Foreign Exchange Expectation Errors and Filtration Enlargements

Abstract

Extrapolations of future market forward rates are a better predictor of the 30-days ahead BRL-USD exchange rate than forecasts from the Central Bank Focus survey of Brazilian market participants. This is puzzling because market participants observe forward rates as they submit predictions, and thus these agents perform biased forecasts even though they have access to a set of unbiased forecasts, consistent with a martingale process for the exchange rate. We argue that this rational conundrum can be explained by a mechanism through which new information enlarges the information set (a filtration), changing the underlying measure and inducing a drift into the martingale process, turning the process into a strict local martingale and generating a forecast bias. Empirical results suggest that Focus survey forecasts indeed display characteristics of a strict local martingale, while spot exchange rates and forward rates are consistent with a martingale process.

Brexit Risk Implied by the SABR Martingale Defect in the EUR-GBP Smile

“…with fixed elasticity parameter β = 1 (which is a common choice for FX smile modeling), volatility of volatility ν > 0 and two correlated È £ -Brownian motions W (1) and W (2) with correlation parameter ρ ∈ [−1, 1]. The dynamics of F t (T ) := F t (T ) −1 under the foreign equivalent martingale measure È e are given by…”

“…Strict local martingales have in financial applications been mainly employed to model stock price bubbles in financial markets, see, e.g., [4,10,11,12,13,14,15,17,18]. For applications the context of FX modeling see, e.g., [1,2]. We introduce here a statistical martingale defect indicator based on bid and ask implied volatility quotes which is carefully tailored to account for the uncertainty inherent in FX option markets stemming from the availability of merely 5 implied volatility quotes available for each time to maturity.…”