Actuarial Outpost
 
Go Back   Actuarial Outpost > Exams - Please Limit Discussion to Exam-Related Topics > SoA/CAS Preliminary Exams > Investment / Financial Markets
FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions


Investment / Financial Markets Old Exam MFE Forum

Reply
 
Thread Tools Search this Thread Display Modes
  #1  
Old 10-30-2019, 05:22 PM
lilj0825 lilj0825 is offline
CAS SOA
 
Join Date: Apr 2017
College: college graduate
Posts: 16
Default Example 10.1.3

Hello, people. Can I ask a question about example 10.1.3?

I understand why the answer is C, but could't it be also A by using what was used in example 10.1.1, using a call option instead of a put option?
Reply With Quote
  #2  
Old 10-30-2019, 11:42 PM
tkt's Avatar
tkt tkt is offline
Member
CAS SOA
 
Join Date: Jun 2011
Location: Des Moines
College: Drake University
Posts: 531
Default

It'd help to state the what resource you are referring to.
__________________
Tong Khon Teh, FSA, CFA
Product Manager, Actuarial
coachingactuaries.com
Reply With Quote
  #3  
Old 10-31-2019, 04:34 PM
lilj0825 lilj0825 is offline
CAS SOA
 
Join Date: Apr 2017
College: college graduate
Posts: 16
Default

I am sorry. I forgot to mention which book it is. It is Actex IFM summer 2018 edition.
Reply With Quote
  #4  
Old 10-31-2019, 06:07 PM
tkt's Avatar
tkt tkt is offline
Member
CAS SOA
 
Join Date: Jun 2011
Location: Des Moines
College: Drake University
Posts: 531
Default

Can you post the question and the answer choices here? That way, people from the forum can take a look and chime in.
__________________
Tong Khon Teh, FSA, CFA
Product Manager, Actuarial
coachingactuaries.com
Reply With Quote
  #5  
Old 11-01-2019, 02:48 AM
lilj0825 lilj0825 is offline
CAS SOA
 
Join Date: Apr 2017
College: college graduate
Posts: 16
Default

A variable annuity has the following guarantees:
-Guaranteed minimum death benefit with a return of premium guarantee.
-Guaranteed minimum accumulation benefit with a return of premium guarantee, effective
10 years from the date the policy is sold.
-Earnings-enhanced death benefit that pays the beneficiary an additional benefit equal to
20% of any increase in the account value.

P(T) denotes the value of a Euro put option on the annuity value, with the strike price equal to the original amount invested and tie to expiration T.

A) C(t)f(t)dt+Pr(T>=10)*P(10)+0.2*C(t)f(t)dt

C) P(t)f(t)dt+Pr(T>=10)*P(10)+0.2*C(t)f(t)dt
Reply With Quote
  #6  
Old 11-01-2019, 02:37 PM
tkt's Avatar
tkt tkt is offline
Member
CAS SOA
 
Join Date: Jun 2011
Location: Des Moines
College: Drake University
Posts: 531
Default

Quote:
Originally Posted by lilj0825 View Post
A variable annuity has the following guarantees:
-Guaranteed minimum death benefit with a return of premium guarantee.
-Guaranteed minimum accumulation benefit with a return of premium guarantee, effective
10 years from the date the policy is sold.
-Earnings-enhanced death benefit that pays the beneficiary an additional benefit equal to
20% of any increase in the account value.

P(T) denotes the value of a Euro put option on the annuity value, with the strike price equal to the original amount invested and tie to expiration T.

A) C(t)f(t)dt+Pr(T>=10)*P(10)+0.2*C(t)f(t)dt

C) P(t)f(t)dt+Pr(T>=10)*P(10)+0.2*C(t)f(t)dt
The only difference between A and C is the first term, which pertains to a guaranteed minimum death benefit with a return of premium guarantee. This thing pays the larger of the account value and the original amount invested when the policyholder dies.

Let K be in the initial amount invested and S_T be the account value at time T when the policyholder dies. The beneficiary receives the larger of the two values at time T, max(S_T, K), which can be rewritten as:

max(S_T, K) = S_T + max(0, K - S_T)

Without any guarantee, observe the beneficiary would simply receive S_T. Thus, the additional value of this guarantee is max(0, K - S_T), which is the payoff of a European put option. That's why the value of the guarantee is the value of this put option (not call option), and thus we should have P(t) (not C(t)) in the first term.
__________________
Tong Khon Teh, FSA, CFA
Product Manager, Actuarial
coachingactuaries.com
Reply With Quote
  #7  
Old 11-01-2019, 05:04 PM
lilj0825 lilj0825 is offline
CAS SOA
 
Join Date: Apr 2017
College: college graduate
Posts: 16
Default

Bye the way, the question is from question 39 from the official IFM sample question.

I understand why it forms the payoff of a put option. My question is that can it also form the payoff of a call option because max(S_T, K) can also be K + (S_T - K, 0). Question 37 from the official IFM sample question uses this. The reason that question 37 can use the payoff of a call is that it did not state return of premium guarantee?

Moreover, shouldn't the answer of question 39 also have S_T? The answer I think is S_T + P(t)f(t)dt + Pr(T>=10)*P(10) + 0.2*C(t)f(t)dt.
Reply With Quote
  #8  
Old 11-03-2019, 03:59 PM
tkt's Avatar
tkt tkt is offline
Member
CAS SOA
 
Join Date: Jun 2011
Location: Des Moines
College: Drake University
Posts: 531
Default

Quote:
Originally Posted by lilj0825 View Post
Bye the way, the question is from question 39 from the official IFM sample question.

I understand why it forms the payoff of a put option. My question is that can it also form the payoff of a call option because max(S_T, K) can also be K + (S_T - K, 0). Question 37 from the official IFM sample question uses this. The reason that question 37 can use the payoff of a call is that it did not state return of premium guarantee?

Moreover, shouldn't the answer of question 39 also have S_T? The answer I think is S_T + P(t)f(t)dt + Pr(T>=10)*P(10) + 0.2*C(t)f(t)dt.
The value of the first guarantee is given by the P(t)f(t)dt piece, and the value of the annuity with the guarantee is given by S_T + P(t)f(t)dt. Since the question is only looking for the combined value of all guarantees, not of the entire annuity, we don't need to include the S_T term.
__________________
Tong Khon Teh, FSA, CFA
Product Manager, Actuarial
coachingactuaries.com
Reply With Quote
  #9  
Old 11-11-2019, 01:53 PM
lilj0825 lilj0825 is offline
CAS SOA
 
Join Date: Apr 2017
College: college graduate
Posts: 16
Default

Ok. Thank you for answering my question!
Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


All times are GMT -4. The time now is 04:12 AM.


Powered by vBulletin®
Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.
*PLEASE NOTE: Posts are not checked for accuracy, and do not
represent the views of the Actuarial Outpost or its sponsors.
Page generated in 0.30889 seconds with 9 queries