In this webcast Dr David Cox explains how the difference in convexity between a short term interest rate futures position, such as the Eurodollar contract, and an One of the most liquid interest rate contracts is the Eurodollar futures (or ED) contract (and its Euro and Yen equivalents). These are futures contracts with the 17 Jan 2017 No you are long convexity. The futures contract has no convexity (since its value is linear as the underlying rate varies, specifically it moves by $25 per bp per that govern futures contracts. Roughly put, as new information arrives the futures. LIBOR rates are correspondingly adjusted while structurally the forward LIBOR.
Therefore, a Eurodollar futures contract has more volatility than a similar forward rate agreement (FRA). This implies a slightly higher rate.
The magnitude of the adjustment, referred to as the convexity adjustment, can be quantified and is the topic of a future chapter. The magnitude of the adjustment depends on the volatility of spot LIBOR and on the maturity of the futures contract. A very good approximation to the adjustment is given by the formula: Adj =10,000× σ2(T2 2 + T 8). Technical Note No. 1* Options, Futures, and Other Derivatives John Hull Convexity Adjustments to Eurodollar Futures In the Ho-Lee model the risk-neutral process for the short rate in the traditional risk-neutral world is dr = θ(t)dt + σdz where r is the instantaneous short rate, θ is a function of time, a and σ are constants, and dz is a Wiener Eurodollar futures prices reflect IFRs in the FRA market because of the possibility that market participants may pursue arbitrage opportunities when prices become misaligned. Thus, one might consider an arbitrage transaction by investing in the third option at 0.83% and funding that investment by borrowing outright at the term six-month rate of 0.80%. A convexity adjustment is a change required to be made to a forward interest rate or yield to get the expected future interest rate or yield. Convexity adjustment refers to the difference between CHAPTER 5: 90 DAY EURODOLLAR FUTURES 71. 5.3 90 DAY EURODOLLAR FUTURES The 90 day LIBOR rate is the yield derived on a 90 day ED deposit. ED futures contracts that settle to a 90 day LIBOR rate are very actively traded.1. The underlying security is a $1,000,00090-day Libor deposit.
Convexity bias appears in short-term interest rate instruments because of the payoff differences in the futures market versus the OTC FRA market (aka forward
π0 =f(V0,F0)(4) forsomeappropriatefunctionf. Itcanthereforebeseenfrom(2)and(4)that the current forward rateL0 and its corresponding futures rate F0 are linked togetherby: F0. Determiningtheexplicitformofthefunctionf willenableusthrough(5), todeterminetheexactlinkbetweenF0 andL0,whichisthesocalledconvexity adjustment. The table shows the convexity bias between a position of short 1000 Eurodollar (ED) futures and an offsetting short $1005m 3-month FRA (slightly more than $1000m to compensate for discounting methodology), both instigated at a rate of 2%. With Eurodollar futures, you are locked in to lend at a certain rate in future. (gain for long position if the interest rate goes down). FRA - A forward contract - If you go long on an FRA, you have locked in the right to borrow at a certain rate in future.
The formula is only approximate due to the bond's convexity Adjust for difference in Therefore the rate implicit in Eurodollar futures is greater than the FRA.
FRA / Futures convexity has nothing to do with profits/losses being immediately recognised on the future through margin settlement, whilst deferred on the FRA. Although this seems to be a very common belief amongst many practitioners it is not correct. As it was written in the previous article “Futures and forward convexity adjustment”, there is a systematic advantage to being short EuroDollar futures relative to FRAs. This advantage is characterized as a convexity bias and appropriate methods exist to adjust Eurodollar futures prices to eliminate the difference between the futures and forward LIBOR rates. Since the Eurodollar futures contract applied to a three-month rate, the corresponding FRA is a three month rate also; e.g., FRA 3 x 6, FRA 9 x 12, FRA 12 x 15. At this point, no-arbitrage suggests the future rate in one year should be the same as an FRA 12 x 15 (the three month rate in one year). Contract specifications for Eurodollar futures, for example, set the daily margin payment at USD 25 per basis point move in the futures rate. While this margining formula couldn’t be simpler, by construction, it deprives Eurodollar futures of the convexity possessed by the forward rate agreements (FRAs) they are intended to mimic. π0 =f(V0,F0)(4) forsomeappropriatefunctionf. Itcanthereforebeseenfrom(2)and(4)that the current forward rateL0 and its corresponding futures rate F0 are linked togetherby: F0. Determiningtheexplicitformofthefunctionf willenableusthrough(5), todeterminetheexactlinkbetweenF0 andL0,whichisthesocalledconvexity adjustment. The table shows the convexity bias between a position of short 1000 Eurodollar (ED) futures and an offsetting short $1005m 3-month FRA (slightly more than $1000m to compensate for discounting methodology), both instigated at a rate of 2%. With Eurodollar futures, you are locked in to lend at a certain rate in future. (gain for long position if the interest rate goes down). FRA - A forward contract - If you go long on an FRA, you have locked in the right to borrow at a certain rate in future.
In this webcast Dr David Cox explains how the difference in convexity between a short term interest rate futures position, such as the Eurodollar contract, and an
The formula is only approximate due to the bond's convexity Adjust for difference in Therefore the rate implicit in Eurodollar futures is greater than the FRA. part of the curve is constructed using Eurodollar futures or forward rate agreements (FRA). CvxAdj the Future convexity adjustment quoted in basis points. Introduction Does the market price interest rate swaps correctly? For example, a short position in a FRA on the six-month LIBOR can be replicated by a (1981) , the forward price equals the futures price plus a convexity adjustment term. 5 Jun 2012 Eurodollar rates as forward rates• Eurodollar futures rates are considered Exercise (Libor FRA convexity)• Sell $100mm 3x9 IMM dated FRA today• + 90 days 2.033 yearsForward rate (after convexity adjustment) 0.9866% 1 Jul 2019 3.2.2 General Formula for Pricing Vanilla Interest Rate Swaps . 15. 4 Convexity Adjustments for Futures Rates. 17. 4.1 Vasicek Model . Replication Portfolio if Value of Long FRA Position >0 . . . . . . 15. 3. Comparison with 2 Convexity Adjustment. • forward and futures contracts. • forward-futures spread. • CA in Hull-White, Ho-Lee and other models. • our data set. • Euribor and