Skip to content
All library documents

Replicating a Call Option with a One-Step Binomial Portfolio

Article QuantStart
Read the original

Summary

The document introduces replication as a third way to price a call option in a one-step binomial model, alongside hedging and risk-neutral pricing. The central method is to find a portfolio of other traded instruments whose future payoff matches the option in every possible state. If such a portfolio reproduces the option’s payoff, the two positions must have the same value today under the no-arbitrage principle.

The explanation establishes the logic behind replication pricing but stops before showing how to construct the portfolio or calculate its price. It provides no numerical example, parameter estimates, or empirical evidence, and it does not discuss transaction costs or market frictions. Its value is as a concise statement of the payoff-matching argument that supports binomial option pricing.

Key ideas

  • Replication prices an option by matching its payoff with a portfolio of other instruments.
  • The portfolio must reproduce the option’s payoff in every possible future state.
  • No-arbitrage implies that positions with identical future payoffs must have equal values today.
  • The document states the pricing principle but does not work through a portfolio construction or numerical example.

Tags

OptionsDerivatives pricingArbitrage

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.