Risk-Neutral Measure
A risk-neutral measure is a probability measure used in financial mathematics where all investors are assumed to be indifferent to risk. Under this framework, the expected return on all assets is equal to the risk-free rate, and the actual probabilities of various outcomes are replaced by risk-neutral probabilities. This measure is commonly used in pricing derivatives, such as options, where the price of an asset is calculated based on the assumption that investors require no extra compensation for taking on risk.
Example
In option pricing models like the Black-Scholes model, the risk-neutral measure is used to calculate the present value of expected future payoffs, assuming the asset grows at the risk-free rate.
Key points
• A probability measure where all investors are indifferent to risk, expecting returns equal to the risk-free rate.
• Used in pricing derivatives and financial models like the Black-Scholes model.
• Assumes no risk premium, simplifying the calculation of asset prices under uncertainty.
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