Empirical performance of alternative pricing models of currency options

This article examines the out‐of‐sample pricing performance and biases of the Heston’s stochastic volatility and modified Black‐Scholes option pricing models in valuing European currency call options written on British pound. The modified Black‐Scholes model with daily‐revised implied volatilities performs as well as the stochastic volatility model in the aggregate sample. Both models provide close and similar correspondence to actual prices for options trading near‐ or at‐the‐money. The prices generated from the stochastic volatility model are subject to fewer and weaker aggregate pricing biases than are the prices from the modified Black‐Scholes model. Thus, the stochastic volatility model may provide improved estimates of the measures of option price sensitivities to key option parameters that may lead to more effective hedging and speculative strategies using currency options. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:265–291, 2000     

The interrelation of price volatility and trading volume of currency options

This article examines the interrelations between future volatility of the U.S. dollar/British pound exchange rate and trading volume of currency options for the British pound. The future volatility of the exchange rate is approximated alternatively by implied volatility and by IGARCH volatility. The results suggest the presence of strong contemporaneous positive feedbacks between the exchange rate volatility and the trading volume of call and put options. Previous option volumes have significant predictive power with respect to the expected future volatility of the dollar/pound exchange rate. Similarly, lagged volatilities jointly have significant predictive power for option volume. Although option volume (volatility) responds somewhat differently to individual volatility (volume) terms under the two volatility measures, the overall volume‐volatility relations are broadly similar between the implied and IGARCH volatilities. The results generally support the hypothesis that the information‐based trading explains more of the trading volume in currency options on the U.S. dollar/British pound exchange rate than hedging. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:681–700, 2003     

Currency‐Protected Swaps and Swaptions with Nonzero Spreads in a Multicurrency LMM

Despite the fact that currency‐protected swaps and swaptions are widely traded in the marketplace, pricing models for zero‐spread swaps, and swaptions have rarely been examined in the extant literature. This study presents a multicurrency LIBOR market model and uses it to derive pricing formulas for currency‐protected swaps and swaptions with nonzero spreads. The resulting pricing formulas are shown to be feasible and tractable for practical implementation and their hedging strategies are also provided. Our pricing formulas provide prices close to those computed from Monte Carlo simulation, but involve far less computation time, and thereby offering almost instant price quotes to clients and daily marking‐to‐market trading books, and facilitating efficient risk management of trading positions.     

Pricing and hedging of quanto range accrual notes under Gaussian HJM with cross‐currency Levy processes

This study analyzes the pricing and hedging problems for quanto range accrual notes (RANs) under the Heath‐Jarrow‐Morton (HJM) framework with Levy processes for instantaneous domestic and foreign forward interest rates. We consider the effects of jump risk on both interest rates and exchange rates in the pricing of the notes. We first derive the pricing formula for quanto double interest rate digital options and quanto contingent payoff options; then we apply the method proposed by Turnbull (Journal of Derivatives, 1995, 3, 92–101) to replicate the quanto RAN by a combination of the quanto double interest rate digital options and the quanto contingent payoff options. Using the pricing formulas derived in this study, we obtain the hedging position for each issue of quanto RANs. In addition, by simulation and assuming the jump risk to follow a compound Poisson process, we further analyze the effects of jump risk and exchange rate risk on the coupons receivable in holding a RAN. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:973–998, 2009     

Valuation and Hedging of Differential Swaps

This paper derives a general‐form formula for pricing and hedging differential swaps with the principal denominated either in a domestic, foreign, or third‐country currency. We first derive the formula for differential swaps with the principal in a domestic currency and identify an error in the formula of Wei (1994). We then show the pricing duality between differential swaps with the principal in a domestic currency and differential swaps with the principal in a foreign currency. Finally, we complete the pricing and hedging analysis on differential swaps by deriving a formula for differential swaps with the principal denominated in a third‐country currency. Simulation results indicate that constant margin rates are generally smaller than interest rate differentials and decline with the tenor of swaps. Correlation parameters associated with the exchange rate play a more important role than correlation parameters among interest rates in pricing differential swaps. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:73–94, 2002     

Pricing models of equity swaps

This article provides a generalized formula for pricing equity swaps with constant notional principal when the underlying equity markets and settlement currency can be set arbitrarily. To derive swap values using the risk‐neutral valuation method, the swap payment is replicated at each settlement date by constructing a self‐financing portfolio. To obtain the foreign equity index return denominated in the domestic or in a third currency, equity‐linked foreign exchange options are used to hedge the exchange rate risk. It is found that if the swap involves international equity markets, then the swap value contains an extra term which reflects the currency hedging costs. This methodology can easily be applied to price various types of equity swaps simply by modifying the specifications of the model presented here as required. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:751–772, 2003     

