Optimal discrete hedging of American options using an integrated approach to options with complex embedded decisions

In order to solve the problem of optimal discrete hedging of American options, this paper utilizes an integrated approach in which the writer’s decisions (including hedging decisions) and the holder’s decisions are treated on equal footing. From basic principles expressed in the language of acceptance sets we derive a general pricing and hedging formula and apply it to American options. The result combines the important aspects of the problem into one price. It finds the optimal compromise between risk reduction and transaction costs, i.e. optimally placed rebalancing times. Moreover, it accounts for the interplay between the early exercise and hedging decisions. We then perform a numerical calculation to compare the price of an agent who has exponential preferences and uses our method of optimal hedging against a delta hedger. The results show that the optimal hedging strategy is influenced by the early exercise boundary and that the worst case holder behavior for a sub-optimal hedger significantly deviates from the classical Black–Scholes exercise boundary.     

Performance of utility-based strategies for hedging basis risk

The performance of optimal strategies for hedging a claim on a non-traded asset is analysed. The claim is valued and hedged in a utility maximization framework, using exponential utility. A traded asset, correlated with that underlying the claim, is used for hedging, with the correlation ρ typically close to 1. Using a distortion method (Zariphopoulou 2001 Finance Stochastics 5 61–82) we derive a nonlinear expectation representation for the claim’s ask price and a formula for the optimal hedging strategy. We generate a perturbation expansion for the price and hedging strategy in powers of ε²?=1?ρ². The terms in the price expansion are proportional to the central moments of the claim payoff under the minimal martingale measure. The resulting fast computation capability is used to carry out a simulation-based test of the optimal hedging program, computing the terminal hedging error over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the non-traded one. The distribution of the hedging error acts as a suitable metric to analyse hedging performance. We find that the optimal policy improves hedging performance, in that the hedging error distribution is more sharply peaked around a non-negative profit. The frequency of profits over losses is increased, and this is measured by the median of the distribution, which is always increased by the optimal strategies. An empirical example illustrates the application of the method to the hedging of a stock basket using index futures.     

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.     

Empirical performance of multifactor term structure models for pricing and hedging Eurodollar futures options

This article compares two one-factor, two two-factor, two three-factor models in the HJM class and Black's [Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3, 167-179.] implied volatility function in terms of their pricing and hedging performance for Eurodollar futures options across strikes and maturities from 1 Jan 2000 to 31 Dec 2002. We find that three-factor models perform the best for 1-day and 1-week prediction, as well as for 5-day and 20-day hedging. The moneyness bias and the maturity bias appear for all models, but the three-factor models produce lower bias. Three-factor models also outperform other models in hedging, in particular for away-from-the-money and long-dated options. Making Black's volatility a square root or exponential function performs similar to one-factor HJM models in pricing, but not in hedging. Correctly specified and calibrated multifactor models are thus important and cannot be replaced by one-factor models in pricing or hedging interest rate contingent claims.     

Credit derivatives with multiple debt issues

We evaluate the most actively traded types of credit derivatives within a unified pricing framework that allows for multiple debt issues. Since firms default on all of their obligations, total debt is instrumental in the likelihood of default and therefore in credit derivatives valuation. We use a single factor interest rate model where the exponential default frontier is based on total debt and is made coherent with observed bond prices. Analytical formulae are derived for credit default swaps, total return swaps (both fixed-for-fixed and fixed-for-floating), and credit risk options (CROs). Price behaviors and hedging properties of all these credit derivatives are investigated. Simulations document that credit derivatives prices may be significantly affected by terms of debt other than those of the reference obligation. The analysis of CROs indicates their superior ability to fine-tune the hedging of magnitude and arrival risks of default.     

