In option pricing theory, the risk-neutral measure is a measure that allows for the valuation of financial instruments such as options. The risk-neutral measure is obtained by assuming that investors are indifferent to the risk and that the expected rate of return on all assets is equal to the risk-free rate of return.
Under the risk-neutral measure, the price of an option is its expected future payoff discounted to the present using the risk-free rate. The risk-neutral measure is widely used in financial mathematics and allows for the valuation of a wide range of financial derivatives, including options, futures, and other complex financial instruments. It is important to note, however, that the risk-neutral measure is a theoretical concept and does not necessarily reflect the actual risk preferences of market participants.
Reference [1] developed a market factor-based option pricing model using the business-cycle CAPM. It allows for the evaluation of options traversing between the risky and risk-neutral probability measures. The authors pointed out,
The business-cycle CAPM transforms the measure of the risky output variable to the risk-neutral predicted values. Therefore, it accomplishes option pricing through rational expectations and martingale. Martingale suggests the possibility of an arbitrage-free hedging strategy. The option pricing process demonstrates the stochastic discount factor pricing model straddling between factor and stochastic expectation pricing models. The business-cycle CAPM assumes liquidity and credit risks due to asymmetric information. The volatility of the risk-neutral predicted values shows jumps. Therefore, we are dealing with options data of market incompleteness. Consistent with the risk-neutral probability of the predicted values, we develop the underlying stock distribution around the market stock price using its market information of volatility and kurtosis. For LinearReg, the risk-neutral regression finds the hedging parameters of the delta-hedge stock-money portfolio with the regression mean equal to the market option price.
This is another interesting article that attempts to go beyond risk-neutral pricing.
Let us know what you think in the comments below or in the discussion forum.
References
[1] Tse, Wai Man, Factor-Based Option Pricing with Perfect Dynamic Delta Hedge (2023). https://ssrn.com/abstract=4149481
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