# Tag Info

9

ED contracts are quoted as: $100-LIBOR_{3M}$, where the three-month LIBOR rate is annualized. For instance, an annualized rate of 3.00% would yield a quote of 97. A one basis point change would now yield a quote of 96.99 or 97.01, resulting in a loss or gain in \$25. By construction, the DV01 is \$25, which effectively results in the fact that the ...

6

Having traded these options for a number of years I have some insight. It’s my belief that those that make a living specifically out of these options do have tree-style models that take into account early exercise. On the other hand , those that have occasional use of these options (such as interest rate derivatives dealers who might use them to hedge otc ...

5

The quoting convention must be explained somewhere in your book. For Eurodollar futures, this convention is 100 - yield, 92 means the yield is 8% per annum, so for one quarter you need to divide this discount by 4 to get the price (100% - (8% × (3month/12month)) = 100% - 2% = 98%

4

Yield of Dec19 Future - Current 3Months Libor / 25 bps (1 rate hike) Libor 3M = 1.84 % Price of Dec 19 Future (Ticker EDZ9) = 97.18 = 2.82 % Number of hikes = (2.82 - 1.84)/0.25 = 4 Please note these are very simplifying assumptions, as the 3 months Libor is just a proxy on the Fed Funds Target rate.

3

The future is at 92, so the interest rate is 8% per year (!the good old days!) or 2% a quarter. Two percent interest on one million is 20,000. So one future covers the interest on 980,000 initial amount and allows you to repay 1,000,000 at maturity 3 months later. You initially borrow 4,820,000 so you need 4,820,000/980,000 futures (for a three month loan)....

3

Futures trading are settled on a daily basis meaning in the end of day, your account will be adjusted by your PnL. So of course your payment on T1 is not discounted. However forward is settled only once at expiration, hence you discount the whole duration.

3

In general futures contracts are leverage instruments. They never require the investment of principal. They do however require margin: you need to fund your account at a futures exchange so that they have insurance against any losses you incur, as an example this might be 2 days standard volatility. On 1 ED contract for 5bps a day thats probably 10bps margin ...

3

Jacob nailed it, but I'll add something else that might have been confusing you. You can never buy eurodollar futures part way through the 3-month period. They always have 3 month of life to them, starting just after the expiration of the futures contract. So they will always be paying/receiving 3 months worth of interest. And therefore Jacob's math ...

3

Consider a fixed-for-floating swap with reset dates $T_0, \ldots, T_{n-1}$ and payment dates $T_1, \ldots, T_n$, where $0<T_0 < \cdots < T_n$. We assume that the swap exchanges the floating rate payments $L(T_{i-1}; T_{i-1}, T_i)\Delta T_i$ and the fixed rate payments $K\Delta T_i$, for $i=1, \ldots, n$, where $\Delta T_i = T_i -T_{i-1}$. The ...

2

To answer the first question directly, the swap in question is a 1 Year swap of a fixed rate vs 3 month Libor. The swap starts in Mid-June (the date of the ED futures expiration) and goes until the next June. There are 4 quarterly payments. To understand things better, look carefully at Table 8.4 and see how the three columns on the right are computed from ...

2

I just checked Google Finance and the EUR/USD = 1.1190.... for arguments sake lets say it goes up by 0.10 to 1.2190 the percentage change = 1.2190/1.1190-1 = +8.94% in terms of USD/EUR the beginning quote would be 1/1.1190 = 0.8937 but would be 1/1.2190 = 0.8203 after the EUR/USD went up by 0.10. Therefore the change in terms of USD/EUR = 0.8203/0.8937-1 = -...

2

There are quite a few reasons: Fed funds futures rate and Eurodollar futures rate do not reflect market expectations alone. Technically speaking, a risk-free interest rate is the sum of 1) rate expectations, 2) term premium, and 3) convexity bias. Term premium is typically positive, since investors demand a higher yield for taking on more duration risk (i.e....

2

Two things: 1) The eurodollar implied futures rates need to be convexity-adjusted before they can be used as forward rates (futures rate = forward rate + convexity bias). 2) Discounting should be done using the OIS discount curve, not the LIBOR curve. More specifically (and ignoring market conventions such as day count), let's say you're pricing a 1-year ...

