Pricing Foreign Exchange Options Under Intervention by Absorption Modeling

We consider option pricing for a foreign exchange (FX) rate where interventions by an authority may take place when the rate approaches to a certain level at the down side. We formulate the forward FX model by a diffusion process which is stopped by a hitting time of an absorption boundary. Moreover, for a deterministic volatility case with a moving absorption whose level is described by an ordinary differential equation, we obtain closed-form formulas for prices of a European put option and a digital option, and Greeks of the put option. Furthermore, we show an extension of the pricing formula to the case where the intervention level is unknown. In numerical examples, we show option prices for different strikes for the absorption model and the extended model. We compare the model prices with the market prices for EURCHF options traded before January 2015 with the absorption model, and also show experiments of the extended model as an application to the pricing under uncertain views on the intervention.     

Forecasting Emerging Market Exchange Rates from Foreign Equity Options

The use of derivatives to infer future exchange rates has long been a subject of interest in the international finance literature. With the recent currency crises in Mexico, Southeast Asia, and Brazil, work on exchange rate expectations in emerging markets is of particular interest. For some emerging markets, foreign equity options are the only liquid exchange‐traded derivatives with currency information embedded in their prices. Given that emerging markets sometimes undergo currency realignment with discrete jumps in their exchange rate, estimation of risk‐neutral probability density functions from foreign equity option data provides valuable evidence concerning market expectations. To illustrate the use of foreign equity options in estimating market beliefs, we consider Telmex options around the 1994 peso devaluation and find evidence that markets anticipated the change in the Mexican government's foreign exchange policy.     

Pricing American Put Options on Defaultable Bonds

In the last two decades, the market of credit derivativeshas expanded rapidly, and the importance of pricing problemsfor credit derivatives has been recognized especially in the last decade.Among these securities, the pricing problems of credit derivativeswith an early exercise, such as American put options,have not received enough attention. In view of this need, this paper develops a continuous stochastic modelof American put options on defaultable bonds.The method of obtaining a solution is based on a new result of the optimalstopping problem for a diffusion process with a jump.Some characterizations of American put options are providedusing partial differential equations.     

The Accuracy of Density Forecasts from Foreign Exchange Options

Financial decision makers often consider the information incurrency option valuations when making assessments about futureexchange rates. The purpose of this article is to systematicallyassess the quality of option-based volatility and density forecasts.We use a unique dataset consisting of more than 10 years ofdaily data on over-the-counter (OTC) currency option prices.We find that the OTC implied volatilities provide largely unbiasedand fairly accurate forecasts of one-month- and three-month-aheadrealized volatility. Furthermore, we find that the one-monthoption implied density forecasts are well calibrated for thecenter of the distribution, but we find evidence of misspecificationin the tail density forecasts.     

Pricing Bonds and Bond Options with Default Risk

The pricing of bonds and bond options with default risk is analysed in the general equilibrium model of Cox, Ingersoll, and Ross (1985). This model is extended by means of an additional parameter in order to deal with financial and credit risk simultaneously. The estimation of such a parameter, which can be considered as the market equivalent of an agencies' bond rating, allows to extract from current quotes the market perceptions of firm's credit risk. The general pricing model for defaultable zero-coupon bond is first derived in a simple discrete-time setting and then in continuous-time. The availability of an integrated model allows for the pricing of default-free options written on defaultable bonds and of vulnerable options written either on default-free bonds or defaultable bonds. A comparison between our results and those given by Jarrow and Turnbull (1995) is also presented.     

Locally Complete Markets,Exchange Rates and Currency Options

This paper extends the Heath, Jarrow and Morton model (1992) to atwo country setup. In the presence of common shocks and country specificshocks, we retrieve each country's pricing kernel implied by itsterm structure dynamics and show that the pricing kernels impose a constrainton the exchange rate to be the ratio of the pricing kernels. Under therisk neutral measure, the drift of the exchange rate is the interest ratedifferential, and the volatility reflects the forward rate risk-premiumdifferential of the two countries. The result implies that the risk premiumwill enter the currency option pricing model through the volatility term.Under the assumption of non-stochastic forward rate drift and volatility,we are able to derive closed-form solutions for currency options.     

Modeling and Pricing Longevity Derivatives Using Stochastic Mortality Rates and the Esscher Transform

The Lee-Carter mortality model provides a structure for stochastically modeling mortality rates incorporating both time (year) and age mortality dynamics. Their model is constructed by modeling the mortality rate as a function of both an age and a year effect. Recently the MBMM model (Mitchell et al. 2013) showed the Lee Carter model can be improved by fitting with the growth rates of mortality rates over time and age rather than the mortality rates themselves. The MBMM modification of the Lee-Carter model performs better than the original and many of the subsequent variants. In order to model the mortality rate under the martingale measure and to apply it for pricing the longevity derivatives, we adapt the MBMM structure and introduce a Lévy stochastic process with a normal inverse Gaussian (NIG) distribution in our model. The model has two advantages in addition to better fit: first, it can mimic the jumps in the mortality rates since the NIG distribution is fat-tailed with high kurtosis, and, second, this mortality model lends itself to pricing of longevity derivatives based on the assumed mortality model. Using the Esscher transformation we show how to find a related martingale measure, allowing martingale pricing for mortality/longevity risk–related derivatives. Finally, we apply our model to pricing a q-forward longevity derivative utilizing the structure proposed by Life and Longevity Markets Association.     

