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.     

To Hedge or Not to Hedge: Managing Demographic Risk in Life Insurance Companies

Demographic risk, i.e., the risk that life tables change in a nondeterministic way, is a serious threat to the financial stability of an insurance company having underwritten life insurance and annuity business. The inverse influence of changes in mortality laws on the market value of life insurance and annuity liabilities creates natural hedging opportunities. Within a realistically calibrated shareholder value (SHV) maximization framework, we analyze the implications of demographic risk on the optimal risk management mix (equity capital, asset allocation, and product policy) for a limited liability insurance company operating in a market with insolvency‐averse insurance buyers. Our results show that the utilization of natural hedging is optimal only if equity is scarce. Otherwise, hedging can even destroy SHV. A sensitivity analysis shows that a misspecification of demographic risk has severe consequences for both the insurer and the insured. This result highlights the importance of further research in the field of demographic risk.     

Corporate risk management and firm value: evidence from the UK market

The paper evaluates the effect of corporate risk management activities on firm value, using a sample of large UK non-financial firms. Following recent changes in financial reporting standards, we are able to collect detailed information on risk management activities from audited financial reports. This enables us to gain a better understanding of risk management practices and to investigate value implications of different types of hedging. Overall 86.88% of the firms in the sample use derivatives to manage at least one type of price risk. The hedging premium is statistically and economically significant for foreign currency derivative users, while we provide weak evidence that interest rate hedging increases firm value. The extent of hedging and the hedging horizon have an impact on the hedging premium, whereas operational risk management activities do not significantly influence the market value of the firm.     

Corporate Risk Management under Information Asymmetry

This paper examines the financial and operational hedging activities of US pharmaceutical and biotech firms that are subject to a high level of information asymmetry stemming from R&D investments during 2001–2006. We find evidence in support of the information asymmetry hypothesis à la Froot, Scharfstein and Stein (1993) that hedging helps mitigate the under‐investment problem. Specifically, we find that the use of financial derivatives is associated with greater firm value and that the value enhancement is larger for firms subject to greater information asymmetry and better growth opportunities. There is a synergy between financial hedging and operational hedging where the latter is used to counter product development risk. The results are robust with respect to alternative performance measures, industry‐specific growth measures, and the endogeneity problem. Our work is differentiated from existing studies that examined commodity‐based industries without addressing information asymmetry.     

Pricing and managing risks of European-style options in a Markovian regime-switching binomial model

We discuss the pricing and risk management problems of standard European-style options in a Markovian regime-switching binomial model. Due to the presence of an additional source of uncertainty described by a Markov chain, the market is incomplete, so the no-arbitrage condition is not sufficient to fix a unique pricing kernel, hence, a unique option price. Using the minimal entropy martingale measure, we determine a pricing kernel. We examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as Value at Risk and Expected Shortfall. The impacts of the frequency of re-balancing the hedging portfolio and the transition probabilities of the modulating Markov chain on the quality of hedging are also discussed.     

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.     

Downside Risk Management of a Defined Benefit Plan Considering Longevity Basis Risk

To control downside risk of a defined benefit pension plan arising from unexpected mortality improvements and severe market turbulence, this article proposes an optimization model by imposing two conditional value at risk constraints to control tail risks of pension funding status and total pension costs. With this setup, we further examine two longevity risk hedging strategies subject to basis risk. While the existing literature suggests that the excess-risk hedging strategy is more attractive than the ground-up hedging strategy as the latter is more capital intensive and expensive, our numerical examples show that the excess-risk hedging strategy is much more vulnerable to longevity basis risk, which limits its applications for pension longevity risk management. Hence, our findings provide important insight on the effect of basis risk on longevity hedging strategies.     

Risk management and market conditions

In this paper, we investigate the relation between hedging activity by commercial/merchant/producers to commodity prices and commodity market volatility using Commitments of Traders reports from commodity futures markets exchanges. Qualifying the body of literature which attributes hedging activity to departures from Modigliani-Miller theory, market imperfections and transactions cost, we address the paradoxes of hedging which is not value creating and the absence of hedging when firms might benefit, arguing that it may be related to the market conditions and risk appetite. We discover that prices and volatility are generally statistically significant contributors to hedging activity by commercial/merchant/producers’ users but with marked differences in their elasticities. For some commodities, price levels alone and not volatility are significant. We demonstrate that analysis of hedging in commodity markets should take cognisance of conditions and the degree of risk aversion, otherwise the implicit assumption is that hedging is invariant to such matters. Through considering both market conditions and the degree of risk aversion, understanding the motivation for hedging may be enhanced.     

