Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks

Recent variable annuities offer participation in the equity market and attractive protection against downside movements. Accurately quantifying this additional equity market risk and robustly hedging options embedded in the guarantees of variable annuities are new challenges for insurance companies. Due to sensitivities of the benefits to tails of the account value distribution, a simple Black–Scholes model is inadequate in preventing excessive liabilities. A model which realistically describes the real world price dynamics over a long time horizon is essential for the risk management of the variable annuities. In this article, both jump risk and volatility risk are considered for risk management of lookback options embedded in guarantees with a ratchet feature. We evaluate relative performances of delta hedging and dynamic discrete risk minimization hedging strategies. Using the underlying as the hedging instrument, we show that, under a Black–Scholes model, local risk minimization hedging can be significantly better than delta hedging. In addition, we compare risk minimization hedging using the underlying with that of using standard options. We demonstrate that, under a Merton's jump diffusion model, hedging using standard options is superior to hedging using the underlying in terms of the risk reduction. Finally, we consider a market model for volatility risks in which the at‐the‐money implied volatility is a state variable. We compute risk minimization hedging by modeling at‐the‐money Black–Scholes implied volatility explicitly; the hedging effectiveness is evaluated, however, under a joint model for the underlying price and implied volatility. Our computational results suggest that, when implied volatility risk is suitably modeled, risk minimization hedging using standard options, compared to hedging using the underlying, can potentially be more effective in risk reduction under both jump and volatility risks.     

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.     

Hedging of Asian options under exponential Lévy models: computation and performance

In this paper we consider the problem of hedging an arithmetic Asian option with discrete monitoring in an exponential Lévy model by deriving backward recursive integrals for the price sensitivities of the option. The procedure is applied to the analysis of the performance of the delta and delta–gamma hedges in an incomplete market; particular attention is paid to the hedging error and the impact of model error on the quality of the chosen hedging strategy. The numerical analysis shows the impact of jump risk on the hedging error of the option position, and the importance of including traded options in the hedging portfolio for the reduction of this risk.     

Financial Regulation,Exchange Rate Exposure,and Hedging Activities: Evidence from Korean Firms

ABSTRACT

In this article, we attempt to estimate whether firm-specific exchange rate exposures affected by hedging activities can be improved through financial regulation or supervision. To analyze this, we compose three-step estimations by using a sample of KOSPI 200 firms during 1,803 trading days between 2005 and 2012. We first estimate the relationship between exchange rate exposure and hedging activities and see whether financial regulation had any effect on hedging activities. Furthermore, using TSLS analysis, we estimate the effect of hedging activities on exchange rate exposure, which is caused by tightened financial regulation in the form of corporate governance. We report the following findings. First, firms are less likely to be exposed to exchange risk with more hedging activities. Second, corporate governance has a strongly positive effect on the hedging activities. Firms use more hedging tools when they have a strong structure of shareholder’s protection, clear outside ownership, and a better monitoring system; but the relationship becomes weaker in times of crisis.     

Asset allocation in markets with contagion: The interplay between volatilities,jump intensities,and correlations

We study the impact of financial contagion on the dynamic asset allocation problem of a CRRA investor facing an incomplete market with two risky assets. We apply a Markov chain regime-switching framework with state-dependent jump intensities, diffusion volatilities and diffusion correlations. The key model feature that a switch to the bad contagion regime is triggered by a loss in one of the risky assets allows for the implementation of a hedging demand against contagion risk. Moreover, a state-dependent diffusion correlation combined with heterogeneity in jump intensities and volatilities can, e.g., generate a flight to quality effect upon a systemic jump.     

Selective hedging strategies for crude oil futures based on market state expectations

This paper studies the ex-ante selective hedging strategies of crude oil futures contracts based on market state expectations and compares the hedging performances to the traditional minimum variance routine hedging strategies. The main advantage of the proposed method is that it achieves a trade-off between return and risk, rather than hedges risk at all costs. Specifically, we first use a multi-input Hidden Markov Model(HMM) to identify the market state, assess the market’s herding impact, and then integrate the findings of identification and measurement to forecast the price trend. We offer an adjustment criterion for the hedge ratios driven by GARCH²-type models based on the anticipated market state. We conducted an empirical analysis to examine the hedging effect of WTI and Brent crude oil futures, the results indicate that the proposed state-dependent hedging strategies are superior to the traditional model-driven hedging strategies concerning the hedged portfolio based on four criteria. The robustness check reveals that the proposed hedging strategies still outperform in different market situation. The findings can help traders in the crude oil markets, and the methodology can be applied to other energy markets.     

沪深300股指期货套期保值模型选择与绩效评价

摘要：基于不同套期保值模型,本文对沪深300股指期货的套期保值效应进行了实证分析,并通过“风险最小化”原则和“效用最大化”原则分别比较不同模型的套期保值绩效。结果发现,在“风险最小化”原则下,无论是对于样本内还是样本外数据,对角ECM．BGARCH（1,1）模型的套期保值绩效都为最优;在“效用最大化”原则下,无论风险系数水平如何,样本内DCC．GARCH模型的套期保值绩效最优,样本外标量ECM—BGARCH（1,1）模型的套期保值绩效最优。     

Exchange options under clustered jump dynamics

Exchange options are one of the most popular exotic options, and have important implications for many common financial arrangements and for implied beta as a measure of systematic risk. In this study, we extend the existing literature on exchange options to allow for clustered jump contagion dynamics in each single asset, as well as across assets, using the Hawkes jump-diffusion model. We derive the analytical pricing formulae, the Greeks, and the optimal hedging strategy via Fourier transforms. Using an illustrative numerical analysis, we present the relationship between the exchange option price and clustered jump intensities and jump sizes in the underlying assets. We discuss the managerial insights on financial arrangements with exchange option characteristics. Furthermore, we discuss the implications of incorporating clustered jumps into the estimation of implied beta with exchange options, in which the applications can be insightful and useful in finance practice.     

