SERVING THE QUANTITATIVE FINANCE COMMUNITY

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Topic Author
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

Trying to enter to the previous thread I got an automatic message: This thread has been locked. Posting to this thread is not allowed. That means that it looks better to stop. to Dave: if you want to ask something you need to ask as it usually do. I have not seen that you ever ask a question you know everything so it might be a reason why you forgot how to ask question. You used some numbers that I never wrote and ask me whether this correct. I do not know. If you understand what was written by me the talking about price of the option in continuous time or binomial scheme to write any number does not a price, ie you are always incorrectly interpret what was stated. Do not be lazy if you want to say something related to my point read 1or two pages of simple algebra and i could understand if you will say that a formula ... is incorrect because ... . to cridds01: " but isn't the call worth $33.33, with a risk neutral probability of 1/3?" /// Can you show where you find that?"It could be years before he finds out money actually has a time value"The equation used for call option pricing is C ( t , x ) = 0 for scenarios from { S ( T ) < K } and [ S ( T ) / S ( t ) ]* I { S ( T ) > K } = [ S ( T ) - K ] / C ( t , x )Indeed S ( T ) and k are related to the moment T while S ( t ) but it is a common practice in interest rate definition. On the other hand if you the values S ( T ) , K will replace by B ( t , T )S ( T ) , B ( t , T ) K nothing will be changed in the equations. daveangel Posts: 17031 Joined: October 20th, 2003, 4:05 pm ### option hedging remark* Quote I have not seen that you ever ask a question you know everything so it might be a reason why you forgot how to ask questionsadly, I don't know everything. I wish I did.Quote You used some numbers that I never wrote and ask me whether this correctno I posed a problem, asked you for a price. you were not able to provide one. i made you a two-way in it and you couldn't or wouldn't deal.Quote stated. Do not be lazy if you want to say something related to my point read 1or two pages of simple simple algebra is beyond my competence I am afraid. I am an old bloke who has forgotten more stuff than he can remember. knowledge comes, wisdom lingers ACD Posts: 107 Joined: April 19th, 2004, 8:09 am ### option hedging remark* Last try (I swear, I know that you can get this, I believe in you!):Do you understand the following things:1) What arbitrage is?2) If you can construct a portfolio that replicate the payoff of a derivate in *any* future scenario and this portfolio is unique (i.e. no arbitrage is possible) then the value of the derivative is equal to the value of the portfolio.QuoteOriginally posted by: listThe equation used for call option pricing is C ( t , x ) = 0 for scenarios from { S ( T ) < K } and [ S ( T ) / S ( t ) ]* I { S ( T ) > K } = [ S ( T ) - K ] / C ( t , x )Points I think you should address:1) You have two equations for the present price of the option which are not equal.2) Both equations require knowledge of the future. Which means they cannot be used in the present.3) To say that prices can be derived from this equation the return must match under every scenario not just those where the option expires with a value greater than zero.Can you see the inconsistencies here?Finally the example you were given in previous thread:Assume the following:1) Transaction costs are zero2) We have 2 times t (now) and T (some point in the future when the call expires)3) Interest rates are zero (i.e. there exists a zero coupon bond with the following price, B(t)=B(T)=1, its price in the future is known)4) There exists a stock S with current price 100 (S(t)=100), in the future its value is given by a Bernoulli distribution, at time T it can take value S(T)=200 with probability p or S(T)=50 with probability (1-p). Where p is in (0,1) pick any value you like for p, the rest of us don't need one (note that 0 & 1 are excluded since they permit arbitrage between the stock and the bond).5) There is a European call option available that has strike 100, that is at time T it's value is C(T)=max(S(T)-100,0).6) From (3) & (4) C(T)=100 if S(T)=100 and C(T)=0 if S(T)=50We need to find C(t), please show where the fault in the following line of reasoning is:1) If we purchase 66 2/3 of S at time t and sell 33 1/3 of the bond B at time t then we have spent in total 33 1/3 (66 2/3- 33 1/3 = 33 1/3) which is its present value.2) At time T the bond purchase will still be worth 33 1/3 (interest rate is zero), the stock purchase is worth either 133 1/3 or 