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by emac
April 2nd, 2015, 9:32 am
Forum: Careers Forum
Topic: Which of these PhD is better for quant industry?
Replies: 40
Views: 8933

Which of these PhD is better for quant industry?

QuoteOriginally posted by: GamalBetter than Nicole El Karoui?What does that even mean?You saidQuoteOriginally posted by: GamalThere are two places to learn good stochastic analysis - Moscow State University and Ecole Polytechnique.By pretty much any measure, that is not true.
by emac
April 1st, 2015, 7:32 am
Forum: Careers Forum
Topic: Which of these PhD is better for quant industry?
Replies: 40
Views: 8933

Which of these PhD is better for quant industry?

<t>QuoteOriginally posted by: GamalStochastic analysis is the hard kernel of quantitative finance, optimization and C++ are important but not that crucial. There are two places to learn good stochastic analysis - Moscow State University and Ecole Polytechnique.They are good places but obviously not ...
by emac
February 18th, 2015, 9:59 am
Forum: General Forum
Topic: How to take borrow rate (cost of short stock) into BS model?
Replies: 24
Views: 6599

How to take borrow rate (cost of short stock) into BS model?

<t>QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: emacQuoteOriginally posted by: hdzhangI am wondering if there is any way to take borrow rate (especially cost of short stock) into an option pricing model. There is only one rate in the BS model. Is there any way to adjust BS model t...
by emac
February 18th, 2015, 9:28 am
Forum: Careers Forum
Topic: Statistician Career Change
Replies: 11
Views: 4426

Statistician Career Change

<t>QuoteOriginally posted by: katastrofaSince "regression, generalized linear models, hierarchical modeling, Bayesian statistics, meta-analysis, categorical, survival and longitudinal data analysis" is something you used in your statistics work, they should possibly open the list of your mathematica...
by emac
February 17th, 2015, 9:23 am
Forum: General Forum
Topic: How to take borrow rate (cost of short stock) into BS model?
Replies: 24
Views: 6599

How to take borrow rate (cost of short stock) into BS model?

<t>QuoteOriginally posted by: hdzhangI am wondering if there is any way to take borrow rate (especially cost of short stock) into an option pricing model. There is only one rate in the BS model. Is there any way to adjust BS model to include two different rate?See slide 4 and 5 here. You get a BSDE ...
by emac
February 10th, 2015, 11:48 am
Forum: Student Forum
Topic: Derivative of expecation vs expectation of derivative
Replies: 1
Views: 3570

Derivative of expecation vs expectation of derivative

<t>QuoteOriginally posted by: campione99HiDoes anyone know if:d/dx (E[X^n]) = E[d/dx(X^n)] ?So whether the derivative of the expectation equals the expectation of the derivative?I assumed yes in a calculation I was doing and managed to get the correct answer but I am not sure it was mathematically s...
by emac
January 30th, 2015, 8:46 am
Forum: Student Forum
Topic: A question regarding not changing diffusion under equivalent measures.
Replies: 4
Views: 3356

A question regarding not changing diffusion under equivalent measures.

See here - Theorems 8 and 11Basically, in this setting, Girsanov transformations are the only transformations between equivalent measures. Once you know this, you know that they can only affect the drift and not vol of your process.
by emac
January 23rd, 2015, 11:40 am
Forum: Student Forum
Topic: Radon?Nikodym theorem
Replies: 39
Views: 7642

Radon?Nikodym theorem

I know what almost sure means. You did not say two random variables were equal almost surely, you saidQuoteit is a a.s. r.v What is an almost sure random variable?
by emac
January 23rd, 2015, 11:22 am
Forum: Student Forum
Topic: Radon?Nikodym theorem
Replies: 39
Views: 7642

Radon?Nikodym theorem

<t>QuoteMore rigorous than 'notation' dQ_T/dQ. That's what worries about the _original_ example you posted.Don't n, a.s., r.v.? this is worrying..a..s used to be p.p. (Presque partout). dQ_T/dQ is perfectly rigorous. The R-N states the existence of a measurable function, which most people call dQ_T/...
by emac
January 23rd, 2015, 10:52 am
Forum: Student Forum
Topic: Radon?Nikodym theorem
Replies: 39
Views: 7642

Radon?Nikodym theorem

<t>QuoteWhy is the integral form of RN not referred to? It more intuitive and rigorous. More intuitive and rigorous than what? We were asked for the simplest Radon-Nikodym derivative we can think of. I picked one which is a function on a set with two elements. This is extremely simple.QuoteTake the ...
by emac
January 22nd, 2015, 8:29 am
Forum: Student Forum
Topic: Radon?Nikodym theorem
Replies: 39
Views: 7642

Radon?Nikodym theorem

<t>Maybe I should be clearer: the Radon-Nikodym theorem is about the existence of a density between two absolutely continuous measures. In finance, the measures could be, for example, the risk-neutral measures corresponding to different numeraires (e.g. foreign and domestic bonds), or the physical m...
by emac
January 21st, 2015, 11:58 am
Forum: Student Forum
Topic: Radon?Nikodym theorem
Replies: 39
Views: 7642

Radon?Nikodym theorem

<t>I am simply looking at the probability space [$](\Omega, F, \mu)[$] where [$]\Omega=\{\omega_1, \omega_2\}[$], [$]F[$] is the power set of [$]\Omega[$] and [$]\mu[$] is defined as I did it. The OP asked for the simplest possible example. A probability space with two possible outcomes is about as ...
by emac
January 8th, 2015, 11:33 am
Forum: Student Forum
Topic: Radon?Nikodym theorem
Replies: 39
Views: 7642

Radon?Nikodym theorem

<t>Discrete probability space with two outcomes [$]\omega_1[$] and [$]\omega_2 [$]. Let the probability measure [$]\mu[$] assign them each [$]\mu(\omega _1)=\mu(\omega_2)=1/2[$]. Define a new probability measure $\nu$ which assigns them [$]\nu(\omega_1)=1/4[$] and [$]\nu(\omega_2)=3/4[$]. Then, the ...
by emac
October 29th, 2014, 8:22 pm
Forum: Book And Research Paper Forum
Topic: Nonlinear Option Pricing
Replies: 22
Views: 12175

Nonlinear Option Pricing

<t>QuoteOriginally posted by: CollectorQuoteOriginally posted by: emacQuoteOriginally posted by: Collectoroptions must be priced based on Stochastic n.o.p. which leads to jumps, fat-tails etc.What is stochastic n.o.p?something I mentioned shortly before....I have some pages on it in storage in my ba...
by emac
October 29th, 2014, 4:25 pm
Forum: Book And Research Paper Forum
Topic: Nonlinear Option Pricing
Replies: 22
Views: 12175

Nonlinear Option Pricing

QuoteOriginally posted by: Collectoroptions must be priced based on Stochastic n.o.p. which leads to jumps, fat-tails etc.What is stochastic n.o.p?
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