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FRM Part II · FRM Exam Part II · Arbitrage Pricing with Term Structure Models

A desk wants a model that fits today's term structure of volatilities of the short rate as well as today's rate curve. Which approach does this, and what is its trade-off?

Use time-dependent volatility σ(t) calibrated to market volatilities, just as time-dependent drift fits the curve. The trade-off is that the implied future volatility structure is dictated by today's data and may be unrealistic, so the model fits the market but may not forecast well.

  1. AUse constant σ in Ho-Lee; the trade-off is that rates cannot be negative
  2. BUse a time-dependent σ(t) calibrated to market volatilities; the trade-off is that the implied future volatility term structure may be unrealisticCorrect
  3. CUse CIR with constant parameters; the trade-off is that it cannot match any volatility
  4. DUse a zero-volatility model; the trade-off is that drift cannot be calibrated

Explanation

Allowing σ to vary with time lets the model fit an observed volatility term structure, in the same way a time-dependent drift fits the rate curve. The cost is that the calibrated future volatilities are fixed by today's market and may imply unrealistic future volatility behavior. Constant-σ Ho-Lee permits negative rates but that is not the issue asked.

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