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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.
Jun
12
comment Physical or Real-world Probability Measure
so then let me ask you, how do you discount your terminal payoff when you price a derivative under the real-world probability measure ?
Jun
12
comment Physical or Real-world Probability Measure
Can you elaborate on your statement because in its current form I would tend to disagree. There are many real world probability measures, in fact there are countless real world probability measures even for a single asset hence the interest of market participants to price in risk neutral terms. Real world probability measures are a function of utility.
Jun
12
comment Calculating the rate of return over a year then the data for a year before does not exist
Very simple, you calculate the absolute return over the two data points and then convert to an annualized rate...done.
Jun
11
comment Black-Scholes under stochastic interest rates
is this homework or an assignment?
Jun
11
comment Distribution of Black Scholes call option price at time 0<t <T
is this homework or an assignment?
Jun
11
comment Why using the swap curve as riskfree rate and no longer gov bonds?
Nice answer, additional comment to OP: The answer of the interviewer is actually imprecise and I would expect from the interviewer to state that the OIS curve is used. There are a gazillion "swap curves" out there. Obviously for your next interviews if such question comes up again you can also ask back what the interviewer means with "swap curve". 2 things can happen: a) Interviewer appreciates your curiosity and (rightly) deems asking for more details important, b) he/she feels challenged in which case you might consider whether you want to work for someone who takes issue with curiosity.
Jun
10
comment Is R being replaced by Python at quant desks?
Thanks, vonjd, I took a quick look but am frankly not a big fan of generalized comparison reviews because it does not address specific needs (for obvious reasons).
Jun
9
revised How to short an option?
added 131 characters in body
Jun
9
comment How to short an option?
I do not like to hijack this comment section. Please check out some basic text on exchange traded options as your assumptions are quite incorrect.
Jun
9
comment How to short an option?
Yes why not? Of course it depends on certain requirements. For example US citizens (possibly even residents) may not be permitted to trade specific options contracts.
Jun
9
comment How to short an option?
There is no standard vs non standard. Options are options, whether written on corn or toys or a stock index. You can short an option, one of which you do not hold long inventory at any exchange that lists options contracts (subject to certain exchange regulations such as margin requirements). Please see my answer