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IAI Actuarial Core Principles · Economic Modelling · Models of the term structure of interest rates

An insurer calibrates a Vasicek model to historical monthly short-rate data and then uses it to value a long-dated option embedded in a product. Which concern is most relevant about using historical (real-world) calibration for this valuation?

Derivative valuation needs risk-neutral parameters calibrated to current market prices, whereas historical data gives real-world parameters that include a risk premium in the drift. Using historical estimates directly would therefore give valuations inconsistent with the market.

  1. APricing derivatives requires risk-neutral parameters consistent with current market prices, not historical estimatesCorrect
  2. BHistorical data can only estimate volatility, never the mean reversion speed
  3. CVasicek models cannot be calibrated to any data
  4. DRisk-neutral and real-world drifts are always identical, so no concern arises
  5. Option values do not depend on the volatility parameter

Explanation

Market-consistent valuation of derivatives needs a risk-neutral measure calibrated to current market prices. Historical estimates reflect the real-world measure, where the drift includes a risk premium, so the two differ. Historical data can estimate all parameters, and option values rise with volatility.

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