Cost Of Hedging Research Articles

An optimal stochastic control framework for determining the cost of hedging of variable annuities

An implicit partial differential equation (PDE) method is used to determine the cost of hedging for a Guaranteed Lifelong Withdrawal Benefit (GLWB) variable annuity contract. In the basic setting, the underlying risky asset is assumed to evolve according to geometric Brownian motion, but this is generalised to the case of a Markov regime switching process. A similarity transformation is used to reduce a pricing problem with K regimes to the solution of K coupled one dimensional PDEs, resulting in a considerable gain in computational efficiency. The methodology developed is flexible in the sense that it can calculate the cost of hedging for a variety of different withdrawal strategies by investors. Cases considered here include both optimal withdrawal strategies (i.e. strategies which generate the highest possible cost of hedging for the insurer) and sub-optimal withdrawal strategies in which the policy holder׳s decisions depend on the moneyness of the embedded options. Numerical results are presented which demonstrate the sensitivity of the cost of hedging (given the withdrawal specification) to various economic and contractual assumptions.

The valuation of catastrophe bonds with exposure to currency exchange risk

In this paper, we present a new model that takes an arbitrage approach to the valuation of catastrophic risk bonds (CAT bonds). The model considers the sponsor's exposure to currency exchange risk and the risk of catastrophic events. We use a jump-diffusion process for catastrophic events, a three-dimensional stochastic process for the exchange rate and domestic and foreign interest rates, and a hedging cost for the currency risk to derive a semi-closed-form formula for the CAT bond price. We also extend to three factors Joshi and Leung's (2007) Monte Carlo simulation approach to obtain numerical results showing the following: in addition to catastrophic risk, the CAT bond price is affected mainly by the volatility of the exchange rate and its correlations with domestic and foreign interest rates. The first two factors have a negative impact while the third has a positive impact.

The Valuation of Catastrophe Bonds with Exposure to Currency Exchange Risk

In this paper, we present a new model that takes an arbitrage approach to the valuation of catastrophic risk bonds (CAT bonds). The model considers the sponsor’s exposure to currency exchange risk and the risk of catastrophic events. We use a jump-diffusion process for catastrophic events, a three-dimensional stochastic process for the exchange rate and domestic and foreign interest rates, and a hedging cost for the currency risk to derive a semi-closed-form formula for the CAT bond price. We also extend to three factors Joshi and Leung’s (2007) Monte Carlo simulation approach to obtain numerical results showing the following: in addition to catastrophic risk, the CAT bond price is affected mainly by the volatility of the exchange rate and its correlations with domestic and foreign interest rates. The first two factors have a negative impact while the third has a positive impact.

DETERMINATION OF EXPORT VOLUME AND HEDGING STRATEGY: A SURVEY OF EXPORTER’S TRANSACTION AT THE MAKASSAR INDUSTRIAL ESTATE (KIMA)

The study aims to determine factors which influence the export volume of leading commodities in South Sulawesi and investigate which hedging strategy has been implemented by the exporters. The survey was undertaken for 13 managers arranging 250 sales contracts in thirteen companies. They were asked to describe what type of hedging strategy was implemented in protecting their revenue with US dollar as denominated currency to their contract. Several literatures suggested that hedging strategy needs to consist of hedging theory, but in South Sulawesi, the international traders’ belief is in pragmatism way by relying on money market instrument especially for interest rate orientation. Although export import activities for cocoa, cement, lobster, seaweed, box and marbles used US$ for denomination, the respondents were aware of Rupiah fluctuation to foreign currency which also bears transaction exposure. Multiple regression analysis was used to determine variables which affected the volume and export, while hedging strategy was identified using qualitative approach. It was found that the increase on cost of hedging, inflation references and interest rate references affected significantly the increase of the export volume, while the increase of US$ spot rate to Indonesian Rupiah did not significantly affect in reducing export volume. Most of exporters rely on hedging in money market, long forward contract to protect their transactions.