Adapted hedging

Exponentials of squared returns in Gaussian densities, with their consequently thin tails, are replaced by the absolute return to form Laplacian and exponentially tilted Laplacian densities at unit time. Scaling provides densities at other maturities. Stochastic processes with these marginals are identified. In addition to a specific local volatility model the densities are consistent with the difference of compound exponential processes taken at log time and scaled by the square root of time. The underlying process has a single parameter, the constant variance rate of the process. Delta hedging using Laplacian and Asymmetric Laplacian implied volatilities are developed and compared with Black Merton Scholes implied volatility hedging.The hedging strategies are implemented for stylized businesses represented by dynamic volatility indexes. The Laplacian hedge is seen to be smoother for the skew trade. It also performs better through the financial crisis for the sale of strangles. The Laplacian and Gaussian models are then synthesized as special cases of a model allowing for other powers between unity and the square. Numerous hedging strategies may be run using different powers and biases in the probability of an up move. Adapted strategies that select the best performer on past quarterly data can dominate fixed strategies. Adapted hedging strategies can effectively reduce drawdowns in the marked to market value of businesses trading options.     

Pricing and Hedging of Discrete Dynamic Guaranteed Funds

We derive a risk‐neutral pricing model for discrete dynamic guaranteed funds with geometric Gaussian underlying security price process. We propose a dynamic hedging strategy by adding a gamma factor to the conventional delta. Simulation results demonstrate that, when hedging discretely, the risk‐neutral gamma‐adjusted‐delta strategy outperforms the dynamic delta hedging strategy by reducing the expected hedging error, lowering the hedging error variability, and improving the self‐financing possibility. The discrete dynamic delta‐only hedging not only causes potential overcharge to clients but also could be costly to the issuers. We show that a naive application of continuous‐time hedging formula to a discrete‐time hedging setting tends to worsen these possibilities.     

Corporate reputation and hedging activities

This study examines whether corporate reputation affects derivative hedging. We posit that high-reputation firms are more likely to engage in hedging due to greater reputation costs and/or their commitment to lower financial risks. We find that high-reputation firms are more likely to engage in hedging, especially when their hedging efforts or effects are more observable to stakeholders. We also find that high-reputation firms are less likely to disclose the notional values of hedging positions and that interest rate hedging by high-reputation firms is detrimental to firm value. Our results shed light on the impact of reputational concerns on corporate risk management and disclosure policies.     

Hedging the value of waiting

We analyze the optimal hedging policy of a firm that has flexibility in the timing of investment. Conventional wisdom suggests that hedging adds value by alleviating the under-investment problem associated with capital market frictions. However, our model shows that hedging also adds value by allowing investment to be delayed in circumstances where the same frictions would cause it to commence prematurely. Thus, hedging can have the paradoxical effect of reducing investment. We also show that greater timing flexibility increases the optimal quantity of hedging, but has a non-monotonic effect on the additional value created by hedging. These results may help explain the empirical findings that investment rates do not differ between hedgers and non-hedgers, and that hedging propensities do not depend on standard measures of growth opportunities.     

Does Hedging Affect Firm Value? Evidence from the US Airline Industry

Does hedging add value to the firm, and if so, is the source of the added value consistent with hedging theory? We investigate jet fuel hedging behavior of firms in the US airline industry during 1992–2003 to examine whether such hedging is a source of value for these companies. We illustrate that the investment and financing climate in the airline industry conforms well to the theoretical framework of Froot, Scharfstein, and Stein (1993). In general, airline industry investment opportunities correlate positively with jet fuel costs, while higher fuel costs are consistent with lower cash flow. Given that jet fuel costs are hedgeable, airlines with a desire for expansion may find value in hedging future purchases of jet fuel. Our results show that jet fuel hedging is positively related to airline firm value. The coefficients on the hedging variables in our regression analysis suggest that the “hedging premium” is greater than the 5% documented in Allayannis and Weston (2001), and might be as large as 10%. We find that the positive relation between hedging and value increases in capital investment, and that most of the hedging premium is attributable to the interaction of hedging with investment. This result is consistent with the assertion that the principal benefit of jet fuel hedging by airlines comes from reduction of underinvestment costs.     

