Convexity adjustment for Eurodollar futures

A key difference between a futures contract and a forward contract is daily settlement: the instrument is daily marked-to-market. If the value of the futures increases, this creates excess margin cash; if value declines, there will be a margin call (when the maintenance level is reached). Therefore, a Eurodollar futures contract has more volatility than a similar forward rate agreement (FRA). This implies a slightly higher rate.

Category:

Education

Tags:

• Finance
• futures
• forward
• risk
• derivatives
• eurodollar

[McQuack1]

Isn't any continuously compounded rate lower than any other time frequency compounded rate?

Then because 90/360 =1/4, a quarterly compounded rate R means

(1+R/4)^4 = 1 + Q where Q is the annually compounded rate.

Similarly, if r is the continuously compounded rate, by definition

exp ( r * 1) =1 + Q.

In other words, (1+ R/4) ^ 4 = exp (r*1) or r = ln [ ( 1+ R/4)^4 ] = 4 * ln ( 1+R/4).

Numerically r = 4 * ln ( 1 + 6% /4 ) = 4 * ln ( 1+0.015) = 5.9554%

[bionicturtledotcom]

@McQuack1 Yes, you are exactly correct.

Apologies that i did not hover longer on the fact that the formula used is LN(1+6%/4)*365/90. You will notice the multiplier (365/90) is performing DAY COUNT conversion (ie, in addition to the frequency conversion) from actual/360 (money market) to ACT/365 (bond). I followed Hull's example here. So two factors (although the final is correct!).

But your rule is good and useful for checking cals, of course: r[continuous] < r[discrete]. thanks!

[taniya2312]

@JohnBocca01 its a treasury bond. u hav to take day count convention as actual/actual. so the calcu is LN(1.015)=0.014888612 ; 1.489*365/90= 6.04.

[MrDrOli]

Dfuts are Act/360

“Tailing" due to margining is NOT FRA convexity. FRA cvx exists without margining. It’s due to different conventions. Futures = "discount yield"

F=100–f

FRA's rely on simple interest

F*~1/(1+f*T)

Fut = linear price/yield relationship. FRA's = non-linear (i.e. "convexity" in p/y).

Margining issues need, at least, 2 rates (e.g. O/N, & term), correlation, and margins.

BTW, FRA's (anything) can be margined.

see arbitrage-trading. com/TG2_BSandIR_Vol1. htm

[JohnBocca01]

Nice presentation but the conversion of the quarterly compounded interest rate into an equivalent continuously compounded rate is wrong. The correct rate is not 6.04% but 5.9554%. The formula is 4 * ln(1+R/4), where R is the quarterly compounded rate (6%).