Valuing American Derivatives by Least Squares Methods

Least Squares estimators are notoriously known to generate sub-optimal exercise decisions when determining the optimal stopping time. The consequence is that the price of the option is underestimated. We show how variance reduction methods can be implemented to obtain more accurate option prices. We also extend the Longsta¤ and Schwartz (2001) method to price American options under stochastic volatility. These are two important contributions that are particularly relevant for practitioners. Finally, we extend the Glasserman and Yu (2004b) methodology to price Asian options and basket options.

Optimal Martingales and American Option Pricing

Pricing American options is an interesting research topic since there is no analytical solution to value these derivatives. Different numerical methods have been proposed in the literature with some, if not all, either limited to a specific payoff or not applicable to multidimensional cases. Applications of Monte Carlo methods to price American options is a relatively new area that started with Longstaff and Schwartz (2001). Since then, few variations of that methodology have been proposed. The general conclusion is that Monte Carlo estimators tend to underestimate the true option price. The present paper follows Glasserman and Yu (2004b) and proposes a novel Monte Carlo approach, based on designing "optimal martingales" to determine stopping times. We show that our martingale approach can also be used to compute the dual as described in Rogers (2002).

Revisiting the Dollar-Euro Permanent Equilibrium Exchange Rate: Evidence from Multivariate Unobserved Components Models

We propose an alternative approach to obtaining a permanent equilibrium exchange rate (PEER), based on an unobserved components (UC) model. This approach offers a number of advantages over the conventional cointegration-based PEER. Firstly, we do not rely on the prerequisite that cointegration has to be found between the real exchange rate and macroeconomic fundamentals to obtain non-spurious long-run relationships and the PEER. Secondly, the impact that the permanent and transitory components of the macroeconomic fundamentals have on the real exchange rate can be modelled separately in the UC model. This is important for variables where the long and short-run effects may drive the real exchange rate in opposite directions, such as the relative government expenditure ratio. We also demonstrate that our proposed exchange rate models have good out-of sample forecasting properties. Our approach would be a useful technique for central banks to estimate the equilibrium exchange rate and to forecast the long-run movements of the exchange rate.

The Signalling Channel of Central Bank Interventions: Modelling the Yen/US Dollar Exchange Rate

This paper presents a theoretical framework analysing the signalling channel of exchange rate interventions as an informational trigger. We develop an implicit target zone framework with learning in order to model the signalling channel. The theoretical premise of the model is that interventions convey signals that communicate information about the exchange rate objectives of central bank. The model is used to analyse the impact of Japanese FX interventions during the period 1999 -2011 on the yen/US dollar dynamics.

The Signalling Channel of Central Bank Interventions: Modelling the Yen/US Dollar Exchange Rate

This paper presents a theoretical framework analysing the signalling channel of exchange rate interventions as an informational trigger. We develop an implicit target zone framework with learning in order to model the signalling channel. The theoretical premise of the model is that interventions convey signals that communicate information about the exchange rate objectives of central bank. The model is used to analyse the impact of Japanese FX interventions during the period 1999 -2011 on the yen/US dollar dynamics.

Currency Forecast Errors at Times of Low Interest Rates: Evidence from Survey Data on the Yen/Dollar Exchange Rate

Using survey expectations data and Markov-switching models, this paper evaluates the characteristics and evolution of investors' forecast errors about the yen/dollar exchange rate. Since our model is derived from the uncovered interest rate parity (UIRP) condition and our data cover a period of low interest rates, this study is also related to the forward premium puzzle and the currency carry trade strategy. We obtain the following results. First, with the same forecast horizon, exchange rate forecasts are homogeneous among different industry types, but within the same industry, exchange rate forecasts differ if the forecast time horizon is different. In particular, investors tend to undervalue the future exchange rate for long term forecast horizons; however, in the short run they tend to overvalue the future exchange rate. Second, while forecast errors are found to be partly driven by interest rate spreads, evidence against the UIRP is provided regardless of the forecasting time horizon; the forward premium puzzle becomes more significant in shorter term forecasting errors. Consistent with this finding, our coefficients on interest rate spreads provide indirect evidence of the yen carry trade over only a short term forecast horizon. Furthermore, the carry trade seems to be active when there is a clear indication that the interest rate will be low in the future.

Measuring the Euro-Dollar Permanent Equilibrium Exchange Rate using the Unobserved Components Model

This paper employs an unobserved component model that incorporates a set of economic fundamentals to obtain the Euro-Dollar permanent equilibrium exchange rates (PEER) for the period 1975Q1 to 2008Q4. The results show that for most of the sample period, the Euro-Dollar exchange rate closely followed the values implied by the PEER. The only significant deviations from the PEER occurred in the years immediately before and after the introduction of the single European currency. The forecasting exercise shows that incorporating economic fundamentals provides a better long-run exchange rate forecasting performance than a random walk process.