Pricing a Vanilla Call with a Two-State Binomial Model

Summary

This introduction presents a one-period binomial model for a vanilla call option. It starts with an asset priced at 100 today that can move to either 110 or 90 tomorrow, and a call with strike 100. With interest rates temporarily set to zero, the payoff is 10 in the up state and zero in the down state, so the call’s value must fall between those payoffs.

The central problem is to price and hedge the seller’s exposure using information available today, without knowing which state will occur. The article previews three equivalent approaches—hedging, risk-neutral valuation, and replication—and says they produce the same option price in this two-state setting. This excerpt does not carry out those derivations or provide a numerical option price. Its assumptions are deliberately simplified: one time step, two possible asset values, no interest, and a basic call payoff; later extensions would be needed for a more realistic model.

Key ideas

• The one-period model allows the underlying asset to finish in either an up or down state.
• The call payoff is positive only in the up state when the asset exceeds the strike.
• The option seller seeks a hedge based on current information rather than a prediction of the future state.
• Hedging, risk-neutral valuation, and replication are presented as equivalent pricing routes in this model.
• The example ignores interest rates and uses only two possible future prices.

Tags

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