Option-Implied Currency Risk Premia - Princeton University

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Figure 7. The Cross-Section of Model and Realized Currency Risk Premia. The left panel plots the cross-sectional relation between the mean realized currency pair excess return, and the mean option-implied currency pair risk premium obtained from the calibrated model. The right panel plots the cross-sectional relation between the mean realized currency pair excess return and the mean one-month interest rate differential. Each subplot is equipped with a 45-degree line with an intercept of zero. In the left panel, this line corresponds to the hypothesis that the calibrated, option-implied risk premia are an unbiased predictor of currency excess returns. In the right panel, this line corresponds to a random walk model of exchange rate dynamics. The results are plotted for the 24 G10 currency pairs used to calibrate the model (Specification I). This set includes: (a) all X/USD currency pairs (9 pairs); and, (2) cross-pairs formed on the basis of currencies which had the highest or lowest interest rates in the G10 set at any point in our sample (15 pairs). X/USD pairs are additionally denoted with red dots. The plots report data spanning the period 1999:1-2012:6. 0.08 Option−implied risk premia (Adj. R 2 : 77.0%) 0.08 Random walk model (Adj. R 2 : 57.2%) 0.06 NZD/USD AUD/USD NZD/JPY AUD/JPY 0.06 AUD/USD NZD/USD AUD/JPY NZD/JPY 0.04 NOK/USD CAD/USD NOK/JPY 0.04 NOK/USD CAD/USD NOK/JPY Currency Excess Return 0.02 0 −0.02 NOK/CHF SEK/USD CHF/USD EUR/USD GBP/USD CHF/JPY JPY/USD GBP/JPY AUD/NZD GBP/CHF NOK/AUD NOK/NZD GBP/NOK Currency Excess Return 0.02 0 −0.02 NOK/CHF CHF/USD SEK/USD EUR/USD CHF/JPY GBP/USD JPY/USD GBP/JPY AUD/NZD GBP/CHF NOK/NZD NOK/AUD GBP/NOK −0.04 −0.06 CHF/AUD CHF/NZD GBP/AUD GBP/NZD −0.04 −0.06 CHF/NZD CHF/AUD GBP/NZD GBP/AUD −0.08 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 Model Risk Premium −0.08 −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 Interest Rate Differential
Table I Calibrated Model Parameters 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 · (rt,t+1 i − rt,t+1). 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 Fixed ξt i Option Set I No HLX and X/USD pairs II Yes (Ψ t = 0) HLX and X/USD pairs III No All pairs (X/Y) IV Yes (Ψ t = 0) All pairs (X/Y) Panel A: Global Factor Loadings, ξ i Specification AUD CAD CHF EUR GBP JPY NOK NZD SEK USD I and II 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) - III and IV 0.84 0.96 1.02 1.00 0.98 1.27 1.00 0.87 0.99 1.00 (0.0046) (0.0044) (0.0050) (0.0049) (0.0047) (0.0062) (0.0050) (0.0049) (0.0051) - 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 II Mean 0.00 0.53 7.13 -0.74 -1.16 6.21 Volatility - 0.18 3.80 0.17 1.29 4.06 III Mean 2.37 0.53 9.98 -0.74 -1.25 5.72 Volatility 2.26 0.20 6.83 0.15 1.73 4.20 IV Mean 0.00 0.53 7.43 -0.75 -1.12 5.30 Volatility - 0.19 3.16 0.14 1.53 3.46 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 II 1.17 1.09 1.34 1.33 1.22 0.89 III 1.55 1.28 1.77 1.85 1.67 1.19 IV 1.60 1.30 1.83 1.92 1.74 1.22
Page 1 and 2: Option-Implied Currency Risk Premia
Page 3 and 4: a closed-form expression for the ge
Page 5 and 6: We conduct a similar analysis for r
Page 7 and 8: the determination of currency risk
Page 9 and 10: Y j t parameter can be interpreted
Page 11 and 12: where S ji t is the currency exchan
Page 13 and 14: where V g t = κ2 L g and S g t =
Page 15 and 16: coupon bond in country i; otherwise
Page 17 and 18: 2 Data and Model Calibration We cal
Page 19 and 20: How does the identification intuiti
Page 21 and 22: account for the fact that the avera
Page 23 and 24: √ δ requires loadings to range f
Page 25 and 26: volatilities (blue) and their fitte
Page 27 and 28: isk premium can be computed on the
Page 29 and 30: 3.2.1 Slope (carry) factor To const
Page 31 and 32: 3.2.2 Short U.S. dollar factor Lust
Page 33 and 34: Figure 7 contrasts the ability of o
Page 35 and 36: in fact, largely orthogonal to fact
Page 37 and 38: etter than under Specification I. T
Page 39 and 40: A Cumulant Generating Functions of
Page 41 and 42: References [1] Ang, A. and J. Chen,
Page 43 and 44: [27] Ghysels, Eric, Pedro Santa-Cla
Page 45 and 46: Figure 2. Cross-Sectional Relation
Page 47 and 48: Figure 4. Returns to Empirical Fact
Page 49: Figure 6. Option-Implied Currency R
Page 53 and 54: Table III Model Short Reference Cur
Page 55 and 56: Table V Option-Implied Currency Ris
Page 57 and 58: Table A.I State-variable Dynamics a
Page 59 and 60: Table A.III Option-Implied Currency

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