Option-Implied Currency Risk Premia - Princeton University

(Ψ t = 0) vs. time-varying global factor loadings.
2.4 Model parameters
The calibrated model parameters are reported in Table I. Panel A reports the values of global factor loadings,
ξ i , along with estimates of their standard errors (in parentheses), obtained from the first stage of the calibration.
Throughout our implementation the U.S. global factor loading is normalized to one. Panel B reports summary
statistics for the time series of model parameters obtained in the second stage of the calibration, which minimizes
option pricing errors day-by-day. We report the time series mean and volatility of the sensitivity of global factor
loadings to interest rate differentials (Ψ t ), and the parameters governing the distribution of the global pricing
kernel innovation. The latter include the share of variance attributable to the non-Gaussian component of the
innovation, η g t , and estimates of the parameters of the global CGMY jump component, G t (dampening coefficient)
and Y t (power coefficient). To facilitate interpretation we also report the mean instantaneous skewness and
kurtosis of the time-changed global innovation, L g Z t
, induced by variation in the jump parameters and the global
state variable, Z t . Panel C reports the quality of the model’s fit to the data in the form of the root mean squared
fitting error for implied volatilities by strike, and in total, measured in volatility points.
We consider a total of four specifications. Specifications I and II are based on the set of high/low interest
rate cross pairs, combined with the nine X/USD pairs (24 pairs); Specifications III and IV are calibrated using
data on all G10 cross pairs (45 pairs). Specifications II and IV are constrained versions of Specifications I and
III, respectively, which impose the restriction that the global factor loadings remain constant in the time series
(Ψ t = 0). Based on a combination of parsimony and quality of fit to the option data, Specification I is our
preferred model formulation.
2.4.1 Global factor loadings, ξt
i
The global loading parameters (Table I; Panel A) range from a low of 0.79 (AUD) to a high of 1.27 (JPY).
These values are broadly consistent with previously reported estimates from models allowing for asymmetries
in exposures to global risks. For example, using three years of data on a single currency triangle (JPY/USD,
GBP/USD, GBP/JPY), Bakshi, et al. (2008), find loadings of 1.53 (JPY) and 1.01 (GBP). Our estimate of
the loading for the British Pound is slightly lower and ranges from 0.93 to 0.98. These estimates can also be
contrasted with the parameters used in the simulation framework in Lustig, at al. (2011), which was calibrated
to match the historical risk and return properties of currency returns, risk-free rates, and inflation. Under their
“restricted” model with constant loadings, which is most comparable to our first stage output, the calibration
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