Science of Term Structure- Arbitrage pricing multiple periods

[Shau_2207]

Hello David, I have a question under Topic Term Structure Science under that LOS- Arbitrage pricing of derivatives over multiple periods. Page 23

i am unable to follow the attached eq, how do we calculate bond value of P(1,1) and P (1,0) for given risk neutral probabilities. In exam will we be getting these values or we would need to find them?

 

[gsarm1987]

Hello David, I have a question under Topic Term Structure Science under that LOS- Arbitrage pricing of derivatives over multiple periods. Page 23

i am unable to follow the attached eq, how do we calculate bond value of P(1,1) and P (1,0) for given risk neutral probabilities. In exam will we be getting these values or we would need to find them?

@Shau_2207 please allow me to answer:
P(1,1) = from next two branches (Up & down) Expected value is being discounted by the rate prevalent at the node
This is better understood if we use a binomial tree diagram. See page 22, Reading 5 in BT notes.
For exam you may be given info such as:

1. The rate prevalent from year zero to next nodes
2. Up move and down move, from there you calculate probability and sometimes they give you probability
3. Par/face value so you may know end what is the cashflow, then discount all the way back from there, scooping periodic coupons on your way

As a hint:
Plot interest rate tree from left to right, starting from year 0 to 1.5
then, from right to left, start discounting the cashflows taking expected present values (i.e average of what it would be with probability of up and probability of down)
In real world probabilities its farily simple (50%-50%) but in risk neutral, it needs to be calculated q=probability of up = (1+rf-down)/(up-down) where as probability of down is (1-q). some authors use p.


If you need excel workings Look for https://www.dropbox.com/s/ghak7t80e021kcb/T5.b_2012_XLS_bundle_tuckman_v1010.xlsx, Tab: 5b.4 RiskNeutralPricing (p177)

Let me know if its clear.

 

[Shau_2207]

Understood Thank You

 

[Shau_2207]

@gsarm1987 , sorry to come back on this again. can you reshare the spreadsheet? I am not able to open it.

 

[gsarm1987]

@gsarm1987 , sorry to come back on this again. can you reshare the spreadsheet? I am not able to open it.

I think its due to the package you have. did you opt for spreadsheets along with videos? not then you may consider an upgrade?

 

[David Harper CFA FRM]

Hi @Shau_2207 Please see the sheet at "29.7 Three Steps" and the subsequent in the attached "P2.T5.Tuckman_Ch7_v1.4.xlsx"
(also here at https://www.dropbox.com/s/4ords2u1c2l20dy/P2.T5.Tuckman_Ch7_v1.4.xlsx?dl=0)

 

[Shau_2207]

Thank you so much @David Harper CFA FRM

 

[David Harper CFA FRM]

Apologies to you Goher (@gsarm1987 ): your response is the correct response here! I had this thread backlogged, and in haste, I provided the XLS. For future reference @Shau_2207 please know that he's correct: these learning XLS are part of the upgraded package. Thanks for understanding.

 

[Shau_2207]

Apologies to you Goher (@gsarm1987 ): your response is the correct response here! I had this thread backlogged, and in haste, I provided the XLS. For future reference @Shau_2207 please know that he's correct: these learning XLS are part of the upgraded package. Thanks for understanding.

Understood @David Harper CFA FRM . Np

 

[aalirahman]

Hi @David Harper CFA FRM I am tryin to reach the link below (provided in the practice question sets ) to understand 41.2 (Risk neutral derivative pricing ), however I am unable to access it.

https://forum.bionicturtle.com/threads/l2-t5-41-risk-neutral-derivative-14

 

[Nicole Seaman]

Hi @David Harper CFA FRM I am tryin to reach the link below (provided in the practice question sets ) to understand 41.2 (Risk neutral derivative pricing ), however I am unable to access it.

https://forum.bionicturtle.com/threads/l2-t5-41-risk-neutral-derivative-14

Hello @aalirahman I believe you are trying to access this link: https://forum.bionicturtle.com/threads/l2-t5-41-risk-neutral-derivative-pricing-tuckman.3553/. I retrieved that link from the practice question set. Are you seeing something different on your PDF?

 

[aalirahman]

Hello @aalirahman I believe you are trying to access this link: https://forum.bionicturtle.com/threads/l2-t5-41-risk-neutral-derivative-pricing-tuckman.3553/. I retrieved that link from the practice question set. Are you seeing something different on your PDF?

Hi, I see the same link but when I click on the link I see this error and I am unable to access the respective forum page. I am also unable to copy the link from vital source otherwise I can easily copy and paste in the browser. I am facing similar problems with other links as well. Please look at the Screenshot below, this is where it takes me when I click the link in vital source.

 

[aalirahman]

@Nicole Seaman I see the same error when I click the link for 305.3 ( Vasicek Model for Interest Rates) - I am unable to reach the forum. When I click the link in the below screenshot 1 I see the error "No pass zone" (screenshot 2). However the only difference is that the link it takes me to is the same as mentioned in vital source document.

 

[Nicole Seaman]

@Nicole Seaman I see the same error when I click the link for 305.3 ( Vasicek Model for Interest Rates) - I am unable to reach the forum. When I click the link in the below screenshot 1 I see the error "No pass zone" (screenshot 2). However the only difference is that the link it takes me to is the same as mentioned in vital source document.

View attachment 4168
View attachment 4169

@aalirahman I am going to send you a private message, so we are not trying to troubleshoot this in this forum thread. We want to keep the discussion here about the content. I have had other people test the links, and they aren't having any issues, so it seems to be an issue with only your account. Please look for my private message in the forum. Thank you.

 

[FGarc9983]

Hi @Shau_2207 Please see the sheet at "29.7 Three Steps" and the subsequent in the attached "P2.T5.Tuckman_Ch7_v1.4.xlsx"
(also here at https://www.dropbox.com/s/4ords2u1c2l20dy/P2.T5.Tuckman_Ch7_v1.4.xlsx?dl=0)

Hi David,

I do not understand where the value p 0.8024 comes from. It just seems to pop out of nowhere in the readings (the previous value calculated was 80.1% not 80.24%) and in the spreadsheets they are also shown as fixed values. Where did it come from?

 

[gsarm1987]

Hi David,

I do not understand where the value p 0.8024 comes from. It just seems to pop out of nowhere in the readings (the previous value calculated was 80.1% not 80.24%) and in the spreadsheets they are also shown as fixed values. Where did it come from?

Is it tab 27.9 of the spreadsheet? Plz let me know where you are seeing 0.8024 risk neutral probability. I'll be able to help you out.

 

[gsarm1987]

Hi David,

I do not understand where the value p 0.8024 comes from. It just seems to pop out of nowhere in the readings (the previous value calculated was 80.1% not 80.24%) and in the spreadsheets they are also shown as fixed values. Where did it come from?

These are two different tabs. You are looking at 29.7 CMS there 80.24% is given as is, not calculated. Where as in 29.7 replicated portfolio tab it's calculated. You'll find the method up there in chain of comments, I also commented. So basically you are looking at two different cases.

 

[FGarc9983]

These are two different tabs. You are looking at 29.7 CMS there 80.24% is given as is, not calculated. Where as in 29.7 replicated portfolio tab it's calculated. You'll find the method up there in chain of comments, I also commented. So basically you are looking at two different cases.

Thanks! That clarifies it. Since it was pretty similar and it wasn't explicitely mentioned that it was given, I was confused as to where that value came from.