Risk-neutral probabilities (FRM T5-07)

[@shree4403]

The best explanation I've encountered for risk neutral probabilities definition. To summarize in my own words :- Risk neutral probabilities are the implied probabilities, when the market price of your instrument, equals the expected payoff

[@bionicturtle]

Thank you very much, it's a hard idea so I am thrilled you like it. And your summary is EXCELLENT, can i just add a single word (discounted): "Risk neutral probabilities are the implied probabilities, when the market price of your instrument, equals the discounted expected payoff" .... of course you already get that, as the price implies current/discounted. Thank you!

[@kathirkamanathan7407]

@@bionicturtle Great explanation. I was just thinking it should be called Implied Probability, and immediately thereafter saw your comment. Wonder why they had to use a difficult term - evaded my understanding for a long time.

[@syphiliticpangloss]

This is basically wrong. What is the probability distribution when you have one price? Probability distribution is a monontonic function. Nonsense explanation I see a lot. See transformation of random variables is what to look at.

[@shree4403]

@@syphiliticpangloss I was like you in my very early learning stages of probability theory, but you'll eventually get it if you spend enough time and effort. Btw - PDFs are not always monotonic (e.g Normal dist's PDF for x between -Inf to 0, it is increasing and 0 and Inf, it is decreasing) and CDFs are monotonic (Every CDF has to be monotonically increasing as PDF's values are always greater than zero). Further more, here you are dealing with stochastic processes, i.e a set of random variables and not just one random variable. So things are a little more complicated here. Performing operations like addition, etc. on a set of random variables, i.e., on a stochastic process is very different from adding states of a random variable.

[@syphiliticpangloss]

@shreejyot no you are not understanding but you are illustrating point that these kind of explanations mislead and confuse. They are not *wrong* per se, but the context is limited and they don't extrapolate to the general problem which is actually simpler that this special case. First, by "prob dist" I mean CDF, not PDF. The infintessimal generator of certain kinds of stochastic process can probably be determined by a single data point (price). But that is not at all what these kinds of demos are saying. If you have one price, you 100% can not determine the probability distribution in general. See en.wikipedia.org/wiki/Probability_density_function section on Function of random variables and change of variables in the probability density function for instance. So trick is to write down the price as an expectation of a payoff. This is a functional of the probability distribution. How are you going so solve for this using one price? If you have many prices across a set of payoff functions (i.e. options) you can start to do something. You can assume paramtric forms for the probability distribution and this can make some sense in the infinitessimal limit under some conditions. But that is academic.

[@mohammedsaeed7241]

The risk-neutral probs are derived from the market price, and the discount rate is used to derive them is the RISK-FREE rate. Thank you this was very informative.

[@michalcertik249]

Working for over 10 years in quantitative finance, this is so far the best explanation on real-world vs risk-neutral pricing.

[@excelisfun]

You make such great videos! Thanks, Bionic Turtle!!!

[@bionicturtle]

Thank you, support from a genuine KZbin legend is deeply appreciated!

[@SzTz100]

Hay the Bionic man, great to see you are still around.

[@moquant]

Great work!

[@investwithvincent6329]

7:15 It is at this point do i say that reminds me of the blackscholes model because of the concept of implied discount rate being incorporated in this example

[@jiqi353]

Thank you! It is an intuitive way to understand risk neutral probability finally

[@AugustNocturne]

Thank you for your explanation for a hard concept!

[@d0718]

Knew how to calculate and work with risk neutral probabilities but now I actually finally understand what it means :D thank you

[@bionicturtle]

You're welcome! Glad that we could help :)

[@investwithvincent6329]

20:17 I see two different discounted prices 1.46 and .58 .... From my understanding these two prices create a no arbritrage opportunity. How would an investor explore this opportunity?

[@joesgenericbar]

I wish I could understand your language better. It is not your fault - it is mine. I am mathematically trained but not economically or financially. Some of the words and phrases you use to describe a term or an equation throw me but I will try to learn more about this economic/financial language. Great video though since I can understand a lot of this which explains debt market activity and demystifies what "expectations" means. Also, as I consume this kind of material it becomes foundationaly clear that human emotion and mom and pop are not market drivers but suckers in the debt markets. And another thing. Although many pundits swear that the central banks do not have the power to set interest rates, this kind of information shows that they absolutely do and are doing it every second. Their close competition would be the hedge fund people who are using the same formulations to pursue CB policy to "front run" the market, then followed by the pension funds and the others. This was a great video for me.

[@kathirkamanathan7407]

In the bond pricing example, the 1 year risk free rate is available (=5.15%) from the curve. So why should we try to estimate it from the 6-month risk free rate (=5%)?

[@mayoorbhatt2549]

Best explain by you🇮🇳🙏🇮🇳🙏🇮🇳🙏👌

[@Silvertestrun]

Ty

[@sakuranooka]

Why bother with RN probabilities if we could instead use a risk-adapted discount rate (eg 16.3%) together with the real-world probs?

[@syphiliticpangloss]

Please always explain risk neutral properly in terms of transformations of probability distributions. It is not possible to determing the Q from a single observation. The Q is determined from P *and* a transformation function (utility). So under some conditions you can write E_P(f(X)) as E_Q(X) where Q is the f-transformed probability distribution. If f is linear it is called risk-neutral. Please correct me if anything I am saying is wrong. All of the examples with binary events are nice but they are just confusing people or tricking people into thinking they understand something.