Option-Implied Currency Risk Premia

We use cross-sectional information on the prices of G10 currency options to calibrate a non-Gaussian model of pricing kernel dynamics and construct estimates of conditional currency risk premia. We find that the mean historical returns to short dollar and carry factors (HMLFX ) are statistically indistinguishable from their option-implied counterparts, which are free from peso problems. Skewness and higher-order moments of the pricing kernel innovations on average account for only 15% of the HMLFX risk premium in G10 currencies. These results are consistent with the observation that crash-hedged currency carry trades continue to deliver positive excess returns. FIRST DRAFT: MARCH 2013 THIS DRAFT: DECEMBER 2013 ∗Jurek: Bendheim Center for Finance, Princeton University and NBER; [email protected]. Xu: Department of Operations Research and Financial Engineering, Princeton University; [email protected]. We thank John Campbell, Peter Carr, Pierre CollinDufresne, Valentin Haddad, Ian Martin, Peter Ritchken, and seminar participants at Case Western Reserve University, Dartmouth, Georgetown University, Harvard Business School, Princeton University, University of Rochester, the 2 EDHEC-Princeton Institutional Asset Management Conference, and the Princeton-Lausanne Quantitative Finance Workshop for providing valuable comments. USC FBE FINANCE FACULTY RECRUITING FRIDAY, Feb. 21, 2014 10:30 am – 12:00 pm, Room: JKP-104 The absence of arbitrage links the exchange rate between two currencies and the economies’ respective stochastic discount factors. We exploit this link to extract the dynamics of stochastic discount factors from the cross-section of currency options and produce a time series of option-implied currency risk premia. The optionimplied currency risk premia are free of peso problems, and allow us to elucidate the importance of global jump risks in the determination of premia for common risk factors in currency returns. Estimates of currency risk premia are commonly derived by studying the time-series and cross-sectional properties of historical (realized) returns. This paper develops an alternative approach to this question, which does not rely on historical currency returns, but instead uses cross-sectional data on the pricing of exchange rate options. We demonstrate that, even though no single currency option is informative about the expected return of the underlying currency pair, observing a sufficiently broad collection of options on currency cross-rates allows us to deduce the structure of the stochastic discount factors, and therefore the dynamics of currency risk premia.1 In order to operationalize this methodology, we impose a factor structure on the pricing kernel dynamics, which assumes pricing kernels are driven by a combination of common (global) shocks and idiosyncratic (country-specific) shocks, with individual countries differing in their exposure to global shocks.2 Cross-sectional differences in global factor loadings generate variation in option-implied exchange rate distributions, which we exploit to infer the structure of the pricing kernel innovations. We show that currency risk premia can be expressed using the cumulant generating functions of these innovations, similar to Backus, et al. (2011) and Martin (2013), generating a two-factor pricing model for currency returns. The global factor in our model corresponds to the HMLFX risk factor identified by Lustig, et al. (2011) – and is reflected in the returns to currency carry trade strategies – while the second factor represents compensation demanded by investors for being short their own (local) currency. The model of pricing kernel dynamics we calibrate to exchange rate option data can be interpreted as a discretized version of a continuous-time model with time-changed Lévy increments (Carr and Wu (2004)). The global and country-specific pricing kernel innovations in our model are comprised of a Gaussian component and a non-Gaussian component, each of which have time-varying distributions. The non-Gaussian component can intuitively be thought of as capturing the joint effects of intra-period stochastic volatility and jumps (“disaster Our ability to recover risk premia from exchange rate options can be traced back to the fact that option-implied exchange rate distributions reveal the conditional, country-level pricing kernel distributions. It is not an application of the Recovery Theorem (Ross (2013)), and therefore does not rely on its underlying assumptions (e.g. finite-state Markov chains, time-homogenous dynamics, statevariables following bounded diffusions), detailed in Carr and Yu (2012). The presence of asymmetric global factor loadings can be used to rationalize violations of uncovered interest parity (Backus, et al. (2001)), is consistent evidence from historical currency returns (Lustig, et al. (2011), Hassan and Mano (2013)), as well as, evidence from exchange rate option markets (Bakshi, et al. (2008)). Models with imperfect risk-sharing provide a microfoundation for asymmetric global factor loadings (Verdelhan (2010), Ready, Roussanov, and Ward (2013)).