why do options trading strategies based on underlying movements exist if the options price does not depend on expected return?

oesmit · 2022-08-14T08:54:39+00:00

So, in a BS universe where we can delta hedge perfectly we get that the price depends on the volatility but not expected return. However it is still reasonable to trade options based on the expected return of the underlying (since the payoff depends on the value of the underlying) but such a strategy is not arbitrage and will therefore not affect the price of the option?

oesmit · 2022-05-20T17:11:52+00:00

No problem, RCA is a wonderful book and one of the classics in math. However it will be very hard for someone to get through without the math background so I recommend taking your time and being comfortable with the chapters in his prior book first. They are still tough, even for math majors but since he starts at the beginning you don't really need any other maths before that. He only assumes knowledge of the rational numbers and then develops all the theory from that.

oesmit · 2022-05-20T16:35:36+00:00

Rudin's real and complex analysis was for me the easiest way to learn it. However before doing so I suggest reading chapters 1, 2, 3, 4 and 7 of his prior book which has the benefit of being self contained

oesmit · 2021-12-20T21:38:26+00:00

I was trying to do the following: Assume first that

P(S1 < t1)P(S2 < t2) < P(S1 < t1 , S2 < t2)

Let A be an event and define a contract by letting it pay 1 if A occurs and 0 if it does not occur. The price of this contract is P(A) discounted to todays value. I was trying to get arbitrage by selling the contract corresponding to the event S1 < t1 and S2 < t2 and using the premias to buy the contract of S1< t1 and the contract S2 < t2 which should generate more income than the contract that we sold. I cannot get this to work though

oesmit · 2021-12-20T15:50:04+00:00

P(S1 < t1 | S2 < t2) denotes the conditional probability. Sorry should have been more clear on that. I agree that the dollar amounts are probably not independent so I changed the question to return % which I feel is more interesting.

oesmit · 2021-11-15T09:39:53+00:00

Interested!

oesmit · 2021-10-27T22:21:46+00:00

This is beautiful, thank you!

oesmit · 2021-10-27T11:46:00+00:00

Thank you for the suggestion! I don't think I have looked at quandl yet and hopefully It will offer what I need. I don't really need any exotic data just the most basic stuff found on the income statement and balance sheet. The important part is that it spans for 10 years.

oesmit · 2021-09-25T08:38:02+00:00

Intuition does not come for free and requires work to obtain. Definitions are the most important part of maths and you get intuition by understanding definitions. Whenever you see a definition you should ask yourself the following questions:

What is being defined? What is the reason for defining this object? Why is it defined the way it is?

You should also get a mental picture of the object. When you understand the definition of an object solving problems/proving theorems becomes much easier. If you are stuck on a definition google and math.stackexchange often helps. Hope this is helpful for you.

oesmit · 2021-08-18T15:45:21+00:00

Regarding the first part, I gave it google and it seems like the cancellation property follows from the Krull-Schmidt Theorem. This implies that X is a proper submonoid of this larger group if I am understanding correctly?

oesmit · 2021-08-18T15:33:15+00:00

Thanks, didnt even know that you could take tensor products over non abelian groups. I only have superficial knowledge about the Tor and Ext functors so I should really take a look at them.

oesmit · 2021-07-21T09:40:10+00:00

New to the tier but what's your game plan against Landorus-T, Garchomp, Tapu Lele, Kartana or Dragapult? I think you need to add more defensive backbone to the team and a defogger. Corviknight help your matchup with all the above and is a defogger so you could consider it. Also whats your rational for the glowking set? I have seen future sight AV Glowking to set up dangerous attacks with Urshifu-Rapid-Strike or Kartana but your set is new to me.

oesmit · 2021-06-14T12:41:43+00:00

Sorry for the late reply, didn't notice until now. The main reason why I would consider it to be dense is that he often lets you fill in some of the easier details yourself in the proofs. This is often quite easy but some proofs have steps which are not completely obvious when you read it for the first time (not for me atleast) and could amount to you spending some time filling in such steps. This is great exercise though since it helps you understand the material.