Hedging effectiveness under conditions of asymmetry

We examine whether hedging effectiveness is affected by asymmetry in the return distribution by applying tail-specific metrics, for example, value at risk, to compare the hedging effectiveness of short and long hedgers. Comparisons are applied to a number of hedging strategies including OLS and both symmetric and asymmetric generalised autoregressive conditional heteroskedastic models. We apply our analysis to a dataset consisting of S&P500 index cash and futures containing symmetric and asymmetric return distributions chosen ex post. Our findings show that asymmetry reduces out-of-sample hedging performance and that significant differences occur in hedging performance between short and long hedgers.     

Alternative models for hedging yield curve risk: An empirical comparison

We test alternative models of yield curve risk by hedging US Treasury bond portfolios through note/bond futures. We show that traditional implementations of models based on principal component analysis, duration vectors and key rate duration lead to high exposure to model errors and to sizable transaction costs, thus lowering the hedging quality. Also, this quality randomly varies from one model and hedging problem to the other. We show that accounting for the variance of modeling errors substantially reduces both hedging errors and transaction costs for all considered models. Additionally, it leads to much more stable weights in the hedging portfolios and – as a result – to more homogeneous hedging quality. On this basis, error-adjusted principal component analysis is found to systematically and significantly outperform alternative models.     

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.     

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.     

Is operational hedging a substitute for or a complement to financial hedging?

This paper investigates operational hedging by firms and how operational hedging is related to financial hedging by using a sample of 424 firm observations, which consist of 212 operationally hedged firms (firms with foreign sales) and a size- and industry-matched sample of 212 non-operationally hedged firms (firms with export sales). We find that non-operationally hedged firms use more financial hedging, relative to their levels of foreign currency exposure, as measured by the amount of export sales. On the other hand, though operationally hedged firms have more currency exposure, their usage of financial derivatives becomes much smaller than that of exporting firms. These results can explain why some global firms use very limited amount of financial derivatives for hedging purpose despite much higher levels of currency risk exposure. We also show that hedging increases firm value.     

An Intertemporal International Asset Pricing Model: Theory and Empirical Evidence

We extend Campbell's (1993) model to develop an intertemporal international asset pricing model (IAPM). We show that the expected international asset return is determined by a weighted average of market risk, market hedging risk, exchange rate risk and exchange rate hedging risk. These weights sum up to one. Our model explicitly separates hedging against changes in the investment opportunity set from hedging against exchange rate changes as well as exchange rate risk from intertemporal hedging risk. A test of the conditional version of our intertemporal IAPM using a multivariate GARCH process supports the asset pricing model. We find that the exchange rate risk is important for pricing international equity returns and it is much more important than intertemporal hedging 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.     

Pricing methods and hedging strategies for volatility derivatives

We explore the valuation and hedging of discretely observed volatility derivatives using three different models for the price of the underlying asset: Geometric Brownian motion with constant volatility, a local volatility surface, and jump-diffusion. We begin by comparing the effects on valuation of variations in contract design, such as the differences between specifying log returns or actual returns and incorporating caps on the level of realized volatility. We then focus on the difficulties associated with hedging these products. Delta hedging strategies are ineffective for hedging volatility derivatives since they require very frequent rebalancing. Moreover, they provide limited protection in the jump-diffusion context. We study the performance of a hedging strategy for volatility swaps that establishes small, fixed positions in vanilla options at each volatility observation.     

Hedging and liquidity

This article develops a model for evaluating alternative hedgingstrategies for financially constrained firms. A key advantageof the model is the ability to capture the intertemporal effectsof hedging on the firm's financial situation. We characterizethe optimal hedge. A wide range of alternative hedging strategiescan be specified and the model allows us to determine in eachcase if the hedging strategy raises or lowers firms value andby how much. We show that hedging firm value, hedging cash flowfrom operations and hedging sales revenue are not optimal. Thearticle highlights the fact that every hedging strategy comespackaged with a borrowing strategy which requires careful consideration.     

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.