SERVING THE QUANTITATIVE FINANCE COMMUNITY

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June 24th, 2015, 9:11 am
Forum: Numerical Methods Forum
Topic: Finite difference and control variates
Replies: 47
Views: 7806

### Finite difference and control variates

<t>QuoteOriginally posted by: outrunA simple example would be an American option? That's a classical control variates method when using trees/FDM grids.* use FDM to price both European and American options on the grid* use the difference between the closed form and FDM for the European option as mea...
June 8th, 2015, 1:39 pm
Forum: Student Forum
Topic: Market Price of Risk in BS
Replies: 4
Views: 2486

### Market Price of Risk in BS

No, the notation is confusing you. $V:[0,\infty) \times R \to R$ is a deterministic function. For all values of $(t,x) \in :[0,\infty) \times R$ the PDE is satisfied pointwise. Wilmott says that since the stock is a tradeable asset, the function V(t,x)=x must be a solution.
June 8th, 2015, 1:19 pm
Forum: Student Forum
Topic: Market Price of Risk in BS
Replies: 4
Views: 2486

### Market Price of Risk in BS

<t>QuoteOriginally posted by: bcfIn Wilmott's third volume, in the Aside on p. 857 , after stating the PDE$$\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2S^2\frac{\partial^2 V}{\partial S^2} + (\mu - \lambda_S \sigma)S\frac{\partial V}{\partial S} - rV = 0$$he mentioned we may set $V=S$ int...
May 31st, 2015, 12:55 pm
Forum: Careers Forum
Replies: 3
Views: 11050

Just wondering if anyone has any update on this?I still meet people who seem to be doing quantitative prop trading at big IBs (even American ones)... and i can't quite figure out what is going on.
April 24th, 2015, 7:12 am
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnNowadays we have O(h^4) version.For non-constant coefficients? I would very interested to see this.Yep. I'll get the reference for you.BTW 'lin/Duffy schem...
April 23rd, 2015, 9:45 am
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

QuoteOriginally posted by: CuchulainnNowadays we have O(h^4) version.For non-constant coefficients? I would very interested to see this.QuoteOriginally posted by: CuchulainnBTW do you have the I'lin paper in Russian or in English?In English
April 23rd, 2015, 8:15 am
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacBTW I don't understand your comments on Ilin's paper. I quote many articles so I don't understand the cherry picking. Is it the convection/drift term that is the concern? I was looking at the Wilmott article "A Critique of the Cr...
April 22nd, 2015, 8:11 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnThis has become an ideological/weltanschauung discussion (which I BTW don't find repugnant).Emac is happy to tweak to find a solution while I am interested in robust numerical methods that work for a wide range of parameters values as with PDEs.That the gist o...
April 22nd, 2015, 3:31 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnFor me, it does.To me, that is like complaining that the integral$\int_{10^{10}}^{10^{20}} e^x dx$Takes a lot steps to approximate using the trapezoidal rule.The reason why it does is that error in the trapezoidal rule depends on the length of the interval...
April 21st, 2015, 4:02 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnWant another example?Another example of what? My claim is only that MC methods converge in cases where they are proven to co...
April 21st, 2015, 2:59 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnWant another example?Another example of what? My claim is only that MC methods converge in cases where they are proven to converge -- you cannot provide a counterexample to that.You can provid...
April 21st, 2015, 2:50 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnWant another example?Another example of what? My claim is only that MC methods converge in cases where they are proven to converge -- you cannot provide a counterexample to that.You can provide examples where the target random variable has a large variance, bu...
April 21st, 2015, 2:21 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnYou don't give up easy, do you? A better place to look f...
April 21st, 2015, 1:49 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnYou don't give up easy, do you? A better place to look for PDE is Wilmott CFD threadThere are zillions of PDE/FDM threads he...
April 21st, 2015, 1:38 pm
Forum: Numerical Methods Forum
Topic: What does ?convergence? in Monte Carlo simulation mean?
Replies: 96
Views: 9627

### What does ?convergence? in Monte Carlo simulation mean?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: CuchulainnYou don't give up easy, do you? A better place to look for PDE is Wilmott CFD threadThere are zillions of PDE/FDM threads here. //OK, can you price an option using the SDEdv = d(lnV) = (- ½ s^...

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