Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    Doing a financial elective which I am really struggling with. Think this has got something to do with trinomial interest rate models?
    Any help will be really appreciated

    Time is counted from the present t = 0 in years. Suppose for the first 12 years the force of interest is 5%. After that it changes to 3% with probability 0.25, remains unchanged with probability 0.5 and increases to 7% with probability 0.25.

    Find the expected present value of a continuous payment stream of £143 per annum for 20 years, beginning at time 0.
    Offline

    3
    ReputationRep:
    I would do it using recurrence relations, but that's still a fairly labour intensive method of getting to the answer. Would be interested in hearing a better method!

    I'm guessing that calculating an expected interest rate after 12 years will be needed to express the present value as a single function?
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by maxh1994)
    Doing a financial elective which I am really struggling with. Think this has got something to do with trinomial interest rate models?
    Any help will be really appreciated

    Time is counted from the present t = 0 in years. Suppose for the first 12 years the force of interest is 5%. After that it changes to 3% with probability 0.25, remains unchanged with probability 0.5 and increases to 7% with probability 0.25.

    Find the expected present value of a continuous payment stream of £143 per annum for 20 years, beginning at time 0.
    I presume working out the value for a fixed interest rate over a period of time is straight forward for you.

    So, assume it changes to 3% after 12 years, and work out the value.

    Assume it remains at 5% and work out the value.

    Etc.

    Then E(X)=\sum x_iP(X=x_i)

    where x_i ranges over the three values.

    No trinomials required.

    I am presuming that once the interest rate changes after 12 years, it then remains fixed at that new value.
    Offline

    3
    ReputationRep:
    Is the implication of finding the "expected present value" not looking for an expression that can be evaluated to give an answer for any given value 't'?

    If not and just a final answer is being sought, then recurrence relations and the usual method for expected values would be my choice.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by ghostwalker)
    I presume working out the value for a fixed interest rate over a period of time is straight forward for you.

    So, assume it changes to 3% after 12 years, and work out the value.

    Assume it remains at 5% and work out the value.

    Etc.

    Then E(X)=\sum x_iP(X=x_i)

    where x_i ranges over the three values.

    No trinomials required.

    I am presuming that once the interest rate changes after 12 years, it then remains fixed at that new value.
    So once i have worked out the values at 3%,5%, 7%, I then times them by their probabilities and add them all together?
    • Study Helper
    Offline

    15
    Study Helper
    (Original post by maxh1994)
    So once i have worked out the values at 3%,5%, 7%, I then times them by their probabilities and add them all together?
    Yep.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by ghostwalker)
    Yep.
    Thanks man, got it.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: December 5, 2014
Poll
Do I go to The Streets tomorrow night?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.