. 6, 449–471, 2002) as well as others.     

Analyzing hedging strategies for fixed income portfolios: A Bayesian approach for model selection

During the recent European sovereign debt crisis, returns on EMU government bond portfolios experienced substantial volatility clustering, leptokurtosis and skewed returns as well as correlation spikes. Asset managers invested in European government bonds had to derive new hedging strategies to deal with changing return properties and higher levels of uncertainty. In this environment, conditional time series approaches such as GARCH models might be better suited to achieve a superior hedging performance relative to unconditional hedging approaches such as OLS. The aim of this study is to test innovative hedging strategies for EMU bond portfolios for non-crisis and crisis periods. We analyze single and composite hedges with the German Bund and the Italian BTP futures contracts and evaluate the hedging effectiveness in an out-of-sample setting. The empirical analysis includes OLS, constant conditional correlation (CCC), and dynamic conditional correlation (DCC) multivariate GARCH models. We also introduce a Bayesian composite hedging strategy, attempting to combine the strengths of OLS and GARCH models, thereby endogenizing the dilemma of selecting the best estimation model. Our empirical results demonstrate that the Bayesian composite hedging strategy achieves the highest hedging effectiveness and compares particularly favorable to OLS during the recent sovereign debt crisis. However, capturing these benefits requires low transactions cost and efficiently functioning futures markets.     

Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)

We estimate parameters from data on discrete dynamic games, using entry/exit games to illustrate. Semiparametric first‐stage estimates of entry and continuation values are computed from sample averages of the realized continuation values of entrants and incumbents. Under certain assumptions, these values are easy‐to‐compute analytic functions of the parameters of interest. The entry and continuation values are used to determine the model's predictions for entry and exit conditional on the parameter vector, and the estimates compare these predictions with the data on entry and exit rates. Small‐sample properties are discussed and lead to the simplest of estimators.     

Mean-variance hedging in the presence of estimation risk

Review of Derivatives Research - The mean-variance hedging (MVH) with a significant risk-aversion coefficient is approximately equal to the minimum-variance (MV) hedge. However, how large the...     

Multiperiod hedging in the presence of stochastic volatility

In this paper, we characterize the multiperiod minimum-risk hedge strategy within the stochastic volatility (SV) framework and compare it to other hedge strategies on the basis of hedging performance. Using crude oil markets as an example, we demonstrate that the SV model is appropriate in depicting price behaviour. However, ex ante and ex post comparisons indicate that the SV strategy is inferior to conventional hedging strategies. There is also evidence that the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) strategy may be better than the SV strategy, at least in terms of variance reduction.     

A mixed C-vine copula model for hedging price and volumetric risk in wind power trading

When energy trading companies enter into long-term agreements with wind power producers, where a fixed price is paid for the fluctuating production, they are facing a joint price and volumetric risk. Since the pay-off of such agreements is non-linear, a hedging portfolio would ideally consist of not only forwards, but also a basket of e.g. call and put options. Illiquidity and an almost non-existent market for options challenge however the optimal hedging of joint price and volumetric risk in many market places. Here, we consider the case of the Danish power market, and exploit its strong positive correlation with the much more liquid German market to construct a proxy hedge. We propose a three-dimensional mixed vine copula to model the evolution of the Danish and German spot electricity prices and the Danish wind power production. We construct a realistic hedging portfolio by identifying various instruments available in the market, such as real options in the form of the right to transfer electricity across the border and the right to convert electricity to heat. Using the proposed vine copula to determine optimal hedging decisions, we show that significant benefits are to be drawn by extending the hedging portfolio with the proposed instruments.