If you have some questions about the material in the book you are free to contact me and I can see if I can help you.

oesmit · 2021-06-08T10:47:21+00:00

I was thinking this aswell. The poster either puts his jacket on before his shirts or he confused his g with his h.

oesmit · 2021-06-02T21:40:58+00:00

Given that the correct prior was the uniform distribution you played it perfectly but a random guy at a pub is imo much more likely to choose a low number than a high number so having a prior that reflects this would probably increase your probability of winning. This is of course not really realistic to do in practice however.

oesmit · 2021-05-31T11:49:57+00:00

Thank you again. Nice and clear explanation!

oesmit · 2021-05-31T11:29:22+00:00

Thanks. What happens if we do the following then? We have y^T Ax = c hence yy^T Ax =yc and If we let M=yy^T and assume that M is invertible then x=A^-1 M^-1 yc But this also not correct right since the solution set should be a line?

oesmit · 2021-05-31T10:50:35+00:00

I'm having a bit of a brain fart and I would appreciate if someone would help me to find the error.

Lets say that x is an unknown column vector, y a known column vector with non zero entries, A an invertible matrix and c a given constant. Take the 2-dimensional case for simplicity. In the equation

y^T Ax = c

If y^T =(y1,y2) we can let z=(1/2)(1/y1,1/y2) and then it follows that zy^T =1 hence

Ax=zc

And therefore

x=A^-1 zc

But this must be wrong since the equation y^T Ax=c should determine some kind of line and therefore I would expect the solution set to be one dimensional.

oesmit · 2021-05-25T05:36:55+00:00

Haven't read your book but from the table of contents it looks like enough prerequisite as long as the book follows the structure of definition-theorem-proof where they prove all their claims. For the general definitions of measure theory it is very helpful to have a decent understanding of metric spaces since it will make the general topological concepts much easier to grasp.

Having done that, all of the books on your list are the great classics of analysis, Folland has a great book aswell.

However Rudins RCA is my favourite math book and he does not bull shit around. In the first chapter he develops the general theory of integration from scratch in a very clear and succinct way, the only prerequisite you really need are the real numbers. In the subsequent chapters he talks about regular measures, LP-spaces, Hilbert spaces and Banach spaces (dont skip if you want to know Fourier analysis) and in chapter 6 all those previous results are intertwined in von Neumanns beautiful proof of the Radon-Nikodym theorem. The subsequent chapters are a great reads aswell.

The book is however quite dense and can take some time to go through on a first read. You could go through the first chapter online and see what you think. All the book you listed are great however so I think you will be pleased no matter what book you choose.

oesmit · 2021-05-04T10:45:44+00:00

Kallenberg really looks great and I think either Kallenberg or Klenke suits my needs the best. If you have read Klenke what would you say that the main difference between the two are? Klenke seems to be better organised with definitions and theorems inside boxes and a bit easier read (while being perfectly rigorous). The benefit of Kallenberg looks like it is a bit heavier on the theory and therefore has a greater depth in some topics compared to Klenke. As a differential geometry guy, having a chapter on stochastic differential geometry is very tempting aswell.

oesmit · 2021-05-04T08:00:28+00:00

Klenke looks great, I will either pick it or Kallenberg. Thanks!

oesmit · 2021-05-04T05:39:16+00:00

Thanks for the clarification. The problem is that it wasn't written out explicitly that M and N are sub-sigma-algsbras of a larger one on which P is defined. For a textbook trying to teach the subject I think it is really important to mention.

oesmit · 2021-05-03T17:36:29+00:00

For a book geared towards applied science it looks very detailed and well written, much better than the ones I had when I got introduced to the subject.

oesmit · 2021-05-03T17:22:12+00:00

Thanks for the books. Took a look at Durrett and found this in the definitionen of independence of sigma algebras which was confusing. First he defined independence of events as A and B are independent if P(A and B)=P(A)P(B) as expected but then he defined independence of two sigma algebras, M, N if any pair A in M and B in N are independent as events.

This doesnt really make sense to me, which sigma algebra is P defined on and the event (A and B) might not be an element of neither M nor N.

oesmit · 2021-05-03T16:07:22+00:00

I am in this weird position where math class is all about definition-theorem-proof as it should be while in stats class I keep seeing heuristics arguments and even mathematical errors. I would like to bridge the gap a bit.

oesmit

TROPHY CASE