# Tag Info

16

The OIS is not the secured (collateralised) lending rate. It represents the cost of repeated overnight unsecured lending over periods of up to two weeks (sometimes more). Because it is based on overnight lending, it is assumed to have a lower credit risk than longer term interbank loans based on say 1M, 2M or 3M Libor and this is what drivers the OIS-Libor ...

13

The PCA analysis does not really tell you what the bonds do but it tells you how the rates move together. The variations of $n$ rates (i.e. 1 y, 2y, ...) are split up in (at first) abstract factors like $$\Delta R_i = \sum_{j=1}^n e_{i,j} f_j$$ where $\Delta R_i$ is the change in the rate $i$ and $f_j$ is factor $j$ and $e_{i,j}$ is the (factor loading=) ...

7

The main problem is that you cannot achieve Libor in the markets. So the old-fashioned method of discounting at Libor doesn't work any more. As an example, if you compound up the 3m Libor with today's price on a 3x6 FRA, you won't get 6m Libor. Traditionally, that would mean arbitrage, but these days it's just a fact of life. You cannot achieve 3m Libor for ...

6

This has been posted a few times now, so I will invest the time on a full response. 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. Let me ...

6

It is not reasonable because rates display a stationarity but brownian motion is not stationary. The variance of libor at a future time $t>0$ conditional on the value at time $t=0$ does not scale as $\sqrt{t}$

4

The rate is the return on your investment. Since you'll receive 100\$after 12 months,$\frac{100 - P}{P} = \frac{100 - 89.0}{89.0} = \frac{11}{89} = 12.36 \%$. Same for the 6-month T-Bill:$\frac{100 - P}{P} = \frac{100 - 94.0}{94.0} = \frac{6}{94} = 6.38 \%$. 3 The fixed leg of the OIS is an unsecured rate that is very close to Risk Free Rate (RFR) because of the combination of several reasons: it is akin to a money market term deposit rate swapped against overnight deposit rates, compounded geometrically over the swap lifespan, so a net expected present value at inception of zero (Feynman-Kac) should reflect ... 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 Secured and unsecured refers to lending. However OIS is a swap based on FF, not a loan. It is a different animal. So OIS is a derivative, or a bet, based on the average of future (unsecured) FF rates over a period.. For example my name is Noob Rademayer, I am not a bank so I can't lend or borrow FF in the interbank market, but I can bet on the rate at ... 2 If a bank lends 6m Libor and finances it by borrowing 3m Libor and borrowing forward 3x6 libor, this is not arbitrage, as the bank is assuming 6m credit risk whilst his financing is 3m credit risk. (There are also other factors like regulatory capital, tying up balance sheet for 6m, etc.) So the text book case where the 3x6 FRA (or front Eurodollar) is equal ... 2 Strictly speaking, any risk-free interest rate can be composed into three components: The rate expectations component is the market's "true" expectation for future interest rate. A bond risk premium component: longer maturity bonds have higher duration risk than cash. Accordingly market participants will demand more compensation for taking on duration risk;... 2 General fact: From a mathematical standpoint, we can write the PV of a flow to be received at$T$as the value of its expectation under the$T$-forward measure (which is also the value of the forward at$t$:$F(t, T)$) discounted using the zero-coupon bond. We can show this by changing measures from the risk-neutral measure$\mathbb{Q}$to the$T$-forward ... 1 To answer this question, we must fix a bit of the vocabulary, first. I will try to stick as close as possible to your conventions: Spot rate: (also called zero rate) is the annualised rate of return on a non-coupon-bearing bond (hence zero coupon bond). For a given maturity$t$, let us call$r_t$the corresponding spot rate, i.e. we have $$PV_0(t)=\left(\... 1 The forward rate is estimated at the Libor valuation date = reset date + the reset gap (namely 1, 2 or 3 days) (not the accrual start date). In the case of standard vanilla swaps, the accrual start date is equal to the reset date + the reset gap: this I believe is the case that Davide Duarte talks about. However, for the general case, the accrual date could ... 1 I believe the duration constraint and the proceeds constraint are not self consistent. You cannot satisfy both. The duration constraint alone fixes N_1/N_2 and N_3/N_2, so you cannot also satisfy the proceeds constraint. 1 Futures actually have a negative basis all the time without having to have negative interest rates. Dividends can have a rate that is higher than the interest rate and that makes the basis negative. Futures on the Dow Jones Real Estate Index are almost always negative. Here are the DJUSRE Sep and Dec futures. The "Spread" column shows you the negative ... 1 When you call ql.FlatForward it simply means you are constructing a rate curve that will lead to flat forward rates. The constructor of this curve takes the forward rate as an input. If you want to change the input (say, because the market moved and forward value changed), then you can change the quote value with the new value like this. First, keep a ... 1 As for any European vanilla option you can infer the cumulative distribution function under the pricing measure by taking the derivative w.r.t. strike. In the case of European swaptions the natural numeraire is the annuity A(t), the pricing measure is the annuity probability measure P^A, and$$ \text{receiver swaption premium} = A(0) E^A[(K - S_T)^+]$...

1

Do you want to model the returns in a risk-neutral framework (for derivatives) or in the real world measure (for risk analysis/portfolio construction)? For the first approach (say modelling under $Q$) you should go to the literature on bond and FX-derivatives. I would go more into detail if this is your aim. The formulation $N(\mu-\sigma^2/2,\sigma)$ ...

1

These models do exist. They are known as "macro-finance" models. From "Macro-Finance Models of Interest Rates and the Economy": During the past decade, much new research has combined elements of finance, monetary economics, and macroeconomics in order to study the relationship between the term structure of interest rates and the economy. In this survey, I ...

1

I think I've found the answer in another forum (which fits my initial intuition). So just to share: FRA-OIS is traded via swap. So if you think the spread would widen you pay on the swap. So you would pay OIS + Spread and receive Libor. https://www.wallstreetoasis.com/forums/tech-questions-on-eurodollar-and-fed-funds-futures-hedging

1

When the convention is ACT/360, it means that 365 calendar days of interest is calculated as 365/360 years. I knows it seems stupid, but before industrial use of computers, it was convenient for a year to be a nice round number like 360. I forget how the 30/360 convention is handled - I once coded up all the conventions, but they have worked really well ...

1

The 1x4 FRA rate is where you can lock in 3 mo libor , 1 mo from now. To construct this rate , you must build a 3 mo libor curve. The first point in this curve is 0x3 libor , which is spot 3 mo libor. The next point on this curve is the next Eurodollar futures contract. These expire every month on the third Wednesday. Then you have to interpolate ...

1

The 1x4 FRA rate is given by $F(1,4) = \frac{12}{3} \left(\frac{(1+ 4/12 \times L(4))}{(1+ 1/12 \times L(1))}-1 \right)$ where $L(T)$ is the $T$-month Libor rate seen today. Clearly $F(1,4)$ depends on the 1M and 4M LIBOR rates. So if the market 1M rate $L(1)$ is below the market 3M rate $L(3)$ you will be understating the true FRA rate if you set \$L(1)...

1

Here you go. On Page 935 "A.4. Global Government Bonds Bond index returns come from Bloomberg and Morgan Markets, short rates and 10-year government bond yields are from Bloomberg, and inflation forecasts are obtained from investment bank analysts’ estimates as compiled by Consensus Economics. We obtain government bond data for the following 10 ...

1

1) JPY yield curve is currently upward sloping, not inverted... 2) Empirically, an upward sloping yield curve predicts recessions, not an inverted one. See this famous paper http://newyorkfed.org/research/current_issues/ci2-7.pdf

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