Volatility options: Hedging effectiveness,pricing, and model error

Motivated by the growing literature on volatility options and their imminent introduction in major exchanges, this article addresses two issues. First, the question of whether volatility options are superior to standard options in terms of hedging volatility risk is examined. Second, the comparative pricing and hedging performance of various volatility option pricing models in the presence of model error is investigated. Monte Carlo simulations within a stochastic volatility setup are employed to address these questions. Alternative dynamic hedging schemes are compared, and various option‐pricing models are considered. It is found that volatility options are not better hedging instruments than plain‐vanilla options. Furthermore, the most naïve volatility option‐pricing model can be reliably used for pricing and hedging purposes. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:1–31, 2006     

The robust pricing–hedging duality for American options in discrete time financial markets

We investigate the pricing–hedging duality for American options in discrete time financial models where some assets are traded dynamically and others, for example, a family of European options, only statically. In the first part of the paper, we consider an abstract setting, which includes the classical case with a fixed reference probability measure as well as the robust framework with a nondominated family of probability measures. Our first insight is that, by considering an enlargement of the space, we can see American options as European options and recover the pricing–hedging duality, which may fail in the original formulation. This can be seen as a weak formulation of the original problem. Our second insight is that a duality gap arises from the lack of dynamic consistency, and hence that a different enlargement, which reintroduces dynamic consistency is sufficient to recover the pricing–hedging duality: It is enough to consider fictitious extensions of the market in which all the assets are traded dynamically. In the second part of the paper, we study two important examples of the robust framework: the setup of Bouchard and Nutz and the martingale optimal transport setup of Beiglböck, Henry‐Labordère, and Penkner, and show that our general results apply in both cases and enable us to obtain the pricing–hedging duality for American options.     

Static and semistatic hedging as contrarian or conformist bets

In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semistatic portfolios should more properly be thought of as separate classes of derivatives, with nontrivial, model‐dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from the Carr–Madan representation, and suggest approximations of the idealized static hedging/replicating portfolio using vanillas available in the market. We study the dependence of the hedging error on a model used for pricing and show that the variance of the hedging errors of static hedging portfolios can be sizably larger than the errors of variance‐minimizing portfolios. We explain why the exact semistatic hedging of barrier options is impossible for processes with jumps, and derive general formulas for variance‐minimizing semistatic portfolios. We show that hedging using vanillas only leads to larger errors than hedging using vanillas and first touch digitals. In all cases, efficient calculations of the weights of the hedging portfolios are in the dual space using new efficient numerical methods for calculation of the Wiener–Hopf factors and Laplace–Fourier inversion.     

The Demand for Hedging with Futures and Options

The optimal hedging portfolio is shown to include both futures and options under a variety of circumstances when the marginal cost of hedging is nonzero. Futures and options are treated as substitute goods, and the properties of the resulting hedging demand system are explained. The overall optimal hedge ratio is shown to increase when the marginal cost of trading options is reduced. The overall optimal hedge ratio is shown to decrease when the marginal cost of trading futures is decreased. One implication is that hedging demand can be stimulated by a reduction in the perceived cost of trading options through the education of hedgers about options and the initiation of programs such as the Dairy Options Pilot Program. The demand approach is applied to estimate optimal hedge ratios for dairy producers hedging corn inputs in five regions of Pennsylvania. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:693–712, 2001     

Static hedging and pricing of exotic options with payoff frames

We develop a general framework for statically hedging and pricing European‐style options with nonstandard terminal payoffs, which can be applied to mixed static–dynamic and semistatic hedges for many path‐dependent exotic options including variance swaps and barrier options. The goal is achieved by separating the hedging and pricing problems to obtain replicating strategies. Once prices have been obtained for a set of basis payoffs, the pricing and hedging of financial securities with arbitrary payoff functions is accomplished by computing a set of “hedge coefficients” for that security. This method is particularly well suited for pricing baskets of options simultaneously, and is robust to discontinuities of payoffs. In addition, the method enables a systematic comparison of the value of a payoff (or portfolio) across a set of competing model specifications with implications for security design.     

How electronic trading affects bid‐ask spreads and arbitrage efficiency between index futures and options

This paper examines the impact of switching to electronic trading on the relative pricing efficiency of Hang Sang Index futures and options contracts traded on the Hong Kong exchange. The study is motivated by the recent shift in 2000 from the pit to an electronic trading platform. Electronic trading leads to lower bid‐ask spreads and less price clustering than floor trading in both the options and futures markets. Mispricing between futures and options drops significantly after the change. Quicker correction of mispricing indicates a significant improvement in dynamic inter‐market arbitrage efficiency with electronic trading. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:375–398, 2005     

The management of exchange‐rate risk: A case from the manufacturing industry

This article looks into the management of exchange rate risk at a U.K.‐listed company. The focus is particularly on the firm's operating exchange risk, for which it uses a synthesis of three different risk management approaches. These include the use of long‐term financial hedging instruments, operational adjustments based on real options theory, and the currency denomination of debt. Practice at the case company is unique, in that the former approach has been considered inappropriate by the theoretical literature and the latter is seldom used to manage firms' real cash flow exposures. In general, it has important implications for multinationals, especially with reference to the use of operational adjustments and the currency denomination of debt. © 2004 Wiley Periodicals, Inc.     

