Based on the theory of static replication of variance swaps we assess the sign and magnitude of variance risk premiums in foreign exchange markets. We find significantly negative risk premiums when realized variance is computed from intraday data with low frequency. As a likely consequence of microstructure effects however, the evidence is ambiguous when realized variance is based on high-frequency data. Common to all estimates, variance risk premiums are highly time-varying and inversely related to the risk-neutral expectation of future variance. When we test whether variance risk premiums can be attributed to classic risk factors or fear of jump risk, we find that conditional premiums remain significantly negative. However, we observe a strong relationship between the size of log variance risk premiums and the VIX, the TED spread and the general shape of the implied volatility function of the corresponding currency pair. Overall, we conclude that there is a separately priced variance risk factor which commands a highly time-varying premium.
is an FX analyst at the Swiss National Bank in Zurich, Switzerland. ralf.buesser@alumni.unisg.chThis article examines the fine structure of risk-neutral currency returns. For this purpose, I specify models comprising pure or time-changed diffusion risk, pure or time-changed jumps, or both. The models are calibrated to vanilla options and subsequently applied to the one-touch option market. Since one-touches are unspanned by a complete set of vanilla options, they lend themselves to a rigorous out-of-sample test.The results suggest that vanilla and onetouch option markets do not generally agree on the fine structure of currency returns: Evidence from the vanilla market favors a complex model with stochastic volatility and jumps, whereas one-touch options imply purely diffusive currency dynamics. This latter finding gives rise to two interpretations: either the high activity in currency markets is best reflected by the infinite variation of a diffusive risk factor, or the result is an artifact of market makers who anchor their quotes to what the pure diffusion Black-Scholes model implies. Notes: USDJPY pricing performance for the various models. The pricing bias (vertical axis) is depicted against the unskewed TV (horizontal axis), with downside and upside one-touch options (crosses) being depicted left and right of the center, respectively. A kernel estimate of the pricing biases is given by the solid line. E X H I B I T 9 Pricing Errors by Moneyness BucketNotes: Pricing errors for the different models grouped by moneyness buckets. n in the far-left column reveals the number of quotes per bucket. The letters U and D refer to upside respectively downside option quotes. The pricing errors are computed as the percentage absolute pricing bias.Notes: Performance comparison of the various models based on the MAPE. The reported MAPE differences for row j and column k reveals whether model j is superior to model k. t-statistics are computed using Newey-West [1987] robust standard errors. * and ** indicate significance at the 5% and 1% confidence level.
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