Fine‐Tuning a Corporate Hedging Portfolio: The Case of an Airline

Industrial companies typically face a multitude of risks that could cause significant fluctuations in their cash flow. This is a case study of the hedging strategy adopted by an international air carrier to manage its jet‐fuel price exposure.The airline's hedging approach uses “strips” of monthly collars constructed with Asian options whose payoffs are based on average of “within‐prompt‐month” oil prices.Using the carrier's own implicit objective function based on an annual granularity, the authors show how the air carrier could fine‐tune its current hedge portfolio by adding tailored exotic options. The article describes annual average‐price options, provides an explicit valuation of them, and considers how such instruments may affect corporate liquidity. Consistent with its annual objective function, the airline made this exotic derivative the central tool to hedge across all potential realized values of annual jet‐fuel spot prices. The authors believe this modified portfolio is better suited to address the firm's hedging cost and its overall exposure to jet‐fuel price fluctuations.

Stress test design

This paper offers thoughts and ideas on the implementation of a company-specific stress test programme and focuses on the design of the stress test scenarios. In particular, it discusses the integration and coherence of the macroeconomic, market, credit, counterparty and operational risk scenarios. Certain specific features are recommended to enhance the stress test of market, counterparty and operational risks: the explicit consideration of the hedging and liquidity dynamics of trading portfolios, automated reverse stress testing for identification of market risk vulnerabilities, simulation of dynamic hedging costs of credit valuation adjustments (CVAs) and the averaging across different models to mitigate misspecification error and obtain more reliable estimates of stressed operational losses. All the above is framed within the context of the Federal Reserve's Comprehensive Capital Analysis and Review (CCAR) programme.

Long-Only Momentum, Currency Hedging and Transaction Costs: Implications for a Swiss Equity Investor

This study investigates the efficiency of European capital markets by examining the profitability of four long-only momentum strategies, after transaction costs of 0.5%, from the perspective of a Swiss equity investor. The investment universe considered in this study includes securities denominated in CHF, EUR, and GBP. In a first step, momentum strategies are evaluated over a period of fifteen years without hedging exchange rate risk of EUR and GBP. In a second step, the performance of full- and optimal currency hedging strategies is assessed. Results show that momentum strategies, after having considered transaction costs, do not significantly outperform a simple buy-and-hold strategy in risk-adjusted terms. Nevertheless, currency hedging strategies do significantly reduce the return volatility of portfolios.

Longevity Risk, Cost of Capital and Hedging for Life Insurers Under Solvency II

The cost of capital is an important factor determining the premiums charged by life insurers issuing life annuities. Insurers will be able to offer more finely priced annuities if they can reduce this cost whilst maintaining solvency. This capital cost can be reduced by hedging longevity risk with longevity swaps, a form of reinsurance. We assess the costs of longevity risk management using longevity swaps compared to costs of holding capital under Sovency II. We show that, using a reasonable market price of longevity risk, the market cost of hedging longevity risk for earlier ages is lower than the cost of capital required under Solvency II. Longevity swaps covering higher ages, around 90 and above, have higher market hedging costs than the saving in the cost of regulatory capital. The Solvency II capital regulations for longevity risk generates an incentive for life insurers to hold longevity tail risk on their own balance sheets rather than transfer this to the reinsurance or the capital markets. This aspect of Solvency II capital requirements is not well understood and raises important policy issues for the management of longevity risk.

Hedging costs, liquidity, and inventory management: The evidence from option market makers

Hedging the risk of holding undesired inventory is very important for market makers. However, prior studies seldom capture the role of inventory positions in measuring hedging costs. This study measures hedging costs directly using data on inventory positions of market makers in the Taiwan Index Options market. We break down rebalancing costs into two sources: rebalancing costs due to inventory changes and rebalancing costs due to delta changes. Contrary to prior studies on stock options, we find rebalancing costs are more important than initial hedging costs in explaining option spreads. Our findings underscore the importance of inventory management.

Margins, Liquidity, and the Cost of Hedging

Recent financial reforms, such as the Dodd‐Frank Act in the U.S. and the European Market Infrastructure Regulation, encourage greater use of clearing and therefore increased margining of derivative trades. They also impose margining requirements on noncleared derivative trades. Such requirements have sparked a debate about whether a margin mandate increases the cost of hedging by nonfinancial corporations—the so‐called end‐users of derivatives.The authors argue that it does not. They show that a nonmargined derivative is equivalent to a package of (1) a margined derivative and (2) a contingent line of credit. The main effect of a margin mandate is to require that this package be marketed as two distinct products. But it does not change the total financing or capital required to hedge. Nor does it raise the cost to banks or other dealers of offering the package, at least not directly.Nevertheless, there may be indirect effects if, for example, the clearing mandate succeeds in lowering total counterparty exposures and therefore systemic risk. Although the authors do not explore these effects, they do offer one explanation for the popularity of over‐the‐counter, and thus noncleared, derivatives: accounting rules and bank regulations that treat the implicit lines‐of‐credit embedded in nonmargined derivatives differently from explicit lines of credit used to fund margins.