Mean-Variance Hedging for Stochastic Volatility Models

In this paper we discuss the tractability of stochastic volatility models for pricing and hedging options with the mean-variance hedging approach. We characterize the variance-optimal measure as the solution of an equation between Doléans exponentials; explicit examples include both models where volatility solves a diffusion equation and models where it follows a jump process. We further discuss the closedness of the space of strategies.     

Path‐dependent currency options with mean reversion

This paper develops a path‐dependent currency option pricing framework in which the exchange rate follows a mean‐reverting lognormal process. Analytical solutions are derived for barrier options with a constant barrier, lookback options, and turbo warrants. As the analytical solutions are obtained using a Laplace transform, this study numerically shows that the solution implemented with a numerical Laplace inversion is efficient and accurate. The pricing behavior of path‐dependent options with mean reversion is contrasted with the Black‐Scholes model. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:275–293, 2008     

OPTIMAL STATIC–DYNAMIC HEDGES FOR BARRIER OPTIONS

We study optimal hedging of barrier options, using a combination of a static position in vanilla options and dynamic trading of the underlying asset. The problem reduces to computing the Fenchel–Legendre transform of the utility-indifference price as a function of the number of vanilla options used to hedge. Using the well-known duality between exponential utility and relative entropy, we provide a new characterization of the indifference price in terms of the minimal entropy measure, and give conditions guaranteeing differentiability and strict convexity in the hedging quantity, and hence a unique solution to the hedging problem. We discuss computational approaches within the context of Markovian stochastic volatility models.     

A non‐lattice pricing model of American options under stochastic volatility

In this article, an analytical approach to American option pricing under stochastic volatility is provided. Under stochastic volatility, the American option value can be computed as the sum of a corresponding European option price and an early exercise premium. By considering the analytical property of the optimal exercise boundary, the formula allows for recursive computation of the American option value. Simulation results show that a nonlattice method performs better than the lattice‐based interpolation methods. The stochastic volatility model is also empirically tested using S&P 500 futures options intraday transactions data. Incorporating stochastic volatility is shown to improve pricing, hedging, and profitability in actual trading. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:417–448, 2006     

Exports and hedging exchange rate risks: the multi‐country case

This article examines the optimal production, export allocation, and hedging decisions of a risk‐averse international firm that exports to several foreign markets with different currencies. The firm faces multiple exchange rate risks. Optimal decisions are analyzed under two scenarios. In the first, there is a forward market for one currency only. Then, the export allocation to different markets is separable from the firm's preferences and the joint distribution of the exchange rates. In contrast, total production is not separable except for a special case. In the second scenario, there is a forward market for each currency. Then, both production and export allocation are separable. Hedging with forward contracts depends on risk premia and on the joint distribution of the exchange rates. If tradable exchange rate risk is a linear function of untradable exchange rate risk plus noise, there is a conflict between cross hedging and taking a basis risk. If, alternatively, the untradable exchange rate risk is a linear function of the tradable exchange rate risk and noise, there is no such conflict. A speculative position in a biased forward market for one currency can be cross hedged using an unbiased forward market for another currency. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:843–864, 2000.     

Useful Properties of Exchange Rate Forecasts for Risk Management and Derivative Pricing

We examine three useful properties of the yen/dollar exchange‐rate forecasts that are published in January and July in the Wall Street Journal. Those properties are the level of explanatory power, whether some forecasters are consistently better than others, and whether the dispersion of forecasts can predict the volatility of the exchange rates. The results show that the relative accuracy of the individual forecasts has not been random each period, and the evidence suggests that some forecasters are consistently better than others. The forecasts from the best forecasters explain about half of the variability in the semiannual exchange‐rate series. Finally, the dispersion of all the forecasts each period, as measured by the standard deviation, has predictive power with respect to the daily volatility of the forecasts for the three months following the survey. This final property has implications for the pricing and use of currency options. © 2001 John Wiley & Sons, Inc.     

Pricing Multiasset Cross‐Currency Options

This study develops a general pricing method for multiasset cross‐currency options, whose underlying asset consists of multiple different assets, and the evaluation currency is different from the ones used in the most liquid market of each asset; the examples include cross‐currency options, cross‐currency basket options, and cross‐currency average options. Moreover, in practice, fast calibration is necessary in the option markets relevant for the underlying assets and the currency, which is also achieved in this study. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:1–19, 2014