Replication Portfolios and Assumptions in Binomial Option Pricing

Summary

The document raises foundational questions about pricing a call or put in a two-state binomial model. The method described is replication: combine positions whose payoffs match the option's payoff in each possible future state, then infer the option value from the replicating portfolio. The question asks why the standard portfolio uses the underlying asset and a risk-free bond, whether other portfolios could serve, and whether the assumption of borrowing or lending at a risk-free rate is realistic.

Key ideas

• A two-state option can be valued by matching its payoffs with a replicating portfolio.
• The document asks why replication typically combines the underlying asset with a risk-free bond.
• The assumed ability to borrow or lend at a risk-free rate is identified as a practical concern.
• The document asks whether the setup applies specifically to European options.

Tags

# Replication Portfolios and Binomial Option Pricing


# Replication Portfolios and Binomial Option Pricing












To price a call/put option with two possible future states of the world, I understand we can price the option by essentially calculating the price of a replicating portfolio that gives the same returns in either state of the world. However:

1) Why do we always consider a portfolio with the underlying asset and risk-free bonds? Could we consider other portfolios and price accordingly?

2) The model assumes the agent can borrow/lend at a risk-free rate. Is that plausible?

3) I'm assuming these are European options, is that correct?

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