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Currency Options (currency + option)

Distribution by Scientific Domains
Business, Economics, Finance and Accounting100%

Selected Abstracts

Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates

MATHEMATICAL FINANCE, Issue 1 2004
Viatcheslav Gorovoi
Black's (1995) model of interest rates as options assumes that there is a shadow instantaneous interest rate that can become negative, while the nominal instantaneous interest rate is a positive part of the shadow rate due to the option to convert to currency. As a result of this currency option, all term rates are strictly positive. A similar model was independently discussed by Rogers (1995). When the shadow rate is modeled as a diffusion, we interpret the zero-coupon bond as a Laplace transform of the area functional of the underlying shadow rate diffusion (evaluated at the unit value of the transform parameter). Using the method of eigenfunction expansions, we derive analytical solutions for zero-coupon bonds and bond options under the Vasicek and shifted CIR processes for the shadow rate. This class of models can be used to model low interest rate regimes. As an illustration, we calibrate the model with the Vasicek shadow rate to the Japanese Government Bond data and show that the model provides an excellent fit to the Japanese term structure. The current implied value of the instantaneous shadow rate in Japan is negative. [source]

Value at risk from econometric models and implied from currency options

JOURNAL OF FORECASTING, Issue 8 2004
James ChongArticle first published online: 3 DEC 200
Abstract This paper compares daily exchange rate value at risk estimates derived from econometric models with those implied by the prices of traded options. Univariate and multivariate GARCH models are employed in parallel with the simple historical and exponentially weighted moving average methods. Overall, we find that during periods of stability, the implied model tends to overestimate value at risk, hence over-allocating capital. However, during turbulent periods, it is less responsive than the GARCH-type models, resulting in an under-allocation of capital and a greater number of failures. Hence our main conclusion, which has important implications for risk management, is that market expectations of future volatility and correlation, as determined from the prices of traded options, may not be optimal tools for determining value at risk. Therefore, alternative models for estimating volatility should be sought. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Path-dependent currency options with mean reversion

THE JOURNAL OF FUTURES MARKETS, Issue 3 2008
Hoi Ying Wong
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 [source]

The pricing of foreign currency options under jump-diffusion processes

THE JOURNAL OF FUTURES MARKETS, Issue 7 2007
Chang Mo Ahn
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 [source]

The interrelation of price volatility and trading volume of currency options

THE JOURNAL OF FUTURES MARKETS, Issue 7 2003
Ghulam Sarwar
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 [source]

The quality of volatility traded on the over-the-counter currency market: A multiple horizons study

THE JOURNAL OF FUTURES MARKETS, Issue 3 2003
Vicentiu Covrig
Previous studies of the quality of market-forecasted volatility have used the volatility that is implied by exchange-traded option prices. The use of implied volatility in estimating the market view of future volatility has suffered from variable measurement errors, such as the non-synchronization of option and underlying asset prices, the expiration-day effect, and the volatility smile effect. This study circumvents these problems by using the quoted implied volatility from the over-the-counter (OTC) currency option market, in which traders quote prices in terms of volatility. Furthermore, the OTC currency options have daily quotes for standard maturities, which allows the study to look at the market's ability to forecast future volatility for different horizons. The study finds that quoted implied volatility subsumes the information content of historically based forecasts at shorter horizons, and the former is as good as the latter at longer horizons. These results are consistent with the argument that measurement errors have a substantial effect on the implied volatility estimator and the quality of the inferences that are based on it. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:261,285, 2003 [source]