2

hypothetically if we assume that $R_{fra}=R_{fut}-\frac{1}{2} \cdot \sigma^2\cdot T^2$ holds (convexity adjustment) and you are able to observe $R_{fra}$, $R_{fut}$ and $T$ then you can extract implied volatility of reference interest rate. If your view on volatility is different then you can make a bet: long convexity position (if you expect volatility ...

2

What you have calculated, correctly as far as I can tell, is a December-starting 1-year compounded Libor 3m forward rate. That's a weird-sounding thing, but it is essentially equivalent to a December-starting 1-year forward swap rate vs Libor 3m. (I've just priced exactly this against a live USD Libor 3m yield curve and I get 97.3 bp.) However, this should ...

2

PAI is the interest paid on the VM. Assuming perfect collateralization (i.e. collateral always reset to the derivative NPV) it is shown (see Piterbarg "funding beyond discounting") that funding is entirely done trough the collateral and therefore the derivative should be valued by each party with discounting at the collateral rate rather than at its own ...

2

Take a 5Y bond, say buying \$10 million dollar notional and calculate the PV01 using you favourite method for calculating bond risks, e.g. some duration formula. Lets say this Pv01 is \$4,500 Now look at the ED strip. Each 3-month contract has a pv01 of \$25 by definition of the instrument. If you purchase 1 each of every contract for 5y then you will have ... 2 there are many ways to solve Vasicek system, for me personally I markov short rate approach. Without going into the details of proofs: Note that eurodollar future is calculated under risk neutral Q measure of libor rate at each settlement$t_{fix}$(on three months interval each) libor rate$l(t_{fix}) = \frac{1}{tenor} e^{A_{diff} - B_{diff} * r(t_{fix})}...

2

Because you are keeping the 6m rate constant. Therefore, if the spot 3m rate goes down, the forward must go up.

1

This book describes something that looks like DV01 hedging of the bond with eurodollar contracts. But the reality is that the underlying rates of the 2 kind of instruments are different. The bond depends on the treasury yield curve whereas the eurodollars depend on the Libor curve. These 2 curves share some common risk factors however there exist a basis ...

1

At least 2 problems here I think. 1) the CME vols are of the implied rate, not the price. Therefore express underlying price and strike in yield terms by taking 100-price and 100-strike. 2) the units of option price need to be the same as the underlying. For example , option whose strike is 2.50 has price 0.03, not 3. Try those adjustments.

1

Unable to take screenshot in my phone. I will post three screenshots of my calculator screen.

1

Your description of the contract is incomplete, is this the december call on the september 19 future or something else ? In all cases it's in basis points as explained in the contract description and the calculator seems ok. Based on your 3.75 picture it seems to be the option expiring in Sep 19 on the Sep 19 contract. And its price is 3.75 basis point.

1

In my experience Chinese whispers between IR traders and bank/institution strategy/researchers and then journalists is rife. Hikes/cuts are predicted by traders based on FedFund futures or meeting period FFOIS rates. The same goes for GBP or EUR where the OIS rates dictate the probability of hikes/cuts. Note that your quote didn't directly say the expected ...

1

The futures contract pays off every day during its life, with the last payment at T. There are no payments after that. When Hull is talking about a payment at T+.25 he is referring to the payoff of an investment that is separate from the futures contract.

1

In my opinion, there is no better reference than The Treasury Bond Basis, which I still read cover-to-cover at least once a year. Since the publication of the 2005 edition, the biggest development is the introduction of the WN (ultra-long bond) contract in 2009. The TN (ultra 10-year) contract was introduced in 2016 as well. But the same set of tools and ...

1

1) convert the futures prices into forward rates by using forward rate= 100- futures price. You now have a chain of forward rates, starting with the rate from Sep 16 to Dec 16. 2) you need a rate from today to Sep 16. Use 2 month spot Libor 3) to calculate a zero coupon rate from today to any given date, chain together the relevant forward rates. eg ...

1

I think you are right that ultimately all dollar movements are reflected in reserve accounts at the Federal Reserve. May I make a couple of additional points: Eurodollar borrowing is really not a close substitute for Fed Funds. First of all, not much volume goes through the term eurodollar markets, so it doesn't have the capacity to replace Fed Funds ...

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