The Determinants of Foreign Currency Hedging–Evidence from Hong Kong Non-Financial Firms

Hong Kong is one of the largest trading economies in the world. Business opportunities attract the presence of more and more multinational companies and different currencies. Hedging currency risks has become an important and vital activity for a success business entity in Hong Kong. This paper empirically tests the determinants of foreign currency hedging for a large sample of Hong Kong non-financial firms. The findings are potentially useful for increasing firms’ economic benefit and shareholders’ wealth as well as improving the economic efficiency of currency hedging for companies in Hong Kong as well as in the mainland of China. JEL classification: F30, G32, G33     

Hedging Long-Term Forwards with Short-Term Futures: A Two-Regime Approach

In this paper we investigate Metallgesellschafts problem of hedging long-term forwards with short-term futures. Very different hedging strategies have been proposed in the literature. We attribute these differences to the underlying valuation approaches for oil futures and empirically compare five model-based hedging strategies. In particular, we consider a strategy which results from a two-regime pricing model. This continuous-time equilibrium model reflects the observation that prices of oil futures exhibit a very different behavior for low and high oil prices. Our empirical study shows that time diversification is the dominant effect for an effective hedging of long-term oil forwards with short-term futures. JEL classification G13, G30     

Insiders' hedging in a jump diffusion model

In this paper, we formulate the optimal hedging problem when the underlying stock price has jumps, especially for insiders who have more information than the general public. The jumps in the underlying price process depend on another diffusion process, which models a sequence of firm-specific information. This diffusion process is observed only by insiders. Nevertheless, the market is incomplete to insiders as well as to the general public. We use the local risk minimization method to find an optimal hedging strategy for insiders. We also numerically compare the value of the insider's hedging portfolio with the value of an honest trader's hedging portfolio for a simulated sample path of a stock price.     

Efficient analytic approximation of the optimal hedging strategy for a European call option with transaction costs

One of the most successful approaches to option hedging with transaction costs is the utility-based approach, pioneered by Hodges and Neuberger [Rev. Futures Markets, 1989, 8, 222–239]. Judging against the best possible trade-off between the risk and the costs of a hedging strategy, this approach seems to achieve excellent empirical performance. However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. We overcome this drawback by presenting a simple yet efficient analytic approximation of the solution. We provide an empirical testing of our approximation strategy against the asymptotic and some other well-known strategies and find that our strategy outperforms all the others.     

备兑权证风险对冲策略分析

我国资本市场金融创新产品接连推出,备兑权证也再次被提上议程。在备兑权证的风险管理上,现有文献多集中于权证定价模型上的Delta对冲策略,却忽视了交易成本与间断交易,也没有深入分析影响该策略的各个因素。本文通过仿真实验Leland模型下的动态Delta对冲策略,发现交易成本、对冲间隔、行权价格以及波动率的变化都会显著影响对冲结果,但发行商仍有机会获取对冲收益,建议发行商略微溢价（5％）发行备兑权证,认为第三方对冲监管和差别对待的机制设计可确保市场繁荣。     

Optimal static quadratic hedging

We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these expectations analytically in a general Markov diffusion market. To illustrate the versatility of our approach, we present several numerical examples, including hedging path-dependent options and options written on a correlated asset.     

Longevity/Mortality Risk Modeling and Securities Pricing

Securitizing longevity/mortality risk can transfer longevity/mortality risk to capital markets. Modeling and forecasting mortality rate is key to pricing mortality‐linked securities. Catastrophic mortality and longevity jumps occur in historical data and have an important impact on security pricing. This article introduces a stochastic diffusion model with a double‐exponential jump diffusion process that captures both asymmetric rate jumps up and down and also cohort effect in mortality trends. The model exhibits calibration advantages and mathematical tractability while better fitting the data. The model provides a closed‐form pricing solution for J.P. Morgan’s q‐forward contract usable as a building block for hedging.     

Commodity futures hedging,risk aversion and the hedging horizon

This paper examines the impact of management preferences on optimal futures hedging strategy and associated performance. Applying an expected utility hedging objective, the optimal futures hedge ratio is determined for a range of preferences on risk aversion, hedging horizon and expected returns. Empirical results reveal substantial hedge ratio variation across distinct management preferences and are supportive of the hedging policies of real firms. Hedging performance is further shown to be strongly dependent on underlying preferences. In particular, hedgers with high risk aversion and short horizon reduce hedge portfolio risk but achieve inferior utility in comparison to those with low aversion.     

Does Operational and Financial Hedging Reduce Exposure? Evidence from the U.S. Airline Industry

We examine the effects of both financial and operational hedging on jet fuel exposure in the U.S. airline industry. Specifically, we investigate two operational hedging strategies: the extent to which airlines operate different aircraft types and the degree to which airlines operate fuel‐efficient fleets. We find that both financial and operational hedging are important tools in reducing airline exposure to jet fuel price risk. However, operational hedging strategies appear to be more economically important, which suggests that hedging with derivatives is more likely to be used to “fine‐tune” risk exposure, whereas operational choices have a higher order effect on risk exposure.     

中国利率互换套期保值有效性实证研究

为了研究我国利率互换的套期保值功能,该文利用协整检验分析利率互换和国债的长期均衡关系,并通过确定套期保值比率的OLS模型和套期保值绩效的衡量指标,对利率互换的套期保值比率和绩效进行了实证研究。结果显示,我国当前利率互换和国债收益率并不存在长期均衡关系;利率互换市场尚未发挥套期保值功能,其运行效率有待进一步提高。