Simplified: Change of Probability Measure, and Risk Neutral Valuation

Рет қаралды 13,823

3 жыл бұрын

Using a discrete state space, roulette!, explains the concept of change of probability measure, and various related concepts such as Risk neutral valuation, stochastic discount factor, and Radon Nikodym derivative.

Пікірлер: 31

@markclintworth6134 3 жыл бұрын

SIr, your ability to explain such concepts, in such a beautifully intuitive manner, to a rather slow retired Banker (e.g. 3 year old child) is something to behold! Thank you (my happy hour today will be a little happier).

@JaGWiREE 3 жыл бұрын

Very nice, best intuitive explanation of a quintessential math finance topic..

@quantpie 3 жыл бұрын

Thanks Brian!!

@jarthur8428 Жыл бұрын

ok... just for the record. You are amaizing explaining things!!! Thanks!

@statisticsplaybook 3 жыл бұрын

This channel is like a hidden gem. xD

@quantpie 3 жыл бұрын

Thanks for the kind words!!

@cheguevera9177 3 жыл бұрын

This channel is god sent.

@quantpie 3 жыл бұрын

Thank you! Glad you found to useful!

@OscarMartinez-cf1hq 2 жыл бұрын

Thank you very much, you deserve more views!!!

@djsocialanxiety1664 3 жыл бұрын

stunning explanation

@quantpie 3 жыл бұрын

Many thanks!!

@zhichen2288 Жыл бұрын

Thank you for your explanation, it is very intuitive to understand the logic. Can I ask one question? At time 20:32, what is the meaning of x0, x1, ... here? Is my following understanding correct? For example, if I bet 1$ on the green, if I win, I will get 4$. But right now I can get extra some money, so I may get 4$ plus say 10$ = 14$. Now I standardize the price, it will be 1/14, which means I pay 1/14$ on green and if the green comes, I get 1$. So the 1/14 = 1/5*x0.

@siddharthsubramanian171 3 жыл бұрын

Fantastic !!! Keep posting more videos

@quantpie 3 жыл бұрын

thank you!! Very kind of you!

@arjaninabil7328 3 жыл бұрын

Thank you ❤️

@quantpie 3 жыл бұрын

Many thanks!!

@edosaodigie1058 3 жыл бұрын

Wow this channel is Just Fantastic

@quantpie 3 жыл бұрын

many many thanks!!

@vatsal9387 3 жыл бұрын

Amazing.

@quantpie 3 жыл бұрын

Thank you!!

@michelebellipanni2373 2 жыл бұрын

What's your accademic background ? This video-lessons are just brillant .

@MegaEliots 3 жыл бұрын

I think that it makes sense that m_i =D z_i. Mathematically we have the definition of the r-n derivative: z_i = q_i/p_i the definition of state price per unit probability m_i = v_i/p_i and we have obtained the risk neutral probabilities q_i=v_i/D Intuitively it makes sense that the state price per unit probability is equal to the q probability per unit probability (z) multiplied by the price of a unit of q probability, which is by definition D. It also makes sense that if we take an expectation value, because E[z]=1, we would have E[m]=D. So the average state price of a unit probability is the value of a risk free dollar return. Is this correct?

@quantpie 3 жыл бұрын

Many thanks for the detailed explanation! The risk free asset is traditionally defined slightly differently (though not massively differently!) as the asset that pays the same amount in all future states. The return on this asset (with payoff of 1, and current price) is then the risk free return.

@xmaranxx 3 жыл бұрын

Thanks! how do you make the animations?

@quantpie 3 жыл бұрын

soz a bit basic, but improving over time! We don't use any fancy softwares, just plain animation, you shall see when we go backstage at some point!

@davide467 3 жыл бұрын

Gold piece

@quantpie 3 жыл бұрын

Thanks! Glad it was useful!

@koenzhu8473 3 жыл бұрын

mi/D=vi/(pi*D)=(vi/D)/pi=qi/pi=Zi, So we can get mi=D*Zi these videos are amazing thank you very much. While I get confused about that risk free security idea in Casino example, if I bid 31/30 money by vi weights in each category, the money I get back should times the Pay odds right? For example, the green wins, 4* 1/5 is not equal to 1. Can you please help me with that confusion?

@Maisbrot47 2 жыл бұрын

this is probably too late for you but maybe it helps somebody else. 4:1 betting odds actually mean you get payed 5$ in case you win and nothing in case you lose. So 5 * 1/5 = 1. So the price to get 1$ if green comes is 1/5$. If you add those prices for every number (0,1,2,3,4,5,6) you get 31/30$. For a payment of 31/30$ you get 1$ for sure, because 1 of your bets will hit.