Coherent hedging in incomplete markets

In incomplete financial markets, not every contingent claim can be perfectly replicated by a self-financing strategy. In this paper, we minimize the risk that the value of the hedging portfolio falls below the payoff of the claim at time T. We use a coherent risk measure, introduced by Artzner et al., to measure the risk of the shortfall. The dynamic optimization problem of finding a self-financing strategy that minimizes the coherent risk of the shortfall can be split into a static optimization problem and a representation problem. We will deduce necessary and sufficient optimality conditions for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0–1 structure. Our results improve those obtained by Nakano. The optimal hedging strategy consists of superhedging a modified claim that is the product of the original payoff and the solution to the static problem.     

Production and hedging implications of executive compensation schemes

This paper connects executive compensation with hedging and analyzes a crucial shareholders and managers agency source that evolves from the pricing of the hedging device. The shareholders are risk-neutral, while the risk-averse manager hedges the price risk of the manufactured quantity, and his compensation package includes equity-linked compensation-stock grants. Only when the hedging instrument's pricing includes a risk premium, hedging is costly to the shareholders, while it is costless to the manager. Then from the owners' point of view, we observe managerial over-hedging, increasing in the equity-linked compensation level. This result leads to a violation of the classical production and hedging separation theorem. We conclude that, in the case where the hedging device's pricing bears a risk premium, shareholders can regulate the corporate value diversion to managers through diminishing the managerial equity-linked compensation scheme or by putting restrictions on the extent of hedging activities of executives.     

Exposure,hedging, and value: New evidence from the U.S. airline industry

For a variety of reasons, the U.S. airline industry is a natural sample to analyze the relation between corporate risk exposure, hedging policy, and firm value. First, we find that airline exposures to fuel prices are higher when fuel prices are high or when they are rising. Second, we analyze the relation between exposure coefficients and the percentage of next year's fuel requirement hedged by airlines. In response to higher fuel price levels, rising fuel prices, and higher levels of exposure to fuel prices, airlines tend to increase their hedging activity. Finally, we explore the previously documented jet fuel hedging premium illustrated in Carter, Rogers, and Simkins (2006). We find a positive hedging premium in our analysis; however, the interaction of hedging and exposure does not affect firm value. We conclude that airlines increasing hedging activity because of higher fuel price exposure are not valued higher compared to those airlines employing more stable hedging policies.     

RISK AND HEDGING BEHAVIOR: THE ROLE AND DETERMINANTS OF LATENT HETEROGENEITY

The notion of heterogeneous behavior is well grounded in economic theory. Recently it has been shown in a hedging context that the influence of risk attitudes and risk perceptions varies for different segments using a generalized mixture regression model. Here, using recently developed individual risk attitude measurement techniques and experimental and accounting data from investors with differing decision environments, we examine the determinants of heterogeneity in hedging behavior in a concomitant mixture regression framework. Allowing for latent heterogeneity, we find that risk attitudes and risk perceptions do not influence behavior uniformly and that the heterogeneity is influenced by manager's focus on shareholder value and the firm's capital structure.     

Analysis of Participating Life Insurance Contracts: A Unification Approach

Fair pricing of embedded options in life insurance contracts is usually conducted by using risk‐neutral valuation. This pricing framework assumes a perfect hedging strategy, which insurance companies can hardly pursue in practice. In this article, we extend the risk‐neutral valuation concept with a risk measurement approach. We accomplish this by first calibrating contract parameters that lead to the same market value using risk‐neutral valuation. We then measure the resulting risk assuming that insurers do not follow perfect hedging strategies. As the relevant risk measure, we use lower partial moments, comparing shortfall probability, expected shortfall, and downside variance. We show that even when contracts have the same market value, the insurance company's risk can vary widely, a finding that allows us to identify key risk drivers for participating life insurance contracts.     

