# Tag Info

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Garabedian, Typically, the "swap curve" refers to an x-y chart of par swap rates plotted against their time to maturity. This is typically called the "par swap curve." Your second question, "how it relates to the zero curve," is very complex in the post-crisis world. I think it's helpful to start the discussion with a government bond yield curve to ...

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I like to present to you a slightly different approach: Historically, only one single yield curve was derived from different instruments, such as OIS, deposit rates, or swap rates. However, market practice nowadays is to derive multiple swap curves, optimally one for each rate tenor. This idea goes against the idea of one fully-consistent zero coupon curve, ...

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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 ...

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I guess it depends on what they're referring to... The traditional swap curve (LIBOR-based) is certainly not risk free, as evidenced by the experience of the financial crisis and the resulting migration to OIS discounting. The OIS curve (which is a kind of swap curve...) is now the standard risk-free curve. The Treasury yield curve is not favored, because ...

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(In addition to the answers of Freddy and Phil H): With "modern" multi-curve setups: You have to distinguish between discount curves (which describe todays value of the a future fixed payoff (e.g. a zero coupon bond)) and forward curve, which describe the expectation (in a specific sense) of future interest rate fixings. Swaps pay LIBOR rates and are ...

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A Basis swap is a broad category of swaps where you exchange one floating rate against another floating rate. Without knowing the specific rates involved it is difficult to say more. An OIS Swap is an Overnight Index Swap, where you exchange a fixed rate against an average of the overnight rates for the tenor of the swap. For example, if the ON rate is ...

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I think your question can be split into two parts: (i) how to value a swap mathematically and (ii) how swaps actually work as a traded product. Part (i): As noob2 pointed out, "theoretically", a swap is valued with the help of two curves: one "forward" curve and one "discounting" curve. Say you want to "value" a 10-...

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You should take a look at the example from Hull's book. Assume that the 6-month, 12-month, 18-month zero rates are 4%, 4.5%, and 4.8%, respectively. Suppose we know that the 2-year swap rate is 5%, which implies that a 2-year bond with a semiannual coupon of 5% per annum sells for par: $$2.5 e^{-0.04 \bullet 0.5} + 2.5 e^{-0.045 \bullet 1.0} + 2.5 e^{-... 9 The reason why you can price a swap without a model is because you can replicate the payoff using only zero-coupon bonds. For the fixed leg this is trivial. For the floating leg, at T_0 invest 1 at Libor, at T_1 you get 1/B(T_0,T_1) = 1 + \tau L(T_0,T_1), you pay the floating coupon \tau L(T_0,T_1) reinvest 1 at Libor etc... at T_{n},... 9 In traditional terminology PV01 is 'present value of a basis point' and DV01 is 'dollar value of a basis point' which are technically only different in different currencies. Bloomberg has decided to bastardise the terminology for different types of curve bumps so I wouldn't place too much attachment to the name. Regardless.. Analytic PV01 What I like to ... 8 Chapter 1: Goldilocks is ousted by the bears Once upon a time, the banks used a fixing called LIBOR as a measure of the risk-free interest rate. Then the big hairy crisis came along and ate all our assumptions, leaving just the bones of the fixing (upon which everything else still fixes) and the mantle of risk-free rate proxy was passed on to a family of ... 8 To elaborate on Freddy's answer: These days you need to maintain a separate funding (usually OIS) curve to your Libor* type curves. Once you have this discounting curve, you can calculate from Libor instrument market data what the market estimations of that Libor are: 3m instruments like Interest Rate Futures, IRS with a 3m float leg, 3m FRAs can be used to ... 8 No, I'm afraid you're comparing apples with oranges. Your calculation of the DV01 of the swap is correct (with a caveat, see below), but the figure returned from swap.fixedLegBPS is not comparable. The DV01 tells you what happens to the NPV if the interest-rate curve change; in the case of the fixed leg, this affects the discount factors used to discount ... 6 There is no contradiction. If the strike of the floor and cap are both equal to the swap rate, and all accrual/payment frequencies, etc. are the same, then put-call partiy implies$$C_{t}-F_{t}=S_{t},where C_{t},F_{t},S_{t} are the values of the cap, floor and swap instruments at time t. Since the (theoretical Black-Scholes) volatility is ... 6 It is incorrect to use 1m euribor or O/N euribor in a 6m Euribor forward curve. You should only use instruments based on 6M euribor, such as 1x7 FRA, 6x12 FRA or swaps v 6m Euribor, as you have done in your second example. The actual 6m euribor fixing itself can be thought of as a 0x6 FRA out of spot. Before the financial crisis basis between different ... 6 Consider a date sequence \begin{align*} 0 \leq t_0 \leq T_s < T_p < T_e, \end{align*} where t_0 is the valuation date, T_s is the Libor start date, T_p is the payment date, and T_e is the Libor end date. Let \Delta_s^e = T_e-T_s. For 0\le t \le T_s, define \begin{align*} L(t, T_s, T_e) = \frac{1}{\Delta_s^e}\bigg(\frac{P(t, T_s)}{P(t, T_e)}-... 6 At most banks, swaption traders have models that allow non atm volatilities to be controlled by two parameters. Specifically , a parameter to control the smile (richness of out of the money options) and the skew (whether implied vol is upward or downward sloping as a function of strike ). Look up papers on the SABR model. In practice, one would ... 6 The key inputs to this calculation are two yield curves obtained from market data: \{v_i\} the discounting factors (value today of \1 received at time i) and \{r_i\} the forecasting curve (forward semiannual rates for period i to i+1). The calculation itself proceeds as follows. There are two legs to a fixed/floating interest rate swap. The fixed leg,... 6 Forward rates are determined from current spot rates bootstrapped from traded instruments. The reason is that if the forwards were different from the ones inferred from the spot rates, there would be arbitrage. For example, you can replicate a forward 6 month rate in 6 months with a long position in the one years rate and a short position in the 6 month ... 6 An Interest Rate Swap (IRS) normally refers a swap between a fixed rate and a floating rate. Floating rate being a single fixing for each accrual period and payment. An overnight indexