Pricing Formulae for Foreign Exchange Options

Weber, Andreas; Wystup, Uwe

doi:10.1002/9780470061602.eqf06004

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…is applied with reciprocal values for B and S, interest rates exchanged and φ replaced by −φ (see Weber and Wystup [2010] and Wystup [2010]). For quotes under the foreign risk-neutral measure, C-6.…”

Section: A P P E N D I X a Measure Change And Laplace Transformmentioning

confidence: 99%

The Fine Structure of Currency ReturnsImplied in One-Touch Options

Buesser¹

2013

JOD

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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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Section: A P P E N D I X a Measure Change And Laplace Transformmentioning

confidence: 99%

The Fine Structure of Currency ReturnsImplied in One-Touch Options

Buesser¹

2013

JOD

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Pricing Foreign Exchange Options with Stochastic Volatility

Ahlip¹

2014

Wiley StatsRef: Statistics Reference Online

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An exhaustive survey of research on pricing foreign exchange options with stochastic volatility and stochastic interest rates is presented in this article. The article also includes contributions to pricing of currency options with fixed volatility and deterministic interest rates, domestic and foreign, and in a systematic way extend to results obtained for cases which include stochastic volatility and stochastic interest rates. Since the literature in pricing foreign exchange currency option is quite extensive, the article considers some of the more important contributions.

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Pricing Formulae for Foreign Exchange Options

Cited by 2 publications

References 9 publications

The Fine Structure of Currency ReturnsImplied in One-Touch Options

The Fine Structure of Currency ReturnsImplied in One-Touch Options

Pricing Foreign Exchange Options with Stochastic Volatility

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