CAIA: Binomial pricing

Explanations, applications and practice for binomial pricing.

• Compare actual expectation with a pricing-weighted value

  Avoid applying the risk-free rate to an arbitrary actual-state expectation.

  Worked examples

• Replicate a call with underlying and borrowing

  Match the call’s two expiry amounts and reconcile its current cost.

  Worked examples

• Current cash and terminal cash in a replication

  Keep the borrowing or lending amount on its correct date.

  Concepts

• Clamping an invalid pricing weight to zero or one

  Resolve the model input inconsistency rather than altering the derived weight.

  Common mistakes

• Model claim value and replicating quantity

  Separate a current currency value from an underlying-unit holding.

  Comparisons

• Reporting a weighted expiry amount as current value

  Apply the period discount after forming the pricing-weighted payoff.

  Common mistakes

• Two-state risk-free domain condition

  Check whether the entered state/rate record supports interior pricing weights.

  Concepts

• Assuming equal weights in every binomial model

  Derive the state weight rather than treating two branches as equally priced.

  Common mistakes

• Two-state claim hedge ratio

  Match the claim’s state difference with a holding in the underlying.

  Formulas

• Value a claim with zero payoff in both modeled states

  Distinguish a zero model value from a universal market conclusion.

  Worked examples

• Explain a two-state valuation model in an interview

  Practice a precise explanation of prices, holdings and probability labels.

  Careers

• Value a call in the money in both model states

  Inspect the linear payoff region and its financing leg.

  Worked examples

• A lower binomial state need not be a price decline

  Order terminal states without imposing an unstated return sign.

  Concepts

• Use a negative period rate in a consistent model

  Check the positive factor and state interval before pricing.

  Worked examples

• Check put–call parity inside a two-state model

  Reconcile claim prices with the same period discount factor.

  Worked examples

• Two-state pricing weights and replication practice

  Check quantities, funding dates and model weights with explained choices.

  Practice

• Binomial domain and probability interpretation

  Check the model setup, state support and actual-versus-pricing weights.

  Practice

• Pricing weights and real-world probabilities

  Compare what the numbers are constructed to answer.

  Comparisons

• Risk-neutral weight is not an observed frequency

  Identify where a pricing weight came from before interpreting it.

  Concepts

• Replicate a put with short underlying and cash

  Interpret a negative hedge holding without reversing state labels.

  Worked examples

• Using an annual rate for a shorter binomial period

  Convert the quotation to the exact model interval before pricing.

  Common mistakes

• Inverting the two-state hedge ratio

  Use claim difference per underlying-price difference for replicating units.

  Common mistakes

• Reconcile replication cost and weighted claim value

  Compare two methods using the same state and period assumptions.

  Lessons

• Reconcile terminal repayment and current borrowing

  Trace the funding date in a stock-and-cash claim replica.

  Worked examples
• 

  Two-state replication check sheet

  Reconcile claim and portfolio amounts in both expiry states.

  Templates

• Replicate a claim with underlying and cash

  Solve one holding that matches both supplied expiry amounts.

  Lessons

• Two-state valuation reconciliation checklist

  Review interval consistency, holdings and state matches before accepting a model price.

  Revision

• Binomial-valuation learning sequence

  Build from expiry amounts to replication and pricing interpretation.

  Study plans

• Build a compatible two-state pricing record

  Set current price, expiry states and the period rate before valuing a claim.

  Lessons

• Reconcile two valuation routes for a mixed claim

  Use a general state payment rather than only a vanilla payoff.

  Worked examples
• 

  Two-state pricing input record

  Keep prices, expiry amounts and the rate interval together.

  Templates

• Binomial inputs, rate interval and domain

  Check current versus terminal values and interpret the model’s rejection conditions.

  Tool guides
• 

  One-period binomial option-value calculator

  Inspect a two-state value, replicating holdings and state-by-state match.

  Tools

• Two-state risk-neutral weight and claim value

  Use one period’s growth factor and discount the weighted claim.

  Formulas

• Derive pricing weights from the underlying model

  Match the risk-free-grown current price before weighting a claim.

  Lessons

• Value a two-state claim at a zero period rate

  Keep state weights and discounting even when the factor is one.

  Worked examples