33.33 (it has either doubled in value S(T)=200 or halved S(T)=50 respectively).3) The value of our portfolio at time T is either 100 if S(T)=200 (133 1/3 - 33 1/3 = 100) or 0 if S(T)=50 (33 1/3 - 33 1/3 = 0). These are the same values are the payoff of the option.4) No other combination of the stock and bond will replicate the payoff of the options under the assumptions above.5) The present value of the call must therefore equal that of the portfolio at time t giving C(t)=33 1/3If you disagree with any point please point it out and explain why it is incorrect (in the thread, don't point to a paper, just copy and paste if you need to use something from one). Last edited by ACD on August 31st, 2011, 10:00 pm, edited 1 time in total. list Topic Author Posts: 2041 Joined: October 26th, 2005, 2:08 pm ### option hedging remark* QuoteOriginally posted by: ACDLast try (I swear, I know that you can get this, I believe in you!):Do you understand the following things:1) What arbitrage is?The definition of the option price based on : call option price is C ( t , x ) = 0 for scenarios from { S ( T ) < K } and [ S ( T ) / S ( t ) ]* I { S ( T ) > K } = [ S ( T ) - K ] / C ( t , x )excludes arbitrage for each scenario. frolloos Posts: 1621 Joined: September 27th, 2007, 5:29 pm Location: Netherlands ### option hedging remark* oh boy.... have we tried pricing forwards yet? ACD Posts: 107 Joined: April 19th, 2004, 8:09 am ### option hedging remark* QuoteOriginally posted by: listQuoteOriginally posted by: ACDLast try (I swear, I know that you can get this, I believe in you!):Do you understand the following things:1) What arbitrage is?The definition of the option price based on : call option price is C ( t , x ) = 0 for scenarios from { S ( T ) < K } and [ S ( T ) / S ( t ) ]* I { S ( T ) > K } = [ S ( T ) - K ] / C ( t , x )excludes arbitrage for each scenario.Not true, if C(t,x)=0 then I'll buy a call off of you and sell the portfolio of the stock and the bond described below giving me 33 1/3. At expiry my portfolio will replicate the option and their values will cancel each other leaving me with a guaranteed 33 1/3 with no risk.Using the second equation we have: 200 / 100 = 100 / C(t, x) => C(t, x) = 50. I can sell you an option for this and buy my portfolio at 33 1/3 leaving me with 16 2/3, at expiry my portfolio will replicate the option and their values will cancel each other leaving me with a guaranteed 16 2/3 with no risk.Arbitrage demonstrated in both cases... and you haven't demonstrated you know what arbitrage is or addressed which price to use given you don't know what S(T) is and there cannot know if S(T) > K or not. Last edited by ACD on September 1st, 2011, 10:00 pm, edited 1 time in total. TinMan Posts: 613 Joined: September 21st, 2006, 9:42 am ### option hedging remark* QuoteOriginally posted by: frolloos oh boy.... have we tried pricing forwards yet?He's got a paper on his SSRN page, basically forward pricing as you know it is wrong.Be warned though, it's got simple algebra in it, so daveangel can't understand it.But you might have a shot. list Topic Author Posts: 2041 Joined: October 26th, 2005, 2:08 pm ### option hedging remark* With forward the situation is somewhat similar in sense that paying a 'cash-and-carry' price either buyer and seller take risk. For buyer for example the risk is that at the settlement the price of the futures can be higher than the underlying. Given probabilistic distribution this risk can be quantify. All this staff in its spirit very close to estimation parameters of the known distribution in math statistics and it will be very useful in order to comprehend pricing in stochastic environment to refresh or to read estimation of mean and volatility for Gaussian distribution say in Kramer or other math statistics book not in finance. TinMan Posts: 613 Joined: September 21st, 2006, 9:42 am ### option hedging remark* What's your formula for a forward? list Topic Author Posts: 2041 Joined: October 26th, 2005, 2:08 pm ### option hedging remark* QuoteOriginally posted by: TinManWhat's your formula for a forward?In theory, given known distribution of an underlying if I say you pay say$30 for the forward because it cash and carry classical price it will sound professionally if you ask me what is probability that spot price of the underlying will be bellow \$30. It will show that you understand trading. Bad is that there is no Poison, Gaussian, or log Gaussian distributions in the real market. Any magic number that usually consider as a derivatives price is only one component of the formal price. Other characteristic is associated with the risk. For each type of derivative it can be different exposure of the price to risk.

