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Jul
25
awarded  Good Answer
Jul
24
comment Libor OIS basis swap equation
The paper @Olorun mentioned looks quite interesting. Keep in mind that for your stated problem you need to derive OIS rates, hence you need to build an OIS curve. A traditional libor curve is of very little help here. Most practitioners nowadays build OIS curves rather than libor curves. So for your situation you need OIS rates as input and need to build an OIS curve. Libor curves are irrelevant in this context.
Jun
23
awarded  Popular Question
Jun
21
comment Interpretation of Drift
as @emcor pointed out you need to average out many discretizations (not just one) in order to meaningfully isolate the drift. Your drift isolation via MLE should come very close to your actual drift.
Jun
18
answered Sharpe ratio and leverage
Jun
16
comment Importance Sampling - where to center the sampling distribution?
usually people carry through with the distributional assumption that underlies BS. Some seem to apply exponential change of measure via a cumulant generating function (but I can't comment on it as I have never used it). Have you considered control variate methods and otherwise QMC?
Jun
15
comment Physical or Real-world Probability Measure
Thats ok then, no worries :-) I simply wanted to confirm whether you talk about probability measures when you refer to "measures" and probability spaces when you refer to "measurable spaces". But seems I overlooked you already rephrased yourself in specifying you are talking about probability measures and probability spaces. By the way I quoted from Shreve's text book, cheers.
Jun
15
comment Physical or Real-world Probability Measure
Do you mind clearly defining what you mean with "measures" vs probability measures and "measurable space" vs probability space? I feel we are dancing around terminology because definitions are not agreed upon.
Jun
15
comment Physical or Real-world Probability Measure
...in the same probability space you can have random variables that have two expectations, "one under the original probability measure $P$..., and the other under the new probability measure $\tilde P$.,... (Shreve, Stochastic Calculus for Finance II, 2004 Edition, P.210). Both probability measures live in the same probability space.
Jun
15
comment Physical or Real-world Probability Measure
...but admittedly the dice example is not a good one, I apologize for that. But it does not change my stance that in the same probability space you can have random variables that have two expectations, "one under the original probability measure $P$..., and the other under the new probability measure $\tilde P$.,... (Shreve, Stochastic Calculus for Finance II, 2004 Edition, P.210). Both probability measures live in the same probability space.
Jun
15
comment Physical or Real-world Probability Measure
that is not what I said. But to clear up the terminology confusion I seemingly have, you are basically saying both dice experiments are underlying one and the same identical real-valued probability function (because that is how your cited Wiki article defines a probability measure.
Jun
15
comment Physical or Real-world Probability Measure
I am happy to stand corrected, could you please help to clear up my confusion in case I am missing something or are we just rubbing elbows in terminology space?
Jun
15
comment Physical or Real-world Probability Measure
what about the example of a 6-sided vs 10-sided dice? Both reside in the real world, both in the same probability space, yet they both represent 2 very different probability measures, meaning, both represent their own real valued functions, defined on events in a shared probability space, and both satisfy measure properties.
Jun
15
comment Physical or Real-world Probability Measure
@AFK, I guess I am confused what you are trying to say here. Are you saying $P$ is the probability measure belonging to probability space ($\Omega, F, P$) and $\tilde P$ belongs to probability space ($\Omega, F, \tilde P$)? I am not a mathematician but this seems to disagree with how Shreve in his book Stochastic Calculus for Finance II defines probability spaces and measures.
Jun
14
comment Physical or Real-world Probability Measure
@Ulysses, one probability space ($\Omega, F, P$) already has two probability measures, $P$ and $\tilde P$
Jun
12
comment Physical or Real-world Probability Measure
Fully concur that terminology is key here. It is easy to get confused about probability space, probability measures, driving brownian motions/ random variables. And I agree that for the purposes OP described all 3 assets (domestic money market account, stock, and foreign money market account) do not have to be martingales.
Jun
12
comment Physical or Real-world Probability Measure
My point was that the precise reason risk-neutral probability measures are used is that there are uncountably many probability measures due to different risk preferences. As long as a probability measure lies between [0;1], the entire probability space sums to 1 and the empty set is 0 and the countable additivity property is satisfied you have a probability measure. There is one probability space but there can and there are many probability measures.
Jun
12
comment Physical or Real-world Probability Measure
...finding such is what drives market practitioners to taking the detour via risk-neutral pricing.
Jun
12
comment Physical or Real-world Probability Measure
every single random variable already has two expectations, one under the "real world" probability measure, one under a "new" probability measure. Radon Nikodym comes to mind and the same Radon Nikodym derivative can be applied to a whole derivative process. So maybe I misunderstood and we are talking on one hand about many different expectations vs a single probability measure. Certainly, it might be possible to not just derive a single additional "risk-free" probability measure but several such, but yes, only one "real world" probability measure exists...
Jun
12
comment Parametrizing the Radon Nikodym
I think what might be referred to here is the "change of measure" process. You can move a real random variable from a "real" probability space to a new probability space by defining a new random variable within the new probability space.