<t>(edited)Here for a fixed value of w, you get a single path, t -> X(w,t).You *can* look at different w for different times t, but when you say sample path you are fixing w, and only letting t varyJust like Brownian motion: for a fixed w in your sample space, you get a single path B_t(w) when you v...

american option should be something like max_{tau} E[ f(S_{tau}}] where tau runs over the stopping times. You can't move the max inside the expectation to take E[ max_{tau} f(S_{tau})].

<t>Give me any system of pde's with unique solution f(x) [x a vector even] , now make up any new variable v and find a function g(x,v) such that g(x,1) = f(x). Then why would you expect g(x,v) = f(x) for all v ? Uniqueness no longer holds for functions of g(x,v) when you add the completely new varia...

<t>Yura,This is way late but --The probability that the stock hits the strike exactly at maturity, but never before is zero. Hence, if the american options pays off, we may assume it pays off strictly before maturity (even if this is one nanosecond before). If we buy 2 of the European versions, then...

<t>Paul:I agree completely that creativity is very important. However, in the same vein, take for example getting a PhD. You typically have to pass a set of qual exams before doing a dissertation. This is because before you can't fly high with lots of creative ideas right off the bat, you need to ha...

<t>Hello,In an analagous manner to the CFA/PRM etc. why isn't there an equivalent designation designed for quant finance positions (more quant than the above mentioned). I.e. questions about pricing vanilla, asian, barrier options, maybe a mathematical section on martingales, brownian motion SDE, Gi...

<t>For the latter part, here are my thoughts: start with our measure P.Find a measure Q (by Girsanov) so that X(t) is brownian motion under Q. Let A be the event that X hits 3 before -5.If T is the stopping time inf{ t : X(t) = 3 or X(t) = -5 }, then X_{min(t,T)} is a martingale and we should get0 =...

<r>Hcova,(Disclaimer: I have no experience in actual pricing)I see sort of 2 general ways to approach this. The first way is the "ends justifies the means" approach of local volatility: You use as the model dS_t = r*S_t dt + v(S,t)*dS_t, and then from the vanillas you deduce the volatility v(S,t). Y...

The expected value of riemann sum conditional on is not going to be the same as just conditioning on the last variable W_j, you should be able to extend this idea in the limit.

<t>Yes that is normal. The Riemann sum consists of random variables W_{t_i}. Since these terms are *jointly* normally distributied, so is any linear combination. Since the riemann sum converges (almost surely) it converges in distrubution, which will be normal: try looking at characteristic function...

<t>Your integral is not an Ito integral, it is a path-by-path integral, i.e. for each w in your sample space you are computing just a plain 'ol integral of a continuous function, so I see no problem - the only care you may have to take with this is remember you are taking the integral of a non-diffe...

<t>Hi,Does anybody here have experience using the NAG library with C++ ? The main problem I am having it is written mainly for C.For example, I want to write a GARCH fitting program, using the NAG library to do the optimization for the MLE. It made sense for me to have a GARCH class, and then have a...

<t>I think I made a typo when I said left hand side, I meant right hand side. I was saying,Let A_t = a * E[ B_t * h(K_1,S_t)]B_t = (1-a) * E [ B_t * h(K_2,S_t) ]I had thatE[ B_t * h(a*K_1 + (1-a)*K_2,S_t) ] <= A_t + B_t.Now taking the max over all {t a stopping time}, the left hand side is the price...

<t>If the payoff function h(K,S) is convex in K, thenh(a*K_1 + (1-a)*K_2, S) <= a*h(K_1,S) + (1-a)*h(K_2,S).Then taking expected value under risk neutral measure, using monotonicity of expected value and linearityE[ B_t * h(a*K_1 + (1-a)*K_2,S_t) ] <= a * E[ B_t * h(K_1,S_t)] + (1-a) * E [ B_t * h(K...

Cause { HHHH } intersect with { HHHT, HHHH} is { HHHH }. There is no singleton set '3 heads' only the event { HHHT, HHHH }