{
  "title": "Jumps, Martingales, and Foreign Exchange Futures Prices",
  "publication": "IMF Working Papers, February 1, 1996",
  "sourceUrl": "https://www.imf.org/en/publications/wp/issues/2016/12/30/jumps-martingales-and-foreign-exchange-futures-prices-2004",
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  "summary": "A common specification about the behavior of foreign exchange spot and futures prices is that they follow continuous diffusion processes. The empirical regularities uncovered from daily and weekly currency futures data, however, cast doubts on the validity of this model.",
  "sections": [
    {
      "heading": "Summary",
      "content": "- Author: Zuliu Hu\n- Date: February 1, 1996\n- 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."
    },
    {
      "heading": "Empirical findings",
      "content": "- Changes in foreign currency futures prices are serially correlated.\n- Variance ratio tests and other related tests overwhelmingly reject Samuelson’s martingale hypothesis.\n- Foreign exchange futures prices do not appear to have continuous sample paths; evidence suggests the presence of a jump component."
    },
    {
      "heading": "Implications and consequences",
      "content": "- The presence of jumps can lead to pricing bias when applying the standard Black-Scholes option pricing formula to foreign exchange markets.\n- Continuous-diffusion models may be misspecified for daily and weekly currency futures data, necessitating models that incorporate serial correlation and discrete jumps."
    },
    {
      "heading": "Subjects and keywords",
      "content": "- Subject: Asset prices, Currencies, Exchange rates, Foreign exchange, Futures\n- Keywords: futures price, WP\n\n---\n\n\nSource: https://www.imf.org/en/publications/wp/issues/2016/12/30/jumps-martingales-and-foreign-exchange-futures-prices-2004"
    }
  ],
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    "[Markdown version](/en/publications/wp/issues/2016/12/30/jumps-martingales-and-foreign-exchange-futures-prices-2004/index.md)",
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    "Authors: Zuliu Hu",
    "Published: February 1, 1996",
    "Series: IMF Working Papers",
    "DOI: https://doi.org/10.5089/9781451921649.001",
    "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.",
    "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.",
    "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.",
    "Subject: Asset prices, Currencies, Exchange rates, Foreign exchange, Futures",
    "Keywords: futures price, WP"
  ],
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