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Topic Title: Risk-Neutral vs. Martingale Measure
Created On Fri Jun 27, 03 07:33 AM

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Reini
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Fri Jun 27, 03 07:33 AM

Hi,
is there any difference between the terms "risk-neutral measure" and "martingale measure". Which one is more common. Furthermore, what is about the difference between "objective measure" and "real-world measure".
Thanks.
Reini

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Nonius
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Fri Jun 27, 03 08:36 AM

Quote
Originally posted by: Reini
Hi,
is there any difference between the terms "risk-neutral measure" and "martingale measure". Which one is more common. Furthermore, what is about the difference between "objective measure" and "real-world measure".
Thanks.
Reini

risk-neutral and martingale measure basically mean the same thing, although martingale measure is the more modern term. It is the measure that is equivalent to the real measure (equivalence means that a set has pos measure in one iff it has pos measure in the other) such that ratios of prices of traded securities/assets to a specific traded security (called the numeraire) are martingales. The original numeraire that B-S used was the money market account. When you use this numeraire, you see that stock prices divided by this numeraire, being martingales, have the property that their drifts must be the risk free drift. Some people confuse risk free with gov rate, but it is your funding rate...the rate at which YOU can borrow and lend cash (either collateralised or un). For bank and securities firms, this is basically Libor +- epsilon for most products.

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Nonius

I'm going to Hell with FDAX as my Kharnak.

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Fri Jun 27, 03 09:10 AM

some people take risk-neutral measure to mean the martingale measure when the numeraire is the money market acccount,.

For further discussion, see "why does risk-neutral valuation work" thread in faqs

MJ

-------------------------
LMM and QuantLib training course London June 2010. http://www.moneyscience.com/training/

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Fri Jun 27, 03 10:18 AM

Edited: Wed Feb 25, 04 at 01:32 PM by gatarek

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Nonius
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Fri Jun 27, 03 10:34 AM

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Originally posted by: gatarek
The notion "risk-neutral measure" is precise while "martingale measure" means nothing - just that some stochastic process (numeraire?) is a martingale.

well, Gatarek, what you are saying is technically precise, but "martingale measure" is a fairly popular term for the (possibly unique) equivalent measure under which prices relative to a numeraire are martingales.....it is sort of like the way mathematicians often abuse notation so that pages of math aren't cluttered with symbology.

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Nonius

I'm going to Hell with FDAX as my Kharnak.

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Val
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Fri Jun 27, 03 10:38 AM

Hi all,

if it's "risk-neutral" it implies martingale.
and vice versa....

One can see it as synonym, diminutif or whatever...

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Valeriu Biniuc

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Val
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Fri Jun 27, 03 10:39 AM

One could also say, what's then the difference between Libor Market Model and BGM ?

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Valeriu Biniuc

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Fri Jun 27, 03 10:53 AM

Quote
Originally posted by: Val
One could also say, what's then the difference between Libor Market Model and BGM ?

There was a discussion on that topic (and some participants didn't keep elementary standards

) - to avoid dicussion who, when, where, why and what for did the model it should be called LMM.

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Rez
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Fri Jun 27, 03 11:00 AM

Quote
Originally posted by: Reini
.... Furthermore, what is about the difference between "objective measure" and "real-world measure".

And to complete the answer: the objective and real-world measures are taken to be synonyms too. On the other hand the 'risk-neutral' and the 'objective' measures are different, with their ratio [the so called Radon-Nikodym derivative] being a quantity that depends on the agent's preferences. The two are equal if the agents are risk neutral, hence the terminology 'risk-neutral'.

Kyriakos

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Nonius
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Fri Jun 27, 03 01:20 PM

<blockquote>Quote
<hr>Originally posted by: gatarek
<blockquote>Quote
<hr>Originally posted by: Val
One could also say, what's then the difference between Libor Market Model and BGM ?

<hr></blockquote>

There was a discussion on that topic (and some participants didn't keep elementary standards

) - to avoid dicussion who, when, where, why and what for did the model it should be called LMM.<hr></blockquote>

why the frown Gatarek? I told you that you could hang with me and drink a few beers in Paris.

P.S. my guess is that you are (and I haven't done the full PI investigation) Cech or Polish or...or...Or....I don't know, maybe you live in Germany (my sympathy goes to you in that case), but, see, most of the French I know don't like getting inebriated on beer while eating heavy, saucy, Jaegermeister-caught meat, so, I AM like that, and perhaps, YOU are like that, plus, you being the clear head, me being the mathematical fallen angel and such...well...er...as I said before, come to Paris....we'll talk all the math you wanna talk about.....could be manifolds or martingales....whatever...It don't matter....will go to the Cafè Cluny in the 5th and I'll hook you up bigtime....trust me on that one.

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Nonius

I'm going to Hell with FDAX as my Kharnak.

Edited: Fri Jun 27, 03 at 01:32 PM by Nonius

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Fri Jun 27, 03 02:38 PM

Edited: Wed Feb 25, 04 at 01:32 PM by gatarek

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Nonius
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Fri Jun 27, 03 02:44 PM

Quote
Originally posted by: gatarek
<a target=new class=ftalternatingbarlinklarge href="http://wilmott.com/310/messageview.cfm?catid=15&threadid=6651&STARTPAGE=1">Pedro, this is the beer thread </a>

ok Gatarek...it's done...Now, what flavor of women do you like?

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Nonius

I'm going to Hell with FDAX as my Kharnak.

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DoneEasily
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Fri Jun 27, 03 07:08 PM

'Risk-neutral' measure is often undestood as such a measure that all the financial products of interest are priced in the same way as the maket does. In this case the words "martingale measure" may be quite misleading as one may be tempted to imply that, say, in the case of equity derivatives the discounted stock price process being a martingale is sufficient for risk neutrality. While in fact the correct (market-consistent) pricing of a set of (all) traded equity derivatives is essential...

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Pat
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Thu Jul 03, 03 01:54 PM

Just to add to the confusion:

Often the term "risk neutral measure" is reserved for the measure induced using a money market numeraire (and the "forward measure" is used for the measure induced by a zero coupon bond, and the "Jamshidean" or "annuity" or "level" measure is used for the measure induced by using the PV01 of a swap as the numeraire)

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Nonius
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Thu Jul 03, 03 02:01 PM

Quote
Originally posted by: Pat
Just to add to the confusion:

Often the term "risk neutral measure" is reserved for the measure induced using a money market numeraire (and the "forward measure" is used for the measure induced by a zero coupon bond, and the "Jamshidean" or "annuity" or "level" measure is used for the measure induced by using the PV01 of a swap as the numeraire)

now I am totally confused...thanks Pat....I'm gonna go get a beer and calm down.

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Nonius

I'm going to Hell with FDAX as my Kharnak.

Posts: 82
Joined: Jul 2002

Fri Jul 04, 03 01:22 AM

Why aren't measures named after numeraires, then? So you would talk about the "bank account measure", the "discount bond measure", the "swap measure" and so on. I think that would be much less confusing.

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Nonius
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Fri Jul 04, 03 09:41 PM

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Originally posted by: doctorwes
Why aren't measures named after numeraires, then? So you would talk about the "bank account measure", the "discount bond measure", the "swap measure" and so on. I think that would be much less confusing.

probably because a) it's a pain caring around the adjective, b) because they are all equivelent to each other anyway and c) actually, some people do qualify the measure with numeraire choice.

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Nonius

I'm going to Hell with FDAX as my Kharnak.

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