Convexity (SOA Exam FM – Financial Mathematics – Module 4, Section 4)

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SOA Exam FM (Financial Mathematics) Module 4, Section 4

After completing this video you should be able to:
- Define and recognize the definitions of the following terms: convexity (Macaulay and modified).
- Calculate:
• The duration and convexity of a set of cash flows.

Definition given in the video:

The Macaulay convexity of a set of payments is the weighted average of the squares of the times of the payments, where the weight assigned to the payment at time 𝑡 is equal to the present value of the payment at time 𝑡 divided by the present value of all the payments.

Example given in the video:

For the set of payments given in the video, using 𝑖=0.06, determine:
(a) the Macaulay convexity, and
(b) the modified convexity.