Risk-neutral probability

The probability of an up move that makes the expected return equal the risk-free rate, used to weight payoffs before discounting at that rate. A computational device, not a forecast.

Where you will meet it

Risk-neutral probability appears in 4 learning outcomes on the CFA syllabus. A few of them:

• Price an option with a single-period binomial model
  CFA Level I · Derivatives

  “Equivalently, the option can be valued by taking the expected payoff under risk-neutral probabilities and discounting at the risk-free rate.”

• Explain the binomial model for valuing options and what each of its terms means
  CFA Level II · Derivatives and Risk Management

  “Equivalently, use the risk-neutral probability π = (1 + r − d) ÷ (u − d) and discount the probability-weighted payoffs at r.”

• Explain replication and valuation under risk neutrality
  CFA Level I · Derivatives

  “It is a computational device: the risk-neutral probabilities are the weights under which the underlying's expected return equals the risk-free rate, and using them lets the expected payoff be discounted at that rate instead of at an unknown risk-adjusted rate.”

• Explain how a European option's value can be viewed as its expected payoff at expiry discounted to today
  CFA Level II · Derivatives and Risk Management

  “A European option is worth its expected payoff at expiry, taken with risk-neutral probabilities and discounted at the risk-free rate.”

See also

Risk-free rate

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

All terms beginning with R · Glossary