Arbitrage, Covered Interest Parity and Long-Term Dependence between the US Dollar and the Yen

Using a daily time series from 1983 to 2005 of currency prices in spot and forward USD/Yen markets and matching equivalent maturity short term US and Japanese interest rates, we investigate the sensitivity over the sample period of the difference between actual prices in forward markets to those calculated from short term interest rates. According to a fundamental theorem in financial economics termed covered interest parity (CIP) the actual and estimated prices should be identical once transaction and other costs are accommodated. The paper presents four important findings: First, we find evidence of considerable variation in CIP deviations from equilibrium that tends to be one way and favours those market participants with the ability to borrow US dollars (and subsequently lend yen). Second, these deviations have diminished significantly and by 2000 have been almost eliminated. We attribute this to the effects of electronic trading and pricing systems. Third, regression analysis reveals that interday negative changes in spot exchange rates, positive changes in US interest rates and negative changes in yen interest rates generally affect the deviation from CIP more than changes in interday volatility. Finally, the presence of long-term dependence in the CIP deviations over time is investigated to provide an insight into the equilibrium dynamics. Using a local Hurst exponent – a statistic used in fractal geometry - we find episodes of both positive and negative dependence over the various sample periods, which appear to be linked to episodes of dollar decline/yen appreciation, or vice versa. The presence of negative dependence is consistent with the actions of arbitrageurs successfully maintaining the long-term CIP equilibrium. Given the time varying nature of the deviations from equilibrium the sample period under investigation remains a critical issue when investigating the presence of longterm dependence.Hurst exponent; Efficient market hypothesis; covered interest parity, arbitrage

Currency trios - using geometric concepts to visualise and interpret relationships between currencies

A currency trio is a set of three currencies and their respective exchange rates, which have a relationship fixed by a triangular arbitrage condition. This condition forms the basis for the derivation of a geometric interpretation of the relationships between the exchange rates. In the geometric framework, the three currencies in a currency trio are represented by a triangle, where each of the vertices represents a currency. The volatilities of the exchange rates are represented by the lengths of the sides joining the respective currencies and the cosine of each angle represents the correlation between the two exchange rates depicted by the angle's adjacent sides. The geometric approach is particularly useful when dealing with implied data as it allows the calculation of implied correlation using implied volatility. This is valuable as implied volatility is frequently quoted in the foreign exchange market; whereas, implied correlation is not directly quoted and is more difficult to extract from market data. This dissertation aims to thoroughly investigate the geometric framework and use it to visualise and interpret the relationships between currencies in a currency trio. The analysis will initially look at currency trios with realised spot data before moving on to implied data. In the implied data context, the framework will be used to extract and evaluate implied correlation estimates using implied volatility data extracted from the foreign exchange market. The framework will be extended to investigate whether an illiquid option can be proxy hedged using options on the two other currencies in a currency trio. Finally, the findings will be discussed and the feasibility of the applications of the framework will be considered

Nonlinear dynamics and covered interest rate parity

Interest rates

Bond risk premia, macroeconomic fundamentals and the exchange rate

We introduce a two-country no-arbitrage term-structure model to analyse the joint dynamics of bond yields, macroeconomic variables, and the exchange rate. The model allows to understand how exogenous shocks to the exchange rate affect the yield curves, how bond yields co-move in different countries, and how the exchange rate is influenced by the interactions between macroeconomic variables and time-varying bond risk premia. Estimating the model with US and German data, we obtain an excellent fit of the yield curves and we are able to account for up to 75 per cent of the variability of the exchange rate. We find that time-varying risk premia play a non-negligible role in exchange rate fluctuations due to the fact that a currency tends to appreciate when risk premia on long-term bonds denominated in that currency rise. A number of other novel empirical findings emerge.exchange rate, term structure, UIP

Is technical analysis in the foreign exchange market profitable? a genetic programming approach

Using genetic programming techniques to find technical trading rules, we find strong evidence of economically significant out-of-sample excess returns to those rules for each of six exchange rates, over the period 1981-1995. Further, when the dollar/deutschemark rules are allowed to determine trades in the other markets, there is a significant improvement in performance in all cases, except for the deutschemark/yen. Betas calculated for the returns according to various benchmark portfolios provide no evidence that the returns to these rules are compensation for bearing systematic risk. Bootstrapping results on the dollar/deutschemark indicate that the trading rules are detecting patterns in the data that are not captured by standard statistical models.Programming (Mathematics) ; Foreign exchange

An analysis of the efficiency of the foreign exchange market in Kenya

This study examined the Efficiency Market hypothesis in its weak form using run tests, unit root tests and the Ljung-Box Q-statistics. The motivation was to determine whether foreign exchange rate returns follow a random walk. The data covered the period starting January 1994 to June 2007 for the daily closing spot price of the Kenya shillings per US dollar exchange rate. The main finding of this study is that the foreign exchange rate market is not efficient. The results showed that most of the rejections are due to significant patterns, trend stationarity and autocorrelation in foreign exchange returns. This is attributed to both exchange rate undershooting and overshooting phenomena.

A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

We extend range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator motivated by a key financial economic consideration, the absence of arbitrage, in addition to statistical considerations. We show that this estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading.

A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

We extend range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator motivated by a key financial economic consideration, the absence of arbitrage, in addition to statistical considerations. We show that this estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading.Range-based estimation, volatility, covariance, correlation, absence of arbitrage, exchange rates, stock returns, bond returns, bid-ask bounce, asynchronous trading

Modeling and Forecasting Realized Volatility

This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen /Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatitilies perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quintile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

Forward premium puzzle and term structure of interest rates: the case of New Zealand

Using monthly data for the United States dollar – New Zealand dollar exchange rate, this paper revisits the forward premium puzzle and applies a discrete no-arbitrage affine model of the term structure of interest rates to obtain historical estimates of the time-varying foreign exchange risk premium. The two-factor model is estimated via maximum likelihood for the period 1995-2006. The results of this study demonstrate that the modeled risk premium satisfies the required Fama’s conditions, and its inclusion in an extended GARCH(1,1) model is significant in explaining both the mean and the volatility of the exchange rate. However, consistently with the extant literature, the estimated risk premium does not preclude the presence of the forward premium anomaly. Lastly, out-of-sample forecasts of the exchange rate for different specifications and time periods reveal that predictions of the proposed model for the exchange rate are far from the accuracy of a simple random walk specification.