SERVING THE QUANTITATIVE FINANCE COMMUNITY

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

### option hedging remarks

some time ago we discussed here the option dynamic hedging in its classical form. I have submitted first part of my vision of the problem on 2.5 pages in http://papers.ssrn.com/sol3/papers.cfm? ... d=1918014I will appreciate any remark.

frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### option hedging remarks

i tried to understand your paper and came to the conclusion that i think you need to go back to the definition & concepts of self-financing strategy and no arbitrage.
Last edited by frolloos on August 26th, 2011, 10:00 pm, edited 1 time in total.

frenchX
Posts: 5911
Joined: March 29th, 2010, 6:54 pm

### option hedging remarks

The Delta is an amount which is kept constant between t and t+delta_t so your formula is wrong. have a look herehttp://www.ederman.com/new/docs/smile-lecture2.pdfand at the book of Paul.
Last edited by frenchX on August 26th, 2011, 10:00 pm, edited 1 time in total.

frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### option hedging remarks

QuoteOriginally posted by: frenchXThe Delta is an amount which is kept constant between t and t+delta_t so your formula is wrong.what happens is that change in delta*(S+dS) = - change in bond holding*(B+dB).
Last edited by frolloos on August 26th, 2011, 10:00 pm, edited 1 time in total.

frenchX
Posts: 5911
Joined: March 29th, 2010, 6:54 pm

### option hedging remarks

Yes I agree but in his formula he differentiated the delta d(Delta*S)=d(Delta)*S+Delta*dS (which is wrong dP is simply df-delta*dS for the portfolio change)that's why I put my "constant delta remark". The best if he wants to understand is that he studies discrete delta hedging and put the time step towards zero.
Last edited by frenchX on August 26th, 2011, 10:00 pm, edited 1 time in total.

TinMan
Posts: 613
Joined: September 21st, 2006, 9:42 am

### option hedging remarks

Dear oh dear.

frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### option hedging remarks

and the frustration is?

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

### option hedging remarks

My point relates not to pricing but for elementary calculus. We have a functionP ( t , S ) = f ( t , S ) + g ( t , S ) S where g is the partial derivative f in S.We consider difference P ( t + h , S ( t + h )) - P ( t , S ( t )) . There are two answers. 1st = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) - S ( t ) ] g ( t , S ( t )) 2nd = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) g ( t + h , S ( t + h ) ) - S ( t ) g ( t , S ( t )) ] 1st answer is from the book2nd answer is that it seems to be correct?

TinMan
Posts: 613
Joined: September 21st, 2006, 9:42 am

### option hedging remarks

QuoteOriginally posted by: frolloos and the frustration is?Oh just the same old same old.Last week the binomial model was 'wrong', this week the BS equation is 'wrong'.

frolloos
Posts: 1621
Joined: September 27th, 2007, 5:29 pm
Location: Netherlands

### option hedging remarks

have to give it to him, it's very gutsy to 'publish' on SSRN a 'critique' of the very foundations of contingent claims pricing...@list: either you're visionary, or, more likely, i think you are still struggling somewhat with the foundations (as I am). there are good books around and it's worth re-reading books and experimenting in excel.

bearish
Posts: 5984
Joined: February 3rd, 2011, 2:19 pm

### option hedging remarks

I think your problem may be exactly that. The derivation of the Black-Scholes equation and its dozens (hundreds?) of generalizations, all of which according to you are wrong, is not a matter of "elementary calculus". On a separate note, why, in 2011, do you produce documents that look like they were written on an IBM Selectric?

TinMan
Posts: 613
Joined: September 21st, 2006, 9:42 am

### option hedging remarks

QuoteOriginally posted by: frolloos @list: either you're visionary, or, more likely, i think you are still struggling somewhat with the foundations (as I am). there are good books around and it's worth re-reading books and experimenting in excel.I know which one I think it is.

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

### option hedging remarks

QuoteOriginally posted by: listMy point relates not to pricing but for elementary calculus. We have a functionP ( t , S ) = f ( t , S ) + g ( t , S ) S where g is the partial derivative f in S.We consider difference P ( t + h , S ( t + h )) - P ( t , S ( t )) . There are two answers. 1st = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) - S ( t ) ] g ( t , S ( t )) 2nd = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) g ( t + h , S ( t + h ) ) - S ( t ) g ( t , S ( t )) ] 1st answer is from the book2nd answer is that it seems to be correct?Here it was asked to choose a right answer 1 or 2. There is no connection with this question to either to BS or to option pricing. All comments bellow are irrelevant to the question and related to other problems that one is trying to make out behind the simple algebra question. Do you think that both of them are correct?
Last edited by list on August 27th, 2011, 10:00 pm, edited 1 time in total.

DoubleTrouble
Posts: 83
Joined: November 9th, 2010, 9:46 pm

### option hedging remarks

QuoteOriginally posted by: listMy point relates not to pricing but for elementary calculus. We have a functionP ( t , S ) = f ( t , S ) + g ( t , S ) S where g is the partial derivative f in S.We consider difference P ( t + h , S ( t + h )) - P ( t , S ( t )) . There are two answers. 1st = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) - S ( t ) ] g ( t , S ( t )) 2nd = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) g ( t + h , S ( t + h ) ) - S ( t ) g ( t , S ( t )) ] 1st answer is from the book2nd answer is that it seems to be correct?What do you mean "there are two answers" ? To what? If what you want to do is to rewrite the difference P(t+h,S(t+h))-P(t,S(t)), then #2 is correct and #1 is wrong.Your paper is full of errors and it is obvious that you have no clue of what the Black-Scholes model is let alone how to derive it. If you believe that Hull's book is a good reference on the derivation of Black-Scholes then you are wrong. It is good for nothing and I wouldn't even call it a derivation. It's just intuition based.You need to spend two years or so studying mathematics and then you can try again.
Last edited by DoubleTrouble on August 28th, 2011, 10:00 pm, edited 1 time in total.

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

### option hedging remarks

QuoteOriginally posted by: DoubleTroubleQuoteOriginally posted by: listMy point relates not to pricing but for elementary calculus. We have a functionP ( t , S ) = f ( t , S ) + g ( t , S ) S where g is the partial derivative f in S.We consider difference P ( t + h , S ( t + h )) - P ( t , S ( t )) . There are two answers. 1st = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) - S ( t ) ] g ( t , S ( t )) 2nd = ? [ f ( t + h , S ( t + h ) ) - f ( t , S ( t )) ] + [ S ( t + h ) g ( t + h , S ( t + h ) ) - S ( t ) g ( t , S ( t )) ] 1st answer is from the book2nd answer is that it seems to be correct?What do you mean "there are two answers" ? To what? If what you want to do is to rewrite the difference P(t+h,S(t+h))-P(t,S(t)), then #2 is correct and #1 is wrong.Your paper is full of errors and it is obvious that you have no clue of what the Black-Scholes model is let alone how to derive it. If you believe that Hull's book is a good reference on the derivation of Black-Scholes then you are wrong. It is good for nothing and I wouldn't even call it a derivation. It's just intuition based.You need to spend two years or so studying mathematics and then you can try again.1. Hull uses formular #1 for his derivation as you noted and therefore I agree with you that it is incorrect. But you can pay attention that other people above did not agree with you.2. I will also thankfull if you will point my errors too.