15 questions linked to/from How to estimate real-world probabilities
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### How does the “risk-neutral pricing framework” work?

I've struggled for a long time to understand this - What is this? And how does it affect you? Yes I mean risk neutral pricing - Wilmott Forums was not clear about that.
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### Risk Neutral Probability

I read that an option prices is the expected value of the payout under the risk neutral probability. Intuitively why is the expectation taken with respect to risk neutral as opposed to the actual ...
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### Why aren't econometric models used more in Quant Finance?

There is a big body of literature on econometric models like ARIMA, ARIMAX or VAR. Yet to the best of my knowledge practically nobody is making use of that in Quantitative Finance. Yes, there is a ...
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### Why quants think that the risk-neutral measure should not be used for financial forecasting?

In posts regarding the $\mathbb{P}$ vs $\mathbb{Q}$ debate (see 1, 2, 3 or 4), most answers conclude that historical-based forecast are better suited than risk-neutral models for financial predictions....
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### Interpret simulation results ($P$ and $Q$ measures)

I am struggling in interpreting results of my simulations. I use Monte Carlo algorithm to simulate stock paths and calculate option price. The notation: $r$ is a risk free interest rate, $T$ is time ...
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### Baye's rule for conditional expectations (Proof review)

The Baye's rule for conditional expectations states $$E^Q[X|\mathcal{F}]E^P[f|\mathcal{F}]=E^P[Xf|\mathcal{F}]$$ With $f=dQ/dP$ - thus being the Radon-Nikodyn derivative and $X$ being ...
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### What is the difference between risk neutral probabilities and stochastic discount factor?

My question is regarding the difference between risk neutral probabilities and stochastic discount factor? I am confused as to how are they related?
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### $\mathbb{P}$ vs $\mathbb{Q}$ Probabilities - Transitioning Between Measures

I'd like this question to definitively guide a practitioner to using both $\mathbb{P}$ vs $\mathbb{Q}$ probabilities in trading and research. Let's take only one fact as given: if I have a risk-...
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### Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
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### How to price this basket option?

Underlying assets are three global stock index : Eurostoxx 50, HSI, KOSPI 200 Maturity: 36 months with advanced redemption date in every 6 months if prices of indexes satisfy given conditions at each ...
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### Data Selection for Empirical Pricing Kernel Estimation (Stochastic Discount Factor)

I want to estimate an empirical pricing kernel for an index. Hence, I need to estimate a physical and risk neutral density. For estimating the physical density, only the index data in an observed time ...
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### Relationship between risk-neutral probability and subjective probability

I recently came across a Paper by a paper of Rubinstein and Jackwerth (1997): http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.441.5214&rep=rep1&type=pdf where they assume that you ...
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### How to infer real world measure from risk neutral measure

Assume we have inferred risk neutral density of stock price at time T from option prices. Assume we have obtained a parameterized density p(S). How can we infer real world measure? I know about ...