Convexity
From WilmottWiki
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Non-mathematical description
Convexity in interest rates is often described as an effect when a payment of a given rate is made on a "non-natural" date. A classical example of this is a Libor rate paid not on its end date, but on its fixing date, resulting in the so-called (confusingly named) Libor-in-arrears payment.
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Types of convexity
The following are the most common types of convexity
- Libor-in-arrears
- Libor-with-payment-delay (Libor rate paid at an arbitrary date different from the end date)
- Averaging Libor (payment is made based on the average of Libor rates over a given observation period)
- CMS rate (swap rate paid at fixing)
- CMS with delay (swap rate paid at some time after fixing)
- Eurodollar future
- Quanto
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Mathematical description
From a mathematical standpoint, convexity arises a measure used to value a contract is different from the one "natural" for the underlying rate. For example, CMS convexity arises because the expected value of the swap rate needs to be evaluated under the payment-date forward measure, and not the swap measure under which the rate is a martingale.
