Pricing a Call Option with a One-Step Binomial Tree
Summary
This introduction explains a one-period binomial model for a call option. The underlying asset starts at 100 and can move to either 110 or 90 by the next day; with a strike of 100 and interest rates set to zero, the call pays 10 in the up state and nothing in the down state. From these payoffs, the text bounds the option premium between zero and 10.
It motivates pricing from the seller’s perspective: the writer faces a loss in the up state and must construct a hedge using information available today rather than predict the outcome. The article names hedging, risk-neutral valuation, and replication as three approaches, and says a later discussion will show that the approaches agree in a two-step treatment. This excerpt does not yet derive the hedge, risk-neutral probabilities, or a specific fair price, and its assumptions—two possible outcomes and zero interest—are deliberately simplified.
Key ideas
- The model gives the asset two possible next-period values: 110 or 90 from an initial value of 100.
- A call with strike 100 pays 10 in the up state and zero in the down state.
- With interest ignored, the option premium is bounded between zero and 10.
- Hedging, risk-neutral valuation, and replication are named as pricing approaches, but not derived in this excerpt.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.