Risk-Neutral Probabilitiy: Intuitive explanation?

[stochastix]

https://www.investopedia.com/terms/r/risk-neutral-probabilities.asp

its basically, so to find an 'objective' price ?

Special Considerations
RIsk neutral is a term that describes an investor’s appetite for risk. Risk neutral investors are not concerned with the risk of an investment. However, risk-averse investors have a greater fear of losing money,


The term risk-neutral can sometimes be misleading because some people may assume it means that the investors are neutral, unconcerned or unaware of risk, or that the investment itself has no risk or has a risk that can somehow be eliminated. However, risk-neutral doesn’t necessarily imply that the investor is unaware of the risk; instead, it implies the investor understands the risks but it isn’t factoring it into their decision at the moment.

The investor prefers to focus on the potential gain of the investment instead. When faced with two investment options, an investor who is risk-neutral would solely consider the gains of each investment, while, for whatever reason, choosing to overlook the risk potential even though they may be aware of the inherent risk.

Why would we do this?

Understanding Risk-Neutral Probabilities
Risk-neutral probabilities are used to try to determine objective fair prices for an asset or financial instrument. You are assessing the probability with the risk taken out of the equation, so it doesn’t play a factor in the anticipated outcome.


By contrast, if you tried to estimate the anticipated value of that particular stock based on how likely it is to go up or down, considering unique factors or market conditions that influence that specific asset, you would be including risk into the equation and thus would be looking at real or physical probability.


The benefit of this risk-neutral pricing approach is that once the risk-neutral probabilities are calculated, they can be used to price every asset based on its expected payoff. These theoretical risk-neutral probabilities differ from actual real-world probabilities, which are sometimes also referred to as physical probabilities. If real-world probabilities were used, expected values of each security would need to be adjusted for its individual risk profile.

Benefits Risk-Neutral Probabilities
Implementing risk-neutral probability in equations when calculating pricing for fixed-income financial instruments is useful. This is because you are able to price a security at its trade price when employing the risk-neutral measure. A key assumption in computing risk-neutral probabilities is the absence of arbitrage. The concept of risk-neutral probabilities is widely used in pricing derivatives.

 

[traderking007]

theoretical are based on a normal distribution and sorry the market is far from normal.
If you pull out a a time analysis of a bell curve you will see that there is correlation between every 1st and second time slice price but the third will have nothing in common or will have a correlation of 0 with the first and this is why theoretical everything must be tweaked all the time to try and best GUESS prices.

none of this will predict with much accuracy over a long time frame but may give you a clue but by the time you take out slippage and fees the relationship and the contracts or shares are gone to the middleman the hft. this is who controls this stuff in microseconds of correlation.

still fun to learn about. it is pretty fascinting when you really start to dig into
auto regressvie etc and the math is not that difficult once you take the time to understand it but i dont think it will help your trading.

 

[Aquarians]

Sweet mother of Jesus that's a lot of words for "intuitive".

Actually the math behind risk neutral is very simple. The purpose is to replicate the price of an option by trading in the underlier. So you can make money by buying cheap replica and selling expensive option. Or vice versa. And thing is you can only do that using the risk neutral probably, not the true (market) probability.

 

[traderking007]

sharpe capm
weiner filters

Auto
Regressive
Moving
A average

and then you can get into it deep with time series because thats the problem with all of it time. HFT tries to stop time by slicing it into as small as possible but it still never stops moving even with the quantum computer at negative what 186 or kelvin or something it still moves or maybe it doesnt and thats where they went with it freeze it if you have too to model it
but even then after all of theat its a best guess with solid determination though
hve a great night

 

[stochastix]

theoretical are based on a normal distribution and sorry the market is far from normal.
If you pull out a a time analysis of a bell curve you will see that there is correlation between every 1st and second time slice price but the third will have nothing in common or will have a correlation of 0 with the first and this is why theoretical everything must be tweaked all the time to try and best GUESS prices.

none of this will predict with much accuracy over a long time frame but may give you a clue but by the time you take out slippage and fees the relationship and the contracts or shares are gone to the middleman the hft. this is who controls this stuff in microseconds of correlation.

still fun to learn about. it is pretty fascinting when you really start to dig into
auto regressvie etc and the math is not that difficult once you take the time to understand it but i dont think it will help your trading.

I dunno, your telling me the entire derivatives industry doesnt really exist, and its all a bunch of traders just winging it?
Just the other day I calibrated a stochastic volatility model and calculated the payoff odds of a spread position I entered, and got the same percentage as the percentage calculated from the implied volatility shown by my brokers software.. it was pretty good feeling to have independent model confirmation

 

[.sigma]

I dunno, your telling me the entire derivatives industry doesnt really exist, and its all a bunch of traders just winging it?
Just the other day I calibrated a stochastic volatility model and calculated the payoff odds of a spread position I entered, and got the same percentage as the percentage calculated from the implied volatility shown by my brokers software.. it was pretty good feeling to have independent model confirmation

very nice man, so my question would be, if your model didn't "confirm", would your model be "wrong" or your brokers numbers "wrong"?

 

[Option_Attack]

Heh, he said "weiner filters."

sharpe capm
weiner filters

 

[stochastix]

theoretical are based on a normal distribution and sorry the market is far from normal.
If you pull out a a time analysis of a bell curve you will see that there is correlation between every 1st and second time slice price but the third will have nothing in common or will have a correlation of 0 with the first and this is why theoretical everything must be tweaked all the time to try and best GUESS prices.

none of this will predict with much accuracy over a long time frame but may give you a clue but by the time you take out slippage and fees the relationship and the contracts or shares are gone to the middleman the hft. this is who controls this stuff in microseconds of correlation.

still fun to learn about. it is pretty fascinting when you really start to dig into
auto regressvie etc and the math is not that difficult once you take the time to understand it but i dont think it will help your trading.

You have no idea what you are talking about. Risk neutral densities do not imply gaussian distributions

 

[traderking007]

im not even about to refute what you said because it speaks for itself do you have any math background what so ever ?

 

[stochastix]

im not even about to refute what you said because it speaks for itself do you have any math background what so ever ?

LMAO. Actually, yes, i've self-published papers and been referenced by major academics in the field.

heres the definition of risk-neutral density:

The risk-neutral density function for an underlying security is a probability density function for which the current price of the security is equal to the discounted expectation of its future prices.

Notice that it says "a probability density function". NOT. A "a Gaussian probability density function".

You know there are other pricing models besides Black-Scholes right?

Oh yeah,. https://pat-laub.github.io/pdfs/honours_thesis.pdf , that guy cited me, "This direct approach is computationally infeasible as the first term’s double sum-mation impliesO(k2)complexity. Fortunately the similar structure of the innersummations allowslto be computed withO(k)complexity (Ogata 1978, Crowley2013)"