bearish
Posts: 6188
Joined: February 3rd, 2011, 2:19 pm

### option hedging remark*

I am curious as to what it takes to get a thread locked around here, since that seems to be a pretty rare occurrence. But I suspect we are heading down that path again... I went back and looked at your ssrn paper collection and noticed that some of your recent comments are verbatim quotes from your work 5-6 years ago. My take is that you have learned nothing in the mean time. I guess your view is that the world was wrong back then and it is still wrong, so there is no reason for you to change your mind. As a simple-minded finance guy, I can actually understand that you don't want to trust my mathematical abilities, but how about world class mathematicians like Marc Yor, Albert Shiryaev, Jean Jacod, or, for that matter, the guy whose name is on this web site. Are they also idiots? Which is, if you don't understand it, what you are actually claiming.The ideas around replication and arbitrage free pricing are not trivial, which is why Nobel prices and various other accolades have been bestowed upon those who helped sort them out. I can testify that these ideas are also being used in practice, although not always in the exact same form that they appear in text books, which should also not be a surprise.

Hansi
Posts: 3300
Joined: January 25th, 2010, 11:47 am

### option hedging remark*

When you've hit the bottom please, stop digging.

list
Topic Author
Posts: 2041
Joined: October 26th, 2005, 2:08 pm

### option hedging remark*

bearish:world class mathematicians deal with given definitions and models developed in finance.for example for stochastic forward the c-a-c is an estimate of the value at settlement = f ( T , t ) while the price at T is assumed to be stochastic F ( T , omega ). The difference between them defines the risk : for buyer it is P { f ( T , t ) > F ( T , omega ) } and for the seller it is 1 - P { f ( T , t ) > F ( T , omega ) }.With every of mathematicians Marc Yor, Albert Shiryaev, Jean Jacod I communicated before when I was mathematician. Send them this message and ask whether this statement makes sense from mathematical point of view. I think they will respond to you. So it is very simple.At the very beginning I tried to communicate with Shiryev as he was first from former USSR who began publish papers in math finance. My attempts failed because it seems ( I have had a number of explicit examples ) to me that my email did not work properly in one of the sides. I also sent some time ago a paper to Jacod, I think it was about BSE. He received it. I also sent a paper to George Papanicolau. I did not get their responds. They might be did not respond or my email did not deliver it. I sent a week ago my remarks on local volatility to D. Duffle and he received it.

daveangel
Posts: 17031
Joined: October 20th, 2003, 4:05 pm

### option hedging remark*

Quote My attempts failed because it seems ( I have had a number of explicit examples ) to me that my email did not work properly in one of the sides. Quote I also sent some time ago a paper to Jacod, I think it was about BSE. He received it. I also sent a paper to George Papanicolau. I did not get their responds. any pattern emerging ?QuoteI sent a week ago my remarks on local volatility to D. Duffle and he received it. let us know if he responds.
knowledge comes, wisdom lingers

Paul
Posts: 11058
Joined: July 20th, 2001, 3:28 pm

### option hedging remark*

We took the, yes, very unusual for us, step of locking the previous thread because there was a sense of bullying about it. But list does seem quite robust or immune to it, for which I commend him.I believe that list is mostly self taught. I see a lot of confusion about quant finance among the self taught and even with those who have done MFEs. When such people take the CQF it can be quite tough at first getting them to really understand the basics. We usually get therein the end though. And I would relish the challenge of teaching list! And I mean that in a nice way.P

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