## Jumps, Martingales, and Foreign Exchange Futures Prices

_IMF Working Papers, February 1, 1996_

## Source details

**Canonical URL:** [Jumps, Martingales, and Foreign Exchange Futures Prices](https://www.imf.org/en/publications/wp/issues/2016/12/30/jumps-martingales-and-foreign-exchange-futures-prices-2004)

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## Bibliographic details
- Authors: Zuliu Hu
- Published: February 1, 1996
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781451921649.001

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### Summary
- Author: Zuliu Hu
- Date: February 1, 1996
- Core proposition: The common specification that foreign exchange spot and futures prices follow continuous diffusion processes is questioned by empirical regularities in daily and weekly currency futures data.

### Empirical findings
- Changes in foreign currency futures prices are serially correlated.
- Variance ratio tests and other related tests overwhelmingly reject Samuelson’s martingale hypothesis.
- Foreign exchange futures prices do not appear to have continuous sample paths; evidence suggests the presence of a jump component.

### Implications and consequences
- The presence of jumps can lead to pricing bias when applying the standard Black-Scholes option pricing formula to foreign exchange markets.
- Continuous-diffusion models may be misspecified for daily and weekly currency futures data, necessitating models that incorporate serial correlation and discrete jumps.

### Subjects and keywords
- Subject: Asset prices, Currencies, Exchange rates, Foreign exchange, Futures
- Keywords: futures price, WP

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_Source: https://www.imf.org/en/publications/wp/issues/2016/12/30/jumps-martingales-and-foreign-exchange-futures-prices-2004_