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     

Cross Hedging with Currency Forward Contracts

This study examines the behavior of a competitive exporting firm that exports to a foreign country and faces multiple sources of exchange rate uncertainty. Although there are no hedging instruments between the home and foreign currencies, there is a third country that has well‐developed currency forward markets to which the firm has access. The firm's optimal cross‐hedging decision is shown to depend both on the degree of incompleteness of the currency forward markets in the third country, and on the correlation structure of the random spot exchange rates. Furthermore, the firm is shown to be more eager to produce and expand its exports to the foreign country when the missing currency forward contracts between the home and foreign currencies can be synthesized by the existing currency forward contracts. In this case of perfect cross hedging, the separation theorem holds but the full‐hedging theorem may or may not hold. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark     

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     

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.     

The Relationship between Exchange Rates and Interest Rate Differentials: A Wavelet Approach

This paper uses wavelet analysis to investigate the relationship between the spot exchange rate and interest rate differential for seven pairs of countries, with a small country, Sweden, included in each case. The key empirical results show that there tends to be a negative relationship between the spot exchange rate (domestic‐currency price of foreign currency) and nominal interest rate differential (approximately the domestic interest rate minus the foreign interest rate) at the shortest timescales, while a positive relationship is more frequently found at the longest timescales. This indicates that among models of exchange rate determination using the asset approach, the sticky‐price models are supported in the short run and flexible‐price models in the long run.     

Interest Rate,Currency and Equity Derivatives Valuation Using the Potential Approach

Based on the potential approach to interest rate modelling, we introduce a simple tractable model for the unified valuation of interest rate, currency and equity derivatives. Our model is able to accommodate the initial term structure of zero‐coupon bond prices, generate positive and bounded interest rates, and handle cross products such as differential swaps, quanto options and equity swaps. As our model is specified under the actual probability measure, it can be directly used for portfolio risk management and the computation of value at risk. Furthermore, our model yields simple analytical formulas that are easy to calibrate and implement.     

Pricing and Hedging the Smile with SABR: Evidence from the Interest Rate Caps Market

This is the first comprehensive study of the SABR (stochastic alpha‐beta‐rho) model (Hagan, Kumar, Lesniewski, & Woodward, 2002) on the pricing and hedging of interest rate caps. I implement several versions of the SABR interest rate model and analyze their respective pricing and hedging performance using two years of daily data with seven different strikes and ten different tenors on each trading day. In‐sample and out‐of‐sample tests show that the fully stochastic version of the SABR model exhibits excellent pricing accuracy and, more importantly, captures the dynamics of the volatility smile over time very well. This is further demonstrated through examining delta‐hedging performance based on the SABR model. My hedging result indicates that the SABR model produces accurate hedge ratios that outperform those implied by the Black model. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 32:773‐791, 2012     

Effects of interest rate swaps

In this paper we examine the effect of interest rate swaps on the firm, and identify characteristics of firms that use interest rate swaps, reporting findings consistent with interest rate swaps being used as a risk-reducing instrument. Relative to nonswappers, firms using swaps are more likely to experience decreased cash flow variance in the five-year period subsequent to swap initiation. In addition, firms that engage in swaps are found to be larger and more highly levered than a control sample of nonswappers. Dividing our sample based upon type of swap, we find different characteristics explain different types of swap. In particular we find evidence consistent with swaps from variable to fixed interest rates being engaged in for risk reduction, i.e., hedging purposes.     

Local currency systemic risk

Emerging country governments increasingly issue local currency denominated bonds and foreign investors have been increasing their holdings of these assets. By issuing debt denominated in local currency, emerging country governments eliminate exchange rate risk. The growing stock of local currency government debt in the financial portfolios of foreign investors increases their diversification and exposure to fast growing economies. In this paper, we highlight some of the risks associated to this recent trend. First, we adopt the CoV aR risk-measure to estimate the vulnerability of individual countries to systemic risk in the market for local currency government debt. Second, we show that our country-level estimates of vulnerability increase with the share of local currency debt held by foreign investors. A version of the old adage “When New York sneezes, London catches a cold,” used often to describe the relationship between the stock markets in these two cities, still applies between individual emerging countries and the aggregate market for local currency government debt.     

