April 2021 Question 2

[Molly]

Hi All,

Just trying part ii of this question. I am able to get to the answer, but i cant reconcile the option values at time 0 and time 1 that the examiners report has?

i would have said that the option value at time 1 would have been
payoff at time 1 (ie 150-120=30)
*q (4/9)
which gives 30*4/9=13.33
but the option value in the solutions in the tree is 12.29?

Please can someone help me on how the solutions have got to this?

Thanks,
Molly

 

[John Potter]

Careful - there is no payoff at time 1. The option value at time 1 (at the 150 node) is the payoff from time 2 (187.5-4-120 = 63.5) multiplied by q, 28.222222. To get the value at time 0, you multiply by q again, 12.54. Easier to multiply by q^2 to begin with.

Spend a bit of time here thinking about what the call option is, WHERE is pays out, etc.

John

 

[Molly]

Careful - there is no payoff at time 1. The option value at time 1 (at the 150 node) is the payoff from time 2 (187.5-4-120 = 63.5) multiplied by q, 28.222222. To get the value at time 0, you multiply by q again, 12.54. Easier to multiply by q^2 to begin with.

Spend a bit of time here thinking about what the call option is, WHERE is pays out, etc.

John

Hi John,

Thank you so much for this. The figures that you have quoted 28.22 and 12.54 are also what I got for option value at node time 1 and node time 0 - I am just confused about the solutions giving figures of 27.94 and 12.94 instead. Could it be an error in the solutions?

thank you also for clarifying on my mistake about having a payoff at time 1 for a call option, that’s helpful!

Regards,
Molly

 

[John Potter]

Hi Molly,

I can't see the 27.94 and 12.9 anywhere in our ASET solution, I really have no clue as to where they come from??

There is an alternative way of dealing with the dividend, where you set aside the discounted value of 4 now (also = 4 since no discounting) and pretend that the share is only worth 116. This method actually makes things easier because the tree still recombines. (The method we've used, the tree would not recombine after the dividend, since (d - 4)*u is not the same as (u-4)*d.)

However, this method leads to 12.10 and not 12.9.

I wouldn't worry about it. What you've done is great, either method would be fine in the exam, though you should probably be aware of the different methods in case the question wording effectively prescribes one of the methods.

John

 

[Molly]

Hi Molly,

I can't see the 27.94 and 12.9 anywhere in our ASET solution, I really have no clue as to where they come from??

There is an alternative way of dealing with the dividend, where you set aside the discounted value of 4 now (also = 4 since no discounting) and pretend that the share is only worth 116. This method actually makes things easier because the tree still recombines. (The method we've used, the tree would not recombine after the dividend, since (d - 4)*u is not the same as (u-4)*d.)

However, this method leads to 12.10 and not 12.9.

I wouldn't worry about it. What you've done is great, either method would be fine in the exam, though you should probably be aware of the different methods in case the question wording effectively prescribes one of the methods.

John

Hi John,

That's really help to know about the other method, thank you so much! The figures come from the solutions on the IFOA past papers site, but your figures and explanation makes much more sense!

Thanks