Option-Implied Currency Risk Premia - Princeton University

Table A.IV
Calibrated Model Parameters: Linking ξ i t to Y i
t
This table reports summary statistics for the calibrated parameters of the pricing kernel factor model. Results are reported for
four specifications which either: (a) match the prices of the high/low interest rate cross pairs and X/USD options (HLX + X/USD
option set; 24 pairs) or the full panel of G10 cross rates (X/Y option set; 45 pairs); and, (b) allow the global factors loadings, ξ i , to
be time-varying or not. All calibrations are performed using daily option quotes from January 1999 to June 2012 (T = 3520 days)
at five individual option strikes (10δ put, 25δ put, at-the-money, 25δ call, 10δ call). In specifications with time-varying global
factor loadings, the loadings are parameterized on the basis of the one-month interest rate differential, ξt i = ξ i − ˜Ψ t · (Yt i − Yt US ).
The slope coefficient, ˜Ψ t , is time-varying, but common to all currencies in the cross-section. Panel A reports the values of the
country-specific loadings, ξ i , obtained from the first stage of the calibration, with standard errors in parentheses. We also report
the mean one-month LIBOR interest rate differential for each country relative to the U.S.. Panel B summarizes the cross-sectional
dependence of the global factor loadings on interest rates differentials, Ψ t , and the characteristics of the global factor innovation,
L g Z t
. We report the share of variance in the global innovations due to jumps, η g t , and estimates of the parameters of the global
CGMY jump component, G g t (dampening coefficient) and Y g
t (power coefficient). Finally, we compute the skewness (Skewness g t )
and kurtosis (Kurtosis g t ) of the global factor innovation induced by variation in the global factor, Z t . We obtain each of these
quantities day-by-day by minimizing option pricing errors for the target option set, and report their time series means and
volatilities. Panel C reports the root mean squared option pricing error measured in volatility points. We compute root mean
squared errors (RMSE) for each pair in the target option set, and report their mean pooled: (a) across all strikes and currency pairs;
(b) across all pairs with a given option strike.
Specification ξt i Parametrization Option Set
I
ξ i − Ψ t · (rt,t+1 i − rUS t,t+1 ) HLX and X/USD pairs
I’ ξ i − ˜Ψ t · (Yt i t US ) HLX and X/USD pairs
Panel A: Global Factor Loadings, ξ i
Specification AUD CAD CHF EUR GBP JPY NOK NZD SEK USD
I and I’ 0.79 1.00 0.96 1.00 0.93 1.17 0.92 0.81 1.00 1.00
(0.0101) (0.0000) (0.0033) (0.0001) (0.0044) (0.0072) (0.0054) (0.0084) (0.0001) -
rt,t+1 i − rUS t,t+1 [%] 2.46 0.20 -1.58 -0.15 1.06 -2.54 1.53 2.78 0.07 0.00
Panel B: Global Factor Summary Statistics
Specification Ψ t η g t G g t Y g
t Skewness g t Kurtosis g t
I Mean 0.42 0.51 7.91 -0.75 -1.10 6.03
Volatility 1.89 0.19 5.60 0.16 1.35 4.04
I’ Mean -0.37 0.54 7.60 -0.74 -1.13 6.19
Volatility 11.94 0.20 4.86 0.17 1.35 4.20
Panel C: Option Pricing RMSE (Volatility Points)
Specification All 10δ p 25δ p 50δ 25δ c 10δ c
I 1.12 1.04 1.27 1.27 1.16 0.85
I’ 1.05 1.01 1.17 1.19 1.05 0.83
Panel D: HML F X Factor Mimicking Portfolio
Conditional Unconditional Difference
Realized Mean 4.96 3.32 1.63
[1.92] [1.32] [1.99]
Model I’ Total (λ) 3.82 3.76 0.06
[8.37] [8.03] [1.19]
Difference Mean 1.14 -0.43 1.57
t-stat [0.42] [-0.17] [1.90]