SERVING THE QUANTITATIVE FINANCE COMMUNITY

Search found 181 matches

  • 1
  • 2
  • 3
  • 4
  • 5
  • 13
by Kamil90
July 4th, 2016, 1:08 pm
Forum: Numerical Methods Forum
Topic: Quantization error
Replies: 12
Views: 1698

Quantization error

barrier option, call option, etc.
by Kamil90
July 4th, 2016, 11:40 am
Forum: Numerical Methods Forum
Topic: Quantization error
Replies: 12
Views: 1698

Quantization error

<t>The link you provided just derived the amplification factor and in fact for CN those are close to 1 for high wave numbers, so it is a known fact the issue arise in this case numerically. However, I am trying to quantify it. Say if we define error to be V-v, i.e. actual function and numerical solu...
by Kamil90
July 4th, 2016, 9:59 am
Forum: Numerical Methods Forum
Topic: Quantization error
Replies: 12
Views: 1698

Quantization error

Yes, when payoff or its derivative is non smooth. I understand what the issue is but would like to see that as part of the formula in some way and as I follow the classic error equation this is not part of it.
by Kamil90
July 4th, 2016, 1:55 am
Forum: Numerical Methods Forum
Topic: Quantization error
Replies: 12
Views: 1698

Quantization error

<t>I was exploring the error estimate and typically [$]L\epsilon =\tau[$]What yields the estimate on the error. This is the error estimate based on truncation error. Now I read that there is another source of error due to discontinuity or kinks called quantization error(Tavella book) but I don't see...
by Kamil90
June 27th, 2016, 4:13 pm
Forum: Student Forum
Topic: Feynmann Kac and solution stability
Replies: 11
Views: 792

Feynmann Kac and solution stability

<t>ok, got your point about the time range. So, basically If I do the analysis on the PDE itself and show the solution exists and it is unique then there is an expectation as well AND it is bounded(provided non explosive F(X_T)). On the other hand, if I have an expectation and it is bounded(say by p...
by Kamil90
June 24th, 2016, 11:24 am
Forum: Student Forum
Topic: Feynmann Kac and solution stability
Replies: 11
Views: 792

Feynmann Kac and solution stability

<t>Sure I did not really mean to find an expectation for all t. All I am considering is some derivative(any in that case) that has some bounded payoff at time T or before that. In that case I assume there is no way I can end up with unstable solution to the PDE. All of such derivatives will have a s...
by Kamil90
June 23rd, 2016, 5:52 pm
Forum: Student Forum
Topic: Feynmann Kac and solution stability
Replies: 11
Views: 792

Feynmann Kac and solution stability

<t>I think you want to say that the equation grows faster than exponential, so it is unstable? I am not sure I follow you here. But then where does it break the theorem?What I understood:1. Any PDE, if it has a unique solution then == some E.2. Any conditional E is bounded by the initial data up to ...
by Kamil90
June 23rd, 2016, 11:29 am
Forum: Student Forum
Topic: Feynmann Kac and solution stability
Replies: 11
Views: 792

Feynmann Kac and solution stability

<t>Feynman Kac tells about the connection between the Expectations and pdes. And I also see that Expectations are bounded by the terminal data up to a constant. Does it imply that for every parabolic PDE there is an expectation that solves the problem and this solution is definitely stable. So, are ...
by Kamil90
June 8th, 2016, 5:24 pm
Forum: Student Forum
Topic: Pricing equity options with stochastic IR
Replies: 41
Views: 2551

Pricing equity options with stochastic IR

<t>I see, thanks. so there is nothing magical about the choice of money market numerraire? Assuming the constant rate, looks like Bond with maturity equal to the expiration T is just as good for the choice of a numerraire. But I can't find it online, everything is derived using the money market as a...
by Kamil90
June 8th, 2016, 4:38 pm
Forum: Student Forum
Topic: Pricing equity options with stochastic IR
Replies: 41
Views: 2551

Pricing equity options with stochastic IR

<t>Hi,I think I understand how the Black Scholes formula is derived, however I see a constant $r$ in the derivation. Now, assume some stochastic model for $r$, then if I still choose the numerraire to be bank account $B_t=e^{\int_0^tr_sds}$, then the price for the European call would be $C(t)=E[e^{\...
by Kamil90
June 8th, 2016, 4:03 pm
Forum: Student Forum
Topic: SABR for equity options
Replies: 1
Views: 453

SABR for equity options

When I am looking online SABR seems to be very popular with IR models, however, I don't see it mentioned for equity? Is that not good? What are the alternatives people use in equity to model vol? Heston?
by Kamil90
April 8th, 2016, 12:39 am
Forum: Student Forum
Topic: beta estimate in SABR
Replies: 4
Views: 1361

beta estimate in SABR

<t>I searched through the forum and was not able to find an answer to how exactly beta estimate is calculated. From Hagan's paper I see the equation of the form:log(sig_atm) = log(alpha)-(1-beta)log(fwd)so I gathered bunch of historical data for receiver swaptions, say a few months back for 5Y10Y on...
by Kamil90
September 4th, 2015, 6:17 pm
Forum: Student Forum
Topic: Futures and Forwards martingale property
Replies: 4
Views: 2291

Futures and Forwards martingale property

ok, so in this case these are the same processes. what if the underlying and rates are uncorrelated? Would that still hold?
by Kamil90
September 4th, 2015, 4:15 pm
Forum: Student Forum
Topic: Futures and Forwards martingale property
Replies: 4
Views: 2291

Futures and Forwards martingale property

<t>The difference between Forwards and Futures depends on the correlation between the underlying and the interest rates. Assume the case of the deterministic interest rates: that implies then For(t,T)=Fut(t,T). Does it mean two stochastic processes are the same and therefore all the properties are i...
by Kamil90
August 26th, 2015, 12:08 pm
Forum: Student Forum
Topic: GARCH vs SABR
Replies: 5
Views: 2505

GARCH vs SABR

<t>so there is no fundamental difference between those models and they all can be called stochastic volatility models with names GARCH, SABR, HESTON? What you have listed so far is more of a property of one specific process, and I wonder why they get usually published in different books: GARCH is mo...
  • 1
  • 2
  • 3
  • 4
  • 5
  • 13
GZIP: On