Skip to content

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

In a one-period binomial interest rate tree, a risk analyst states that the risk-neutral probability of an up move is 0.5 although the true (real-world) probability is believed to be 0.7. Which statement best explains why the pricing model uses 0.5?

The risk-neutral probability is set so that discounting expected payoffs at the risk-free rate reproduces observed prices and prevents arbitrage. It implicitly includes risk premia, so it differs from the real-world probability and is not a forecast of actual outcomes.

  1. AThe risk-neutral probability is chosen so that discounted expected values under it match prices that rule out arbitrage, embedding the risk premiumCorrect
  2. BThe risk-neutral probability is the analyst's best forecast of the actual frequency of up moves
  3. CThe risk-neutral probability removes interest rate volatility from the model
  4. DThe risk-neutral probability is always 0.5 when the tree is recombining

Explanation

Risk-neutral probabilities are those that make traded securities' prices equal to discounted expected payoffs, ensuring no arbitrage. They absorb risk premia and are not forecasts of real-world frequencies. Recombination does not force 0.5 and volatility is not removed.

Did you get it right without looking?

One question tells you little. A timed set on Arbitrage Pricing with Term Structure Models shows your real accuracy, how long you take and where you lose marks.

Practise Arbitrage Pricing with Term Structure ModelsFree diagnostic mock

More Arbitrage Pricing with Term Structure Models questions