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by observer84
November 10th, 2014, 12:11 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

sry for the late reply. Well, thanks for the "subscription"-bonus anyway : )
by observer84
November 7th, 2014, 2:35 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

Ok, I actually have a copy and currently look into it. However, I don't see how the term [$]e^{-iux}\phi(u)[$] ends up being real-valued?
by observer84
November 7th, 2014, 2:17 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

<t>Ok, do you maybe have some good reference? I'm a bit lost.Also, some hint on why the complex-terms do not cancel out in the following would be really helpful:[$]f(x) = \frac{1}{2 \pi} \int_{\mathbb{R}}e^{-iux}e^{iu log(S0) + i \tau (r-q) u - \frac{1}{2} \tau \sigma^2(iu + u^2)}du[$]this should re...
by observer84
November 7th, 2014, 1:58 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

<t>Still stuck the the inversion. For a backcheck I tried to evaluate the density of the log-price under geometric Brownian motion and compare that to my inverted characteristic function (obtained by the cosine-expansion):[$]f(x) = \frac{1}{2 \pi}\int_{\mathbb{R}}e^{-iux}\phi(u) du \approx \sum_0^{N...
by observer84
November 6th, 2014, 2:43 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

<t>Just tried to implement some of the content of the proposed papers.Before starting with the COS-method I wanted to try out the inversion theorem with a standard numerical integration-scheme[$]f(x) = \frac{1}{2 \pi} \int_{\mathbb{R}} e^{-izx}\phi (z) dz[$].. just to try evaluate the density at cer...
by observer84
November 6th, 2014, 8:41 am
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

@localvolatilityThanks a lot! I think this is exactly what I was looking for.bestobs
by observer84
November 5th, 2014, 4:08 pm
Forum: Student Forum
Topic: density of sv-model with jumps
Replies: 10
Views: 3781

density of sv-model with jumps

<t>Hello,currently try to undertake some hedging exercises and look into the impact of premia (see Thread) when hedging in a Heston world (or Heston+ jumps world).In order to get a better feeling for differences in the densities under different measures , I simulated prices and tried to approximate ...
by observer84
October 27th, 2014, 7:16 am
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

My bad, for clarification, what I meant was terminal variance of course:[$]min_h Var_t(C_T - h S_T)[$]I guess, I will have to implement it then Just thought it might be more obvious beforehand.bestobs
by observer84
October 26th, 2014, 9:21 pm
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

<t>As always, thanks a lot for your answer. Now, if we go back to the case of a tradable asset C (which is driven by V_t and S_t):[$]minVar_t(C(S_t,V_t) - hS_t) [$]we have variance and covariance terms:[$]Var_t(C(S_t,V_t) - hS_t) = Var_t(C) + Var(hS)+ 2Cov(C,hS) [$]I wonder under which measure one h...
by observer84
October 23rd, 2014, 4:07 pm
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

[$]minVar_t(V_T - h S_T)[$]with [$]h[$] being the hedge-ratio, V the non-tradable asset and S our underyling.
by observer84
October 23rd, 2014, 2:45 pm
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

@AlanThanks, that makes sense. Statically hedging the terminal variance on the other hand would not work accordingly, I guess?bestobs
by observer84
October 21st, 2014, 12:32 pm
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

<t>QuoteBefore you ask, under SV models, once the volatility SDE adjustments are fixed by the market, the same holds: C and all the various partials of C are (ultimately) fixed. The only part (of the generalization of (*)) that changes with the measure are the Ito expansions of dS and dV. Ah ok. Tha...
by observer84
October 19th, 2014, 3:15 pm
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

<t>QuoteQuoteIsn't this equation (at first) the P-dynamic of C?YesOk. So, the [$]\frac{\partial{C}}{\partial{S}}[$] in the [$]\mathbb{P}[$]-dynamics is not the same one appearing in the BS-valuation-formula?QuoteYes, if you are hedging away both sources of uncertainty (stock price and vol.) in the s...
by observer84
October 19th, 2014, 11:58 am
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

<t>Ok, thanks for your patience Alan. Maybe one last point: Starting from the BS-equation, one uses ITO to get the dynamics of the option [$]C[$] to be priced:[$]dC_t = \frac{\partial{C_t}}{\partial{t}}dt + \frac{\partial{C_t}}{\partial{S}}dS_t + 0.5 \frac{\partial^2{C_t}}{\partial{S^2}}(dS_t)^2 \, ...
by observer84
October 17th, 2014, 4:21 pm
Forum: Student Forum
Topic: Hedging under which measure?
Replies: 27
Views: 7635

Hedging under which measure?

<t>Thanks for the fast reply Alan.QuoteThe terms in your "dynamics of the derivative" SDE must agree with Ito's lemma. I'm going to use superscript i's to mark the two options and subscripts for partial derivatives. Right, my [$]\mu_i[$]'s and [$]\sigma_i[$]'s should actually be functions of [$]V[$]...
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