Temporal Patterns in Foreign Exchange Returns and Options

Although the foreign exchange market is believed to be one of the most efficient financial markets in the world, there is significant evidence that technical analysis is profitable in this market. In this study we investigate the ability of information from the options market to supplement the commonly used information on past prices to predict temporal patterns in foreign exchange returns. We find that strategies using information from at-the-money options were more consistently profitable than the commonly used strategies based on only historical spot exchange rates (past prices). Consequently, options appear to contain information regarding future spot exchange rate movements.     

Forward Foreign Exchange Rates,Expected Spot Rates,and Premia: A Signal-Extraction Approach

In this paper, we implement a methodology to identify and measure premia in the pricing of forward foreign exchange that involves application of signal-extraction techniques from the engineering literature. Diagnostic tests indicate that these methods are quite successful in capturing the essence of the time-series properties of premium terms. The estimated premium models indicate that premia show a certain degree of persistance over time and that more than half the variance in the forecast error that results from the use of current forward rates as predictors of future spot rates is accounted for by variation in premium terms. The methodology can be applied straightforwardly to the measurement of unobservables in other financial markets.     

外汇期权市场与人民币汇率的风险定价

本文利用大量隐含波动率的基础数据和密集的插值计算,编制人民币汇率市场情绪指数,分析情绪指数的信息含义,并在此基础上研究情绪指数与汇率风险定价之间的关系,发现8.11汇改后波动率不确定性的风险已体现在汇率定价中,人民币汇率形成机制更趋成熟。根据研究结论,建议参考市场售汇和美元指数变动情况进一步完善隐含波动率报价。     

中国利率、汇率和资本项目开放优序分析

一国的利率、汇率、资本项目是其金融市场中重要的市场变量,中国金融市场自由化进程中选择利率、汇率、资本项目开放的最优次序应为先利率、再汇率、最后逐步推进资本项目的开放,但在实际过程中可相互交叉、互相配合。在开放进程中需注意在完全放开利率前,需要完善中国的利率体系;在汇率市场化中后期需要外汇管理当局以更高超的管理技巧进行资本流入监管;市场化的汇率改革可以采用汇率目标区制;在资本账户开放过程中要加强资本尤其是短期资本流入管理等。     

GDP挂钩债券定价机理及价格行为模拟

作为结构化金融产品的一种,GDP挂钩债券在国外发展比较迅速。本文从发行人和投资者的视野,分析了GDP挂钩债券的产品结构、定价机理和设计要点等,特别是探讨了GDP挂钩债券定价的理论模型,剖析了GDP挂钩债券的定价特点及GDP期权模型,对GDP挂钩债券与GDP变化之间的关系即敏感性进行了分析。在此基础上通过算例进行了价格模拟,其研究思路和结论对中国宏观经济环境下的金融创新产品定价具有重要的意义。     

Re-examining Cointegration, Unit Roots and Efficiency in Foreign Exchange Rates

This paper examines the cointegrating relationships in seven foreign exchange rates for a sample period from 1974 to 1991 by utilizing Johansen's (1991) method. Three subperiods are also examined to confirm the intertemporal stability of the test results. In addition, subgroups of the seven exchange rates are analyzed to determine the consistency of the empirical results with respect to different dimensions in the system. We find that the test results are sensitive to the choice of test statistics, time trends, subperiods as well as subgroups. All results indicate either one or no cointegrating relationship exists. Further, we study time series properties of twenty one cross-currency rates and the corresponding exchange rates in terms of a common currency. None of cross-currency rates are stationary and hence the pairs of exchange rates are not cointegrated.     

中国外汇储备:增长也烦恼

从今年2月底开始,中国外汇储备规模超过日本,荣登榜首。这又一次触发了由“外汇过度储备”带来的话题。本次“名家论坛”围绕中国的外汇管理制度改革、中国外汇储备适度规模、外汇储备使用、外汇储备收益四个方面的问题展开讨论。专家们这一系列的观点和利弊分析,不可能最终引出一个令所有人拍手称颂的“定论”,人们只能从国家经济安全、不同部门、不同产业甚至私人的角度进行多方比较思考,得出各自不同的结论。     

广义欧式加权算术平均价格一揽子期权定价

本文在一揽子期权（Basket Options）定价理论的基础上，对期权的标的价格引入跳跃一扩散过程进行建模，用几何布朗运动描述其动态变化过程，用Possion过程刻画资产价格受新的信息和稀有偶发时间的冲击所发生跳跃的计数过程，用对数正态随机变量描述跳跃对应的跳跃幅度，有模型限定下，运用Ito-Skorohod微分公式和等价鞅测度变换，得出加权算术平均价格一揽子期权的一个推广的解析定价公式。     

Interest Rates and Exchange Rate Movements: Analyzing Short-term Investments in Long-term Bonds

Tests of the uncovered interest rate parity (UIP) are subject to various data problems when long-term interest rates are applied: due to the long investment period, time intervals for measuring exchange rate movements are usually overlapping and therefore not independent. This shortfall can be prevented by considering short-term investments in long-term bonds instead of investments to maturity. This article analyzes the explanatory power of long-term interest rates with regard to 1- and 3-month exchange rate movements by relating return differences from 1- and 3-month investments in domestic and foreign 10-year government bonds to nine different exchange rates. From a Swiss perspective, there is only weak support for an interrelation between return differences and the corresponding exchange rate movements, whereas from a US perspective, the resulting estimates are much more in line with UIP.The reader may for instance consider Engel (1996) and Froot and Thaler (1990).     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.