Differentiating definite integrals and EMM?

[Alfie]

Hi, Question 8 from april 2012 has pointed me to page 3 of the tables. The formula i am trying to differentiate is

d/dK (1/100 \int^\infty_K D(a)da)

if i was to use the page 3 formula
b(y)=\infty
so b'(y)=0
f(b(y),y)=D(\infty)
a(y)=K
so a'(y)=1
f(a(y),y)=D(K)
putting this in i get
d/dK (1/100 \int^\infty_K D(a)da) = 1/100(-D(k)+\int^\infty_K d/dK D(a)da). Where does the rightmost term go in the solutions as the answer seems to just be 1/100(-D(k))?

Also on the topic of Black Scholes, april 2013 question 9 - mentions 'Q is the EMM', what does this abbreviation mean?

Thank you

 

[Alfie]

Hi, Question 8 from april 2012 has pointed me to page 3 of the tables. The formula i am trying to differentiate is

d/dK (1/100 \int^\infty_K D(a)da)

if i was to use the page 3 formula
b(y)=\infty
so b'(y)=0
f(b(y),y)=D(\infty)
a(y)=K
so a'(y)=1
f(a(y),y)=D(K)
putting this in i get
d/dK (1/100 \int^\infty_K D(a)da) = 1/100(-D(k)+\int^\infty_K d/dK D(a)da). Where does the rightmost term go in the solutions as the answer seems to just be 1/100(-D(k))?

Also on the topic of Black Scholes, april 2013 question 9 - mentions 'Q is the EMM', what does this abbreviation mean?

Thank you

To add to the question about april 2013 question 9 - am seeing quite similar questions , ie sept2014 question 7 asking for max(B_s+\mus) - i cant seem to see anything about this in the course notes, are these types of questions no longer in the syllabus?

 

[John Potter]

Hi Alfie,

d/dK D(a) = 0 since D(a) does not depend on K.
EMM = equivalent martingale measure (a different name for the risk-neutral probability measure)
April 2013 question 9 is tough and would be considered a "higher order skills" question. It's obviously one of those questions where the writer of the time had a bit of an imagination, as well as love for all things Black-Scholes and decided it was a good idea to share their interesting findings in the form of an exam question. TBH it's the kind of thing I do too - just yesterday, for example, an SP6 student of mine asked a very clever question (he/she asked a few in fact) and it made me think of a good question I could write for a Mock exam, say. However, I've enough experience in my job to know in advance that the inner workings of my head on a given topic are not necessarily accessible to everyone else inside 20 minutes, say, no matter how well I word the question. Not all question writers have necessarily had the time for this experience to bed in, shall we say. So, you're going to get these questions where you have to think about it on the day - there simply isn't enough space in the notes to cover every single possible question that could be dreamt up within the Black-Scholes framework.

Importantly, we should do many past papers and any question we hit that we consider to be "higher order skills", we effectively add it to the list of possible non-"higher order skills" questions that we will be prepared for next time. We also learn during this process that we could well hit a "higher order skills" question in the exam, which we simply can't do, possibly even because it was unreasonable to expect anyone could ever do it under the time pressure. We cope with it by "saving it until the end" and scoring well on the rest of the exam paper,

Good luck!
John

 

[Alfie]

Hi Alfie,

d/dK D(a) = 0 since D(a) does not depend on K.
EMM = equivalent martingale measure (a different name for the risk-neutral probability measure)
April 2013 question 9 is tough and would be considered a "higher order skills" question. It's obviously one of those questions where the writer of the time had a bit of an imagination, as well as love for all things Black-Scholes and decided it was a good idea to share their interesting findings in the form of an exam question. TBH it's the kind of thing I do too - just yesterday, for example, an SP6 student of mine asked a very clever question (he/she asked a few in fact) and it made me think of a good question I could write for a Mock exam, say. However, I've enough experience in my job to know in advance that the inner workings of my head on a given topic are not necessarily accessible to everyone else inside 20 minutes, say, no matter how well I word the question. Not all question writers have necessarily had the time for this experience to bed in, shall we say. So, you're going to get these questions where you have to think about it on the day - there simply isn't enough space in the notes to cover every single possible question that could be dreamt up within the Black-Scholes framework.

Importantly, we should do many past papers and any question we hit that we consider to be "higher order skills", we effectively add it to the list of possible non-"higher order skills" questions that we will be prepared for next time. We also learn during this process that we could well hit a "higher order skills" question in the exam, which we simply can't do, possibly even because it was unreasonable to expect anyone could ever do it under the time pressure. We cope with it by "saving it until the end" and scoring well on the rest of the exam paper,

Good luck!
John

Thank you very much John