A Note on Exports and Hedging Exchange Rate Risks: The Multi‐Country Case

This study examines the behavior of an exporting firm that exports to two foreign countries, each of which has its own currency. Hedging is imperfect in that the firm can only trade one of the two foreign currencies forward. Compared to the case wherein hedging is perfect in that both foreign currencies can be traded forward, the firm is shown to produce less in the home country. Furthermore, the firm is shown to export more (less) to the foreign country whose currency can (cannot) be traded forward. The firm's optimal forward position is an over‐hedge or an under‐hedge, depending on whether the spot exchange rates are positively or negatively correlated in the sense of expectation dependence, respectively. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 33:1191–1196, 2013     

Liability dollarization and the bank balance sheet channel

Emerging markets' financial institutions often face a mismatch in the currency denominations of their liabilities (foreign currency-denominated debt raised from foreign lenders) and their assets (domestic currency loans to domestic borrowers). We study the effect of this mismatch on monetary policy in a sticky-price, dynamic general-equilibrium small open economy model in which the country default-risk premium depends on domestic banks' balance sheets due to asymmetric information. A fixed exchange rate rule that stabilizes bank balance sheets offers greater stability than does an interest rate rule that targets inflation to offset the real effects of sticky-prices.     

Equity swaps in a LIBOR market model

This study extends the BGM (A. Brace, D. Gatarek, & M. Musiela, 1997) interest rate model (the London Interbank Offered Rate [LIBOR] market model) by incorporating the stock price dynamics under the martingale measure. As compared with traditional interest rate models, the extended BGM model is both appropriate for pricing equity swaps and easy to calibrate. The general framework for pricing equity swaps is proposed and applied to the pricing of floating‐for‐equity swaps with either constant or variable notional principals. The calibration procedure and the practical implementation are also discussed. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:893–920, 2007     

The pricing of foreign currency options under jump‐diffusion processes

In this article, the authors derive explicit formulas for European foreign exchange (FX) call and put option values when the exchange rate dynamics are governed by jump‐diffusion processes. The authors use a simple general equilibrium international asset pricing model with continuous trading and frictionless international capital markets. The domestic and foreign price level are introduced as state variables that contain jumps caused by monetary shocks and catastrophic events such as 9/11 or Hurricane Katrina. The domestic and foreign interest rates are stochastic and endogenously determined in the model and are shown to be critically affected by the jump risk of the foreign exchange. The model shows that the behavior of FX options is affected through the impact of state variables and parameters on the nominal interest rates. The model contrasts with those of M. Garman and S. Kohlhagen (1983) and O. Grabbe (1983), whose models have exogenously determined interest rates. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:669–695, 2007     

Optimal hedge ratios in the presence of common jumps

This study derives optimal hedge ratios with infrequent extreme news events modeled as common jumps in foreign currency spot and futures rates. A dynamic hedging strategy based on a bivariate GARCH model augmented with a common jump component is proposed to manage currency risk. We find significant common jump components in the British pound spot and futures rates. The out‐of‐sample hedging exercises show that optimal hedge ratios which incorporate information from common jump dynamics substantially reduce daily and weekly portfolio risk. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:801–807, 2010     

Information content of cross‐sectional option prices: A comparison of alternative currency option pricing models on the Japanese yen

This article implements a currency option pricing model for the general case of stochastic volatility, stochastic interest rates, and jumps in an attempt to reconcile levels of risk‐neutral skewness and kurtosis with observed option prices on the Japanese yen and to analyze the information content of the cross section of option prices by investigating the hedging and pricing performance of various currency option pricing models. The study makes use of both a method of moments and a more traditional generalized‐least‐squares (GLS) estimation technique, taking advantage of the fact that methods of moments do not specifically require the use of cross‐sectional option prices, whereas GLS does. Results centered around the Asia economic crisis of 1997 and 1998 indicate that the cross section of option prices surprisingly does not appear to contain superior information as the two estimation techniques yield relatively similar results once idiosyncratic differences between them are acknowledged. Extensions of the G. Bakshi, C. Cao, and Z. Chen (1997) results to currencies are also provided. © 2006Wiley Periodicals, Inc. Jrl Fut Mark 26:33–59, 2006     