The Value of Tail Risk Hedging in Defined Contribution Plans: What Does History Tell Us

Hedging against tail events has been forcefully advocated in the aftermath of recent global financial crisis. Whether this is beneficial to long horizon investors like defined contribution (DC) plan participants, however, has been subject to criticism. We conduct historical simulation since 1928 to examine the effectiveness of active and passive tail risk hedging using OTM put options for hypothetical DC plan investors with 20 years to retirement. Our findings show that the cost of tail hedging exceeds the benefits for a majority of investors during the sample period. However, for a significant number of simulations, hedging result in superior outcomes relative to an unhedged position. Active hedging proves beneficial when investors confront several panic-driven periods characterized by short and sharp market swings over the investment horizon. Passive hedging, on the other hand, only dominates when investors encounter an extremely rare event like the Great Depression when markets go into deep and prolonged decline.

Longevity Risk, Cost of Capital and Hedging for Life Insurers Under Solvency II

Longevity Risk, Cost of Capital and Hedging for Life Insurers Under Solvency II

Active Hedging Greeks of an Options Portfolio integrating churning and minimization of cost of hedging using Quadratic & Linear Programing

This paper proposes a methodology for active hedgingGreeks of an option portfolio integrating churning and minimization of cost of hedging. In the first section, hedging strategy is implemented by taking positions in other available options, while simultaneously minimizing the net premium paid for the hedging and then churning the portfolio to take into account the changed value of Greeks in the new portfolio. In the second section, the paper extends the model to incorporate the transaction cost while hedging the portfolio and churning it in Indian Scenario. Both constant and nonlinear shape of transaction cost has been considered as per the Security Transaction Tax and Brokerage charges in India. A quadratic programming has been presented which has been approximated by a linear programming solution. The prototype software has been developed in MS Excel using Visual Basic.

Optimum Hurricane Futures Hedge in a Warming Environment: A Risk–Return Jump‐Diffusion Approach

AbstractWe develop an optimum risk–return hurricane hedge model in a doubly stochastic jump‐diffusion economy. The model's concave risk–return trade‐off dictates that a higher correlation between hurricane power and insurer's loss, a smaller variable hedging cost, and a larger market risk premium result in a less costly but more effective hedge. The resulting hedge ratio comprises of a positive diffusion, a positive jump, and a negative hedging cost component. Numerical results show that hedging hurricane jump risks is most crucial with jump volatility being the dominant factor, and the faster the warming the more pronounced the jump effects.

Financialization and Structural Change in Commodity Futures Markets

The first decade of the 21st century has perhaps witnessed more structural change in commodity futures markets than all previous decades combined. Not only have trading volumes and open interest increased markedly, but this time period also saw historic changes in both trading and participants. The available literature indicates that the irrational and harmful impacts of the structural changes in commodity futures markets over the last decade have been minimal. In particular, there is little evidence that passive index investment caused a massive bubble in commodity futures prices. There is intriguing evidence of several other rational and beneficial impacts of the structural changes over the last decade. In particular, the expanding market participation may have decreased risk premiums, and hence, the cost of hedging, reduced price volatility, and better integrated commodity markets with financial markets.

An optimal multi-step quadratic risk-adjusted hedging strategy

An optimal multi-step hedging strategy is proposed to minimize one’s exposure to risk. The proposed strategy, called the QRA-hedging, is based on the minimization of the quadratic risk-adjusted hedging costs and extends the result of Elliott and Madan (1998) to the multi-step case. The multi-step QRA-hedging cost is proved to be the same as the no-arbitrage price derived by the extended Girsanov principle. The QRA-hedging strategy is investigated under complete and incomplete market models. A regression-based method is proposed to estimate the QRA-hedging positions. And a dynamic programming is developed to facilitate computation of the QRA-hedging strategy. Simulation and empirical studies are performed to compare the QRA with other hedging strategies under complete and incomplete market models.

