Risk-Neutral and Real-World Measures for Stock and Option Decisions
Summary
The document asks whether a stock forecast based on real-world return probabilities can support decisions among owning shares, buying protective puts, or substituting calls, and what risk-neutral pricing adds. Its proposed real-world model extrapolates historical prices with stochastic volatility features, then adjusts forecasts using company financial analysis; it deliberately leaves current option-implied volatility out of the forecast. The author suggests comparing approaches by long-run portfolio log growth or a lower-tail log-return quantile, including when rebalancing is infrequent.
The discussion is a question rather than an answer, so it supplies no empirical comparison or demonstrated advantage for either measure. It highlights that Monte Carlo can simulate scenarios under either approach, while raising the possibility that risk-neutral methods may aid pricing or yield closed-form results. It does not resolve how to translate between pricing probabilities and real-world forecasts, how to model option prices consistently, or how to account for estimation error and trading costs. The proposed growth criteria are evaluation ideas, not validated recommendations.
Key ideas
- The document contrasts real-world return forecasting with risk-neutral option valuation.
- It proposes using historical price behavior and company financials to build a real-world stock forecast.
- It asks whether risk-neutral modeling offers practical benefits beyond numerical scenario simulation.
- It suggests long-horizon log growth or a lower-tail log-return quantile as possible comparison criteria.
- It raises infrequent portfolio rebalancing as a robustness consideration.
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Full text
# What are practical benefits of Risk Neutral Measure?
# What are practical benefits of Risk Neutral Measure?
Suppose we use real probabilities to predict the annual returns for stock (as the probability distribution of log returns for the $t=+365$ day).
And based on that prediction decide if a) buy the stock or b) buy the stock and protect it with put option or c) buy call option instead of stock, to limit exposure. (Option Prices calculated as simulation of Option Payoff over predicted Stock Price Distribution).
Can you please explain, what will be the benefits if the Risk Neutral Measure would be used instead of the real probabilities?
I can't figure out how using the Risk Neutral approach when we split the model in two parts a) modelling the risk neutral prices b) converting risk neutral prices back to real prices. But how and why is it be better than the direct approach with real probabilities.
The Explainability and Various Scenarios Simulations - seems again, both approaches are even, all the charts and scenarios could be modelled numerically, with Monte Carlo (we won't get symbolic closed form, though, this may be the benefit of Risk Neutrality?).
P.S.
The Real Probabilities Model works as:
- The baseline is historical prices predicted into the future (random walk with accounting for recent volatility, mean volatility reversion and random volatility jumps)
- Baseline prediction then adjusted, based on company's financials analysis.
- The Current Option Prices (Implied Volatility) are not used in the prediction.
UPDATE
The measure of a better approach (real probabilities vs risk neutral) - the Kelly Criterion, optimising the average portfolio growth ratio - mean of annual portfolio log returns $\frac{1}{T} \sum_{i=1}^{T} log(r_i)$ over the interval 3-15 years. Or, maybe a bit safer, optimising some lower quantile say $Q_{0.1}( log(r_i))$.
And ideally should also be robust to slow trading, when portfolio rebalanced only a couple times a week / month.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.