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August 29th, 2011, 10:53 am
Forum: Student Forum
Topic: basic filtration question
Replies: 11
Views: 17888

### basic filtration question

<t>QuoteOriginally posted by: sdlifeI kind of get it, but u>t and so the filtration, F_u, will still hold more information than F_t, even if u is only a tiny bit greater than t? and so the intersections will be F_u which will hold a tiny bit more information than F_t?Ok. But what do you say about th...
August 29th, 2011, 10:22 am
Forum: Student Forum
Topic: basic filtration question
Replies: 11
Views: 17888

### basic filtration question

QuoteOriginally posted by: sdlifeand so by this definitionThis is where you go wrong. This does not hold if you just index with the natural numbers!
August 29th, 2011, 10:00 am
Forum: Student Forum
Topic: option hedging remarks
Replies: 81
Views: 22796

### option hedging remarks

<t>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 ...
August 24th, 2011, 2:33 pm
Forum: Student Forum
Topic: ODE I, Financial Modelling or Investment & Portfolio Mngt.?
Replies: 9
Views: 17835

### ODE I, Financial Modelling or Investment & Portfolio Mngt.?

<t>I know how you feel man.I'm a mathematician as well and for many years I studied all kinds of different topics like multi linear algebra, galois teory, number theory, topology, algebraic topology etc.. And it really distances you from the kind of "engineering mathematics" that is discussed in thi...
August 24th, 2011, 6:24 am
Forum: Student Forum
Topic: ODE I, Financial Modelling or Investment & Portfolio Mngt.?
Replies: 9
Views: 17835

### ODE I, Financial Modelling or Investment & Portfolio Mngt.?

<t>QuoteOriginally posted by: martizzleHi,Lots of people in my department didn't take ODE I (its not a requirement, PDE is). How important is ODE to finance? can I make do with PDE I and II?thnxPDE is fundamental in mathematical finance. Skip ODE and try to take some courses in Integration Theory an...
August 21st, 2011, 7:44 pm
Forum: Student Forum
Topic: Maximum of Brownian Motion
Replies: 5
Views: 18401

### Maximum of Brownian Motion

I realized today that I made a slight error in my first post. That density formula holds only for so the integral should range from 0 to infinity which gives the previous result divided by 2.Right?
August 19th, 2011, 8:46 pm
Forum: Student Forum
Topic: Alternative derivation of the Black-Scholes pricing formula
Replies: 2
Views: 18294

### Alternative derivation of the Black-Scholes pricing formula

<t>Thank you for your reply!QuoteOriginally posted by: frolloosfeynman-kac, as you well know, says the solution of the pde can also be obtained by risk-neutral pricingThe thing was that i think Shreve writes the Feynman-Kac theorem as if there were a one way implication from SDE to PDE. But I see no...
August 18th, 2011, 8:04 am
Forum: Student Forum
Topic: Alternative derivation of the Black-Scholes pricing formula
Replies: 2
Views: 18294

### Alternative derivation of the Black-Scholes pricing formula

<t>Hello!I know how to derive the Black-Scholes PDE and the pricing formula in the usual way (as in Shreve's book). But you're supposed to be able to derive the pricing formula as well as the hedge by starting off from the Black-Scholes equation and then arguing that you're allowed to use the Feynma...
August 16th, 2011, 4:47 pm
Forum: Student Forum
Topic: Help with 2 exercises!
Replies: 1
Views: 17126

### Help with 2 exercises!

<t>Ex 2Derive the Black-Scholes equation with a deterministic function that depends on t and x.My solutionLet the stock be governed by a GBM under the risk neutral measure i.e. The risk neutral pricing formula tells us that the price at time t of a derivative security that pays h(S(T)) at maturity T...
August 16th, 2011, 3:54 pm
Forum: Student Forum
Topic: Help with 2 exercises!
Replies: 1
Views: 17126

### Help with 2 exercises!

<t>Hi all!I think that I've solved two exercises correctly but I'd really appreciate your input on my solutions or thoughts.Ex 1Let S(t) be a stock in the Black-Scholes model and let X(t) be the usual portfolio value process consisting of shares in of the stock and the rest is invested in the money ...
August 15th, 2011, 8:43 am
Forum: Student Forum
Topic: Pricing Barrier option in BSM model
Replies: 8
Views: 19524

### Pricing Barrier option in BSM model

Why didn't I think of that!? I have a copy like not even 2 meters to my right Thanks Joshi!
August 11th, 2011, 10:54 am
Forum: Student Forum
Topic: Pricing Barrier option in BSM model
Replies: 8
Views: 19524

### Pricing Barrier option in BSM model

Thank you very much Alan. That was about the amount of help I needed to solve it!Best regards!
August 9th, 2011, 8:39 pm
Forum: Student Forum
Topic: Pricing Barrier option in BSM model
Replies: 8
Views: 19524

### Pricing Barrier option in BSM model

rprat: It's possible to find an analytic closed expression of the price at time 0Alan: I do seem to be able to figure out how to solve the BS PDE as you suggested. Any hints?Best regards
August 9th, 2011, 7:20 pm
Forum: Student Forum
Topic: Question: Which drift to use for modelling stocks
Replies: 18
Views: 19848

### Question: Which drift to use for modelling stocks

rprat: A model is said to be complete if every -measurable derivative security can be hedged. En example of such a derivative is the one paying at time T and an example of such a model that is the Black-Scholes model.
August 8th, 2011, 7:26 am
Forum: Student Forum
Topic: Pricing Barrier option in BSM model
Replies: 8
Views: 19524

### Pricing Barrier option in BSM model

Hi Alan,thank you for your reply. How do you suggest I do to solve the PDE? Should I do some kind of transformation into something I know has a certain solution? If so, I can't figure out what kind of transformation to do.Thank you in advance EDIT: Oh wait, I should use Feynman-Kac, right?