中国崛起背景下的涉外金融安全问题与对策

中国崛起背景下的涉外金融安全问题,主要表现在三个方面,即资本账户开放的安全问题、外汇储备资产或外汇资产的安全问题、国际支付结算体系的安全问题。导致中国涉外金融安全问题的外部原因是本币不具备储备货币的国际地位,需要从外部获得储备货币,必然缺乏安全;人民币汇率的信用依靠美元等储备货币背书,中国经济崛起也曾经依赖美元顺差;美国可以利用美元账户对资金、资产交易、跨境支付结算等,实施行政处罚、限制、冻结等制裁,乃至剔除出账户系统。内部原因是中国经济崛起,美国要打压和制裁;金融开放如果在汇率制度选择、外汇管制和管控上处理不当,允许储备货币资金完全自由进出而无约束,则必然存在金融危机的可能;国际收支失衡导致涉外金融缺乏安全。解决涉外金融安全问题应从四个方面着手:一是通过货币互换和多元化投资等方式保障外汇(储备)资产安全;二是通过提倡主权货币计价、支付、结算、融资,以及开展相关制度设计等方式建设好交易和支付结算系统;三是把握好资本账户开放;四是做好人民币国际化的基础工作。     

HEDGING STRATEGIES AND MINIMAL VARIANCE PORTFOLIOS FOR EUROPEAN AND EXOTIC OPTIONS IN A LÉVY MARKET

This paper presents hedging strategies for European and exotic options in a Lévy market. By applying Taylor’s theorem, dynamic hedging portfolios are constructed under different market assumptions, such as the existence of power jump assets or moment swaps. In the case of European options or baskets of European options, static hedging is implemented. It is shown that perfect hedging can be achieved. Delta and gamma hedging strategies are extended to higher moment hedging by investing in other traded derivatives depending on the same underlying asset. This development is of practical importance as such other derivatives might be readily available. Moment swaps or power jump assets are not typically liquidly traded. It is shown how minimal variance portfolios can be used to hedge the higher order terms in a Taylor expansion of the pricing function, investing only in a risk‐free bank account, the underlying asset, and potentially variance swaps. The numerical algorithms and performance of the hedging strategies are presented, showing the practical utility of the derived results.     

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.     

Convexity meets replication: Hedging of swap derivatives and annuity options

Convexity correction arises when one computes the expected value of an interest rate index under a probability measure other than its own natural martingale measure. As a typical example, the natural martingale measure of the swap rate is the swap measure with annuity as the numeraire. However, the evaluation of the discounted expectation of the payoff in a constant maturity swap (CMS) derivative is performed under the forward measure corresponding to the payment date. In this study, we propose a generalization of the static replication formula by exploring the linkage between replication, convexity correction, and numeraire change. We illustrate how the static replication of a CMS caplet by a portfolio of payer swaptions is related to convexity correction associated with the bond–annuity numeraire ratio. We also demonstrate the use of the generalized static replication approach for hedging the in‐arrears clean index principal swaps and annuity options © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:659–678, 2011     

Pricing and hedging American fixed‐income derivatives with implied volatility structures in the two‐factor Heath–Jarrow–Morton model

Most previous empirical studies using the Heath–Jarrow–Morton model (hereafter referred to as the HJM model) have focused on the one‐factor model. In contrast, this study implements the Das ( 1999 ) two‐factor Poisson–Gaussian version of the HJM model that incorporates a jump component as the second‐state variable. This study aims at examining the performance of the two‐factor model through comparing it with the one‐factor model in pricing and hedging the Eurodollar futures option. The degree of impact arising from the jump factor also is examined. In addition, three new volatility specifications are constructed to enhance further the pricing performance of the model. Their performances are compared according to three performance yardsticks—in‐sample fitting, out‐of‐sample pricing, and the hedging test. The result indicates that the two‐factor model outperforms the one‐factor model in both the in‐sample and out‐sample price fitting, but the one‐factor model performs better in the hedging test. In addition, the HJM model, coupled with the proposed volatility specification, leads to good fitting results that will be of considerable use to practitioners and academics in guiding model choice for interest‐rate derivatives. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:839–875, 2002