<t>Given a vol surface for a stock with dividends (such as SPX), how do I price vanillas on a dividend reinvested portfolio (such as SPTR)?Intuitively there should be 1-1 mapping from SPX vol to SPTR vol but what is this 1-1 function? For dividend yield, it's obviously just the ratio of forwards, bu...

<t>Thanks for the replies. I understand that it is the option to terminate the cost of carrying the long hedge position in the underlying equity that's making the american put more valuable, but is there a simple way to understand why it is 40 bps for the case I described below and why it is rather ...

<t>A trader asked me why a 1 year American put option is worth .4% (on notional) more than a 1 year European put option with vol = 5% rate = 5% and zero dividend yield stock and I couldn't find a simple explanation why. He was surprised to find that the difference was so large. Can someone shed some...

<t>E[B_t^2 B_s^2] = E[(B_t-B_s+B_s)^2 B_s^2] = E[(B_t-B_s)^2 B_s^2 + 2(B_t-B_s) B_s^3 + B_s^4]so B_t-B_s = B_(t-s) is independent of B_sE[B_(t-s)^2 B_s^2] = E[B_(t-s)^2] E[B_s^2] = (t-s) s2E[B_(t-s) B_s^3] = 0E[B_s^4] = 3 s^2 since it's kurtosisso E[B_t^2 B_s^2] = (t-s) s + 3s^2 = ts + 2s^2.so Cov[B...

<t>method 1)sum i^2 from i = 1 to i = N is of O(N^3) so it must be of the form a + bN + CN^2 + dN^3for the case if N = 1 => 1 = a + b + c+ dfor the case of N = 2 = > 5 = a + 2b + 4c + 8d ... 14 = a + 3b + 9c + 27d 30 = a + 4b + 16c + 64dSolve these four equations leads to a = 0, b=1/6, c=1/2, d=1/3....

I am trying to price a highly path-dependent option with Bermudan exercise structure. I think American Monte Carlo pricing is the best way to go here.Can someone please post some papers on stochastic mesh method by Broadie and Glasserman? Thank you.

<t>Thanks for the references. I found all the papers very helpful. I've decided to implementd=1/2 and d=1 models since there seems to be several issues with d<1/2 and d>3/2 (momentsblow up, becomes only local martingale, vol explosion, etc.). I basically have Monte-Carlodone and hope to implement a ...

<t>It seems that Heston model is the standard stochastic vol model used in practice due to itbeing "solvable", i.e. one has "closed" (up to a Laplace transform) form solution for European optionsand the volatility process can be integrated to give something like V_t ~ Z where Z is a non-centralchi-s...

Thanks MJ for the tip, your advice elimnated 75% of the candidates in a few minutes.

<t>Alan,Thank you for your post, it was very helpful. But one point I seem to be confused is that in the risk-neutral world where we price options, one firm can default while the other cannot. But can we even say that firm 1 can default in risk-neutral world? After all, the drift down by the dividen...

<t> I'll be conducting some on-campus interviews (undergrads) for a quant/programmer position. I hate asking brainteasers because they are unfair, meaning if you seen anything close to how they are solved then you have 10000 times more advantage.For example, there is so many spin-offs to the questio...

<t>Thanks for the responses. About stock being NPV of future dividends, if dividend yield is greater than discount rate, then the stock will be worth infinite amount.Then I guess it makes more sense to discount at a risky rate taking into consideration default of S=0. Can we considerS=0 as default? ...

<t>Let's say we are pricing a 11 year option on a $10 stock that pays quarterly dividend at $0.25. Let's say the interest rate r=0. In the risk-neutral world, this stock willbe expected to worth zero in 10 years. Let's say we want to value the long-dated option on this stock, how do we do this? Of c...

<t>gina, every quant I know and work with went to top ivy schools (Harvard, etc.) or top tech schools like Caltech, MIT, Berkeley, etc. and graduated top in their classes. In fact, many with these credentials can't make it to a top bank. The times are tough and $100k sounds right if not generous for...