Kurtosis CMP Chapter 6

[TryingHardToPass]

On page 32, there is a box which mentions that "a distribution with a high kurtosis is called 'platykurtic', a distribution with low kurtosis is called 'laptokurtic', and a distribution with medium kurtosis is called 'mesokurtic'."

Google definition seem to suggest that the definition in the CMP notes are reversed (i.e. The term “platykurtic” refers to a statistical distribution with negative excess kurtosis. It has fewer extreme events than a normal distribution.) Which is the correct definition?

Thanks in advance

 

[TryingHardToPass]

Sorry another question on the same chapter:

For Question 6.2, the formula to apply to change measure is:
\[E_Q[X_t|F_s]=\frac{1}{M_s}E_P[M_tX_t|F_s] \]

Where does the \[\frac{1}{M_s}\] come from? Page 6 of Chapter 6 mentions that the way to change probability measure is:
\[ E_Q[C]=E_P[\frac{dQ}{dP}C]\]

 

[Steve Hales]

On page 32, there is a box which mentions that "a distribution with a high kurtosis is called 'platykurtic', a distribution with low kurtosis is called 'laptokurtic', and a distribution with medium kurtosis is called 'mesokurtic'."

Hi
Thanks for pointing this out. Leptokurtic definitely refers to having higher kurtosis. I'll make sure this is corrected in the next edition of the Course Notes.
Thanks again.

 

[Steve Hales]

Where does the \[\frac{1}{M_s}\] come from?

Check out page 68 of Baxter and Rennie - the full explanation is given there. Briefly, \(M_t\) represents the change in the measure up to time \(t\), but because in Question 6.2 we're conditioning on \(F_s\) we really only want the change in measure between time \(s\) and time \(t\); this is given by \(M_t/M_s\). Since \(M_s\) is known at time \(s\) it can come outside of the expectation operator.
Hope that helps.

 

[TryingHardToPass]

Check out page 68 of Baxter and Rennie - the full explanation is given there. Briefly, \(M_t\) represents the change in the measure up to time \(t\), but because in Question 6.2 we're conditioning on \(F_s\) we really only want the change in measure between time \(s\) and time \(t\); this is given by \(M_t/M_s\). Since \(M_s\) is known at time \(s\) it can come outside of the expectation operator.
Hope that helps.

Thank you so much Steve for the reference. The explanation was quite intuitive as well, really helpful