according to non-arb pricing, the future price of a non-dividend asset is the risk netral expectationof the asset at a future time. How to prove this?

I am wondering if the asset price with dividend can be the numeraire?or generally, what can be a numeraire? any tradable asset price?

<t>As we seen, European call and puts are highly liquid derivatives, so their pricesis dicided by the market and they can be used to calibrate some models.Question, how about American option? Are they always priced by quants? In other words, since they are not highly liquid, they do not have a equil...

<t>thanks for pointing out this, for example take the payoff as (S^2-K)/S_0, it will be fine in units.I am still confused, Stale says the boundary condition is decided based on financial point of view,then if we excercise it as S-->\infty, does not the payoff approach S^2?I can understand S^2 will n...

<t>about the boundary condition of B-S PDE, for a Euopean call option V(S,t), they are, 1) V(0, t) =0, for all t.2) V(S,t)-->S, for S-->\infty3) V(S,T)=max(S-K,0).Question: is 2) a general condition? For example, if the payoff function is V(S,T)=max(S^2-K,0),shouldn't 2) change to V(S,t)--->S^2, as ...

<t>I have a question about the strong and weak solution of a general SDE regarding X_t.Are the following statements correct?1. As a strong solution, X_t is adapted to the filtration generated bythe Brownian motion B_t (with x_0) appearing in the SDE? 2. As a weak solution, X_t is adapted to the filt...

<t>Hi StaleI did not realize that the first line is the definition of the jump. I thoughtit is a derivation. I got the second line by an intuition, since I thoughtthe jump is from X(t-) to X(t-)+Y, If Y=1 const, that is pure jump process.Since X(t-) is right-cont, we will not have X(t-)=X(t), right?...

Let's construct the compound poisson process as,where Y_n are iid r.v.I read from some notes that, for a function f(X_t),I am wondering why it is not

thank Alan.

<t>As I understand, what you mentioned (i.e.,random number generator) is just the fundamental partof the Monte carlo simulation. That is not the reason of monte carlo. To see why use monte carlo,we can imagine what other alternatives we have got, say finite method for PDE and tree. Asfor finite meth...

<t>I think both Monte-Carlo and binomial tree are numerical techniques while Black Schole formulacan give you a closed form solution. But for some security there is no closed form solution. Inthis case you have to use numerical technique and in many cases you will use Monte-carlo insteadof binomial ...

I have done an excercise to prove that the Poisson process N_t and Brownian motion W_tare independent given that they are adapted to the same filtration F_t.My question: is it possible that N_t and W_t are actually dependent under some condition?

<t>Being a current student of this course, I would like to share my opion with those who are interested. Hope it is helpful.First, I want to talk about the students in our class. 90% of the studentsstudied maths in undergraduate before. Some of them are quite good in maths (especially probability th...

<t>hi, it seems that stochastic volatility models for different types of derivativesare not the same, for example, some models are suitable to FX but notto equity derivative.My question is, what is the popular stochastic volatility models for equity derivatives? why they need to be different from th...

I got an interview for an equity front desk quant internship inthe Hong Kong office of big IB. It is a 6 month internship,do you know what questions supposed to be asked?thanks.