Monte Carlo Variance Reduction using Antithetic Variates (FRM Part 1, Quantitative Analysis)

In this video from FRM Part 1 curriculum, we take a look a the antithetic variates technique to reduce the standard error of our Monte Carlo based estimator. This technique simulates the chosen variable as a pair of values - with the members of the pair having a negative dependence amongst themselves. This negative dependence reduces the variance of the estimator and hence, the standard error. For more videos on FRM Part 1 preparation, please visit the course page: www.finRGB.com....

[@finRGB]

FRM Learning Objective: Explain the use of antithetic and control variates in reducing Monte Carlo sampling error.

[@karimkhaled8040]

An Msc in financial engineering would be impossible without this channel! Thank you!

[@saulmendoza1652]

clear as water!

[@jaquelinemoreira7385]

Amazing explanation! thank you so much, it was really helpful

[@finRGB]

Glad that the video was helpful, Jaqueline.

[@spp626]

Amazing explanation! Thank you.

[@reski6043]

Thank you sooo much!! This is very clear

[@finRGB]

Glad you found the video helpful.

[@georgey.5637]

Wow! Nice explanation! Thank you!

[@MeganBrownprotagonist]

Thank you! You explained that so clearly.

[@finRGB]

Glad that you found the video useful, Megan.

[@ca_saurabhgoyal]

Can someone explain how he equated 1-U1=U2? I didn't get this step ?

[@finRGB]

From U1, we create another random variable U2 = 1 - U1. U2 is intuitively an antithesis of U1 (when U1 is high, U2 is low and vice versa).

[@cheungruth7348]

@@finRGBwhere did 1 come from? If U ~N(0,1) , what would be the U2?

[@finRGB]

@@cheungruth7348 U follows the Unif(0,1) distribution (so does U2).

[@HristosPerhanidis]

You wanted to say squared instead of quadroupled right?

[@randomchick19-c7x]

No quadrupled because sqrt(n*4) = 2* sqrt(n) basically doubling your denominator

[@Mawesome111]

You da man!