Definition
Risk-neutral pricing is a mathematical framework for valuing derivatives without knowing investors' risk preferences. Under the risk-neutral measure, all assets are assumed to grow at the risk-free rate, and probabilities are adjusted (risk-neutral probabilities) so that expected values, when discounted at the risk-free rate, give the correct market price. This elegant approach is the foundation of all modern derivative pricing.
lightbulb Example
To price a call option: instead of estimating the real probability of a stock rising and the appropriate risk premium, risk-neutral pricing assumes the stock grows at the risk-free rate and finds the probability (risk-neutral) that makes the discounted expected payoff equal the option price.
verified_user Key Points
- Foundation of modern derivative pricing
- Assets grow at risk-free rate under risk-neutral measure
- Probabilities are adjusted, not real-world probabilities
- Equivalent to no-arbitrage pricing