LSV Models with a Mixing Weight

We propose new asymptotic results for Local Volatility and Stochastic Volatility. These new results are applied both to pricing, implied volatility and its dynamic. Besides, a correct pricing methodology is derived to match the cost of hedging.

动态避险模型之建立—以远期外汇与一篮子货币避险策略为例The Dynamic Hedging Model —A Combination of Delivery Forward and Currency Basket Hedge

本研究建构一动态避险模型，由传统避险工具与一篮子货币避险策略所构成。由于传统避险工具的好处在于风险的完全规避，而一篮子货币避险之主要目的则在于降低避险成本，因此本研究之动态避险模型，系以一篮子货币避险策略为主，于每期期初比较两种策略之避险成本，择其低者作为该期之避险策略。另外，为建立更为精确的一篮子货币避险部位，本研究亦导入人工智能工具于模型中，试图利用人工智能于汇率预测上的优秀表现，优化篮子内货币之权重，进而达到更佳的避险绩效。经实证，本研究之动态避险模型，确能显着地优于仅执行单一传统避险工具或者一篮子货币避险策略。其中，以两年作为权重估计期间并纳入预测技术之模型，于实验期间内表现最佳，是为本研究所推荐使用之模型。 This paper proposes a “dynamic hedging model”, which adjusts the hedging strategies by the time, to increase the hedging performance. The dynamic hedging model is combined with the traditional hedging strategy (e.g. Delivery Forward) and the basket currency hedging. The traditional hedging strategy covers the whole risk, in the mean time, the basket currency reduce the hedging cost. Therefore, we establish the position of basket currency first, and execute this strategy when its hedging cost is lower than the traditional hedging strategy; otherwise, we execute the traditional hedging strategy. Besides, for establishing a more precise position of basket currency, we also use artificial intelligence to forecast the exchange rate, which is expected to estimate the currency weight in a basket more precisely. Empirically, the dynamic hedging model we propose performs much better than either the traditional hedging strategy or basket currency hedging strategy. In addition, due to the way of using two-year estimation period and adding forecast technology to correct the estimation got the best performance, we recommend this model to be a reference of a company’s hedging behavior.

动态避险模型之建立—以远期外汇与一篮子货币避险策略为例

本研究建构一动态避险模型，由传统避险工具与一篮子货币避险策略所构成。由于传统避险工具的好处在于风险的完全规避，而一篮子货币避险之主要目的则在于降低避险成本，因此本研究之动态避险模型，系以一篮子货币避险策略为主，于每期期初比较两种策略之避险成本，择其低者作为该期之避险策略。另外，为建立更为精确的一篮子货币避险部位，本研究亦导入人工智能工具于模型中，试图利用人工智能于汇率预测上的优秀表现，优化篮子内货币之权重，进而达到更佳的避险绩效。经实证，本研究之动态避险模型，确能显着地优于仅执行单一传统避险工具或者一篮子货币避险策略。其中，以两年作为权重估计期间并纳入预测技术之模型，于实验期间内表现最佳，是为本研究所推荐使用之模型。 This paper proposes a “dynamic hedging model”, which adjusts the hedging strategies by the time, to increase the hedging performance. The dynamic hedging model is combined with the traditional hedging strategy (e.g. Delivery Forward) and the basket currency hedging. The traditional hedging strategy covers the whole risk, in the mean time, the basket currency reduce the hedging cost. Therefore, we establish the position of basket currency first, and execute this strategy when its hedging cost is lower than the traditional hedging strategy; otherwise, we execute the traditional hedging strategy. Besides, for establishing a more precise position of basket currency, we also use artificial intelligence to forecast the exchange rate, which is expected to estimate the currency weight in a basket more precisely. Empirically, the dynamic hedging model we propose performs much better than either the traditional hedging strategy or basket currency hedging strategy. In addition, due to the way of using two-year estimation period and adding forecast technology to correct the estimation got the best performance, we recommend this model to be a reference of a company’s hedging behavior.

Commodity Index Trading and Hedging Costs

Trading by commodity index traders (CITs) has become an important aspect of financial markets over the past 10 years. We develop an equilibrium model of trader behavior that relates uninformed CIT trading to futures prices. The model predicts that CIT trading reduces the cost of hedging. We test the model using a unique non-public dataset which precisely identifies trader positions. We find evidence, consistent with the model, that index traders have become an important supply of price risk insurance.