Option Pricing: Why Replicating Portfolio & Risk-Neutral Valuation Converge

Imagine you’re trying to figure out the fair price of an ice cream cone at a beach stand. There are actually a couple of clever ways to approach this, and surprisingly, they both lead you to the same price. In the world of finance, when we talk about pricing options, which are like contracts to buy or sell something in the future, we have similar methods, and two very important ones in the Binomial Model are the replicating portfolio approach and the risk-neutral valuation approach. They might seem like they’re coming at the problem from completely different angles, but they always arrive at the exact same answer, and that’s quite fascinating.

Let’s first think about the replicating portfolio approach. Imagine you want to create your own homemade version of that ice cream cone. You could buy the cone itself, the ice cream, and maybe some sprinkles. The replicating portfolio approach for options works similarly. It says we can create a portfolio, which is just a combination of investments, that perfectly mimics the payoff of an option. In the Binomial Model, we assume the price of an asset, like a stock,