How fair-value accounting can influence firm hedging

The potential influence of accounting regulations on hedging strategies and the use of financial derivatives is a research topic that has attracted little attention in both the finance and the accounting literature. However, recent surveys suggest that company hedging can be substantially influenced by the accounting for financial instruments. In this study, we illustrate not only why but also how the accounting regulations may affect hedging behavior. We find that under mark-to-market accounting, most firms concerned with earnings smoothness adopt myopic hedging strategies relative to the benchmark, cash flow hedging. The specific influence of the accounting regulations depends on market and firm-specific characteristics, but, in general, the firms dramatically reduce the extent of hedging addressing price risk in future accounting periods. We illustrate that the change in hedging behavior significantly dampens the increase in earnings volatility stemming from fair value accounting of derivatives. However, the adjusted hedging strategies may substantially increase the firms’ cash flow volatility.     

Hedging,speculation, and shareholder value

We document that gold mining firms have consistently realized economically significant cash flow gains from their derivatives transactions. We conclude that these cash flows have increased shareholder value since there is no evidence of an offsetting adjustment in firms’ systematic risk. This finding contradicts a central assumption in the risk management literature that derivatives transactions have zero net present value, and highlights an important motive for firms to use derivatives that the literature has hitherto ignored. Although we find considerable evidence of selective hedging in our sample, the cash flow gains from selective hedging appear to be small at best.     

Discerning the Impact of Derivatives on Asset Risk: The Case of Canadian Banks

The Canadian banks have shown remarkable resilience to the financial crisis that intensified in the late 2008. The interesting question is whether this stability is due to their prudent lending practices to limit the original risk exposures or due to effective risk management through hedging by using financial derivatives. In this paper, we implement the option‐theoretic model of Merton to calculate the implied asset risk and discern the impact of these derivatives on the aggregate risk for Canadian banks over the period 1997–2008. An algorithm of iterative procedure is developed to impute asset value and risk from bank stock prices. Our estimates show that the risk for Canadian banks is low and even decreasing till the unfolding of the recent crises in 2008. Further analyses reveal that such low risks are not due to reliance on hedging, nor is it related to trading in derivatives, after disentangling the intertwined effects of hedging and trading. These results suggest that involvements in derivatives, in and of themselves, should not be blamed for causing the bank crises; rather, it is conservatism in controlling original risk exposures that remains fundamental for safeguarding a healthy financial system.     

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.     

Corporate hedging and the cost of debt

For a large sample of U.S. firms from 1994 to 2009, we empirically examine the impact of corporate hedging on the cost of public debt. We find strong evidence that hedging is associated with a lower cost of debt. The negative effect of hedging on the cost of debt is consistent across industries, and remains economically and statistically significant under various controls and econometric specifications. A cross-sectional analysis based on propensity score matching suggests that hedging initiation firms experience a drop in cost of debt, while suspension firms sustain a jump. We confirm our findings after employing an extensive array of models to address potential endogeneity. The influence of hedging on cost of debt is mainly through the lowering of bankruptcy risk and agency cost, and the reduction in information asymmetry. Finally, hedging mitigates the negative effect of rising borrowing costs on capital expenditure and firm value.     

Risk management strategies for banks

We analyze optimal risk management strategies of a bank financed with deposits and equity in a one period model. The bank’s motivation for risk management comes from deposits which can lead to bank runs. In the event of such a run, liquidation costs arise. The hedging strategy that maximizes the value of equity is derived. We identify conditions under which well known results such as complete hedging, maximal speculation or irrelevance of the hedging decision are obtained. The initial debt ratio, the size of the liquidation costs, regulatory restrictions, the volatility of the risky asset and the spread between the riskless interest rate and the deposit rate are shown to be the important parameters that drive the bank’s hedging decision. We further extend this basic model to include counterparty risk constraints on the forward contract used for hedging.     

Corporate Hedging: The Relevance of Contract Specifications and Banking Relationships

This article examines the contribution of hedging to firm value and the cost of hedging in a unified framework. Optimal hedging and firm value are explicitly linked to firm risk, the type of debt covenants and the relative priority of the hedging contract. It is shown that in some cases hedging is possible only if the counterparty to the forward contract also holds a significant portion of the debt. Also, the spread in the hedging contract reduces the optimal amount of hedging to less than the minimum-variance hedge ratio. Among other results this article elucidates why some firms hedge using forward contracts while other firms hedge in the futures markets, as well as why higher priority forward contracts are more efficient hedging vehicles.