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June 26th, 2012, 1:57 am
Forum: General Forum
Replies: 5
Views: 12407

June 26th, 2012, 1:56 am
Forum: General Forum
Replies: 5
Views: 12407

I think the paper by Lekkos "A critique of Factor Analysis of Interest Rates" should be a prerequisite for all carrying out PCA! Just a thought and well worth a read! I have no connection to Lekkos but agree with his arguments....
June 8th, 2012, 2:32 pm
Forum: Student Forum
Topic: Infinitely Divisible Density Continuous?
Replies: 6
Views: 12217

Infinitely Divisible Density Continuous?

<t>I have worked through some examples with a discontinuity at zero and indeed it does seem to be okay!Suppose f is an infinitely divisible 2-EPT function with no pointmass at zero but is discontinuous at zero. Let f_n be the density function corresponding to the n^th root of the characteristic func...
June 8th, 2012, 11:45 am
Forum: Student Forum
Topic: Infinitely Divisible Density Continuous?
Replies: 6
Views: 12217

Infinitely Divisible Density Continuous?

<t>Thanks eh for your comments,My intuition was coming from the perspective that if an inf div density f exists which has a discontinuity at some point. Then there exist a density function f_n such that an n-fold convolution of f_n with itself gives f. I find it hard to see how an n-fold convolution...
June 8th, 2012, 9:41 am
Forum: Student Forum
Topic: Infinitely Divisible Density Continuous?
Replies: 6
Views: 12217

Infinitely Divisible Density Continuous?

<t>Sorry for ambiguity in my previous post.I understand that discrete distributions can be infinitely divisible.Consider a strictly positive density function f(x) defined for all x\in(-\infty,\infty). Can f be infinitely divisible if it has a discontinuity at a certain point ? e.g. say a discontinui...
June 8th, 2012, 8:36 am
Forum: Student Forum
Topic: Infinitely Divisible Density Continuous?
Replies: 6
Views: 12217

Infinitely Divisible Density Continuous?

<t>Intuitively it seems that an infinitely divisible distribution should be continuous but I don't see how it comes into play in the definition of a Levy process or in the Levy-Khinthcine formula?I am particularly concerned with continuity at the origin? Or whether the density function should even b...
May 30th, 2012, 7:29 pm
Forum: Student Forum
Topic: Decomposing a Levy Process of Finite Variation (I Think!)
Replies: 1
Views: 11955

Decomposing a Levy Process of Finite Variation (I Think!)

<t>I think I remember reading somewhere that a Levy process of finite variation can be decomposed into the sum of two Levy processes (also of finite variation) one positive Levy process and the other a negative Levy process....does this make sense?The Variance Gamma process would be an example of th...
May 8th, 2012, 3:08 pm
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

Intuitively I think a negative Levy measure would imply that the random variable in question is not infinitely divisible but proving that could be a problem!
May 8th, 2012, 2:07 pm
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

A final question although slightly off-topic...In the Levy-Khintchine formula is the Levy measure unique in set of signed measures or is it only unique in the class of non-negative measures?Thanks
May 8th, 2012, 1:57 pm
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

Thanks Alan....greatly appreciated
May 8th, 2012, 12:42 pm
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

A further question if I may please.....As stated in my original post that asset prices under P must be semi-martingales. Typically we model log-returns as Levy processes (semi-martingales). Then, are all exponential-Levy processes semi-martingales?Thanks
May 8th, 2012, 12:37 pm
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

<t>Thanks Eh...Proposition 9.9 from Cont and Tankov states that in an exponential Levy model then an equivalent martingale measure exists if underlying Levy process X satisfies any of the following1) X has a Gaussian component2) X has infinite variation 3) X has positive and negative jumps4) X has p...
May 7th, 2012, 6:05 pm
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

Thanks Alan...will have a look
May 7th, 2012, 10:07 am
Forum: Student Forum
Topic: Change of Measure - Levy Processes
Replies: 12
Views: 14044

Change of Measure - Levy Processes

<t>Hi,Suppose under the real world measure P I have a (pure jump) Levy process and I know the associated Levy triple. For derivatives pricing it is required that we work under the risk neutral measure Q such that the discounted price process is martingale. How do we know if a change of measure exist...
April 24th, 2012, 10:04 am
Forum: Student Forum
Topic: Girsanov Theorem
Replies: 3
Views: 14918

Girsanov Theorem

We know every Levy process is a semi-martingale. Consider a Levy process X_t under a measure P.Does a change of a change of measure exist (for all Levy processes X_t) such that under the risk neutral measure Q that X_t is a martingale?
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