Simplified: Change of Probability Measure, and Risk Neutral Valuation
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- čas přidán 23. 09. 2020
- 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.
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).
Very nice, best intuitive explanation of a quintessential math finance topic..
Thanks Brian!!
This channel is like a hidden gem. xD
Thanks for the kind words!!
This channel is god sent.
Thank you! Glad you found to useful!
ok... just for the record. You are amaizing explaining things!!! Thanks!
Thank you very much, you deserve more views!!!
stunning explanation
Many thanks!!
Fantastic !!! Keep posting more videos
thank you!! Very kind of you!
Wow this channel is Just Fantastic
many many thanks!!
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.
What's your accademic background ? This video-lessons are just brillant .
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?
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.
Thank you ❤️
Many thanks!!
Amazing.
Thank you!!
Thanks! how do you make the animations?
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!
Finally I have a good excuse to get rid of my maths books which only cause confusion.
Thanks Cong!! Nah won’t throw them away, books are precious- but I know what you mean- good books are like gems, so hard to find!!
Gold piece
Thanks! Glad it was useful!
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?
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.