some problems with mathematics and partial derivative

guillaume07 · May 8th, 2007, 7:26 pm

Hi,i wondered what is the result of this partial derivative :is it zero because F doesn't explicitly depend on t or does one have to derive S(t) ?Thanks

guillaume07 · May 8th, 2007, 7:34 pm

guillaume07 · May 8th, 2007, 7:36 pm

by using the chain rule of differentiation i know what is the result of the following king of expressionbut in the first case that i have mentioned , i have a doubt

quantmeh · May 8th, 2007, 7:45 pm

QuoteOriginally posted by: guillaume07in the first case that i have mentioned , i have a doubtwhy?

guillaume07 · May 8th, 2007, 7:53 pm

in one of my courses , a teacher tell us that this expression is equal to zero, and I don't understand why . (perhaps it's me who hasn't understand what teacher wanted meant)

quantmeh · May 8th, 2007, 7:58 pm

QuoteOriginally posted by: guillaume07in one of my courses , a teacher tell us that this expression is equal to zero, and I don't understand why . (perhaps it's me who hasn't understand what teacher wanted meant)i knew there's more context in here. it's something with Ito's lemma or stochastic calc , right?

Skyhawk · May 8th, 2007, 8:00 pm

Is this a basic calculus course? The derivative must be found by the chainrule and is not generally zero. Might be zero at certain points (e.g. whereS'(t) is zero, assuming x is not a function of t)

guillaume07 · May 8th, 2007, 8:02 pm

Quotei knew there's more context in here. it's something with Ito's lemma or stochastic calc , right?exactly yes

quantmeh · May 8th, 2007, 8:18 pm

QuoteOriginally posted by: guillaume07Quotei knew there's more context in here. it's something with Ito's lemma or stochastic calc , right?exactly yeswhat they are sying is this: F depends on x and t, independent variables. so when u get partial derivative of F by t, then you dont look at the fact that x depends on t.r u deriving Ito's lemma?

Maelo · May 9th, 2007, 9:46 am

guillaume07:Boyo, it is you who did not understand...I will refer you to Hull or Wilmott's...I got the feeling you mixed up some ideas in the way...In Hull, 5th Ed. specifically go see section 11.6 Itos' lemma...there (if you have some basic calculus on your side) it is quite clear that, in general, that derivative IS NOT ZERO.M

ppauper · May 9th, 2007, 1:27 pm

Maelo is of course correct.If I've typed this correctly:

Zedr0n · May 9th, 2007, 3:59 pm

Erm, the partial derivative here is zero. E.g.There is no dt component, so the partial derivative is zero by definition(and unfolding dS is the same as converting F to explicitly depend on t).By the way from the above one can derive thatThat's the point of the partial derivative anyway - to treat all the variable independently

mj · May 9th, 2007, 11:28 pm

sounds like someone is doing a derivation of the Black--Scholes equation and dropping the d on the delta.

Fermion · May 10th, 2007, 12:27 am

If S is a stochastic variable that changes with time, but is not explicitly functionally dependent on the value of t then the notation S(t) is misleading. (One usually writes S_t instead.) In this case F also has no explicit dependence on t, and the derivative vanishes.If S has a functional dependence on t, then the time derivative of F vanishes whenever the partial derivative of S wrt t vanishes or the partial derivative of F wrt S vanishes.

guillaume07 · May 10th, 2007, 6:02 am

some precisions :it is precisely that , that i don't understand.According to me , i would have used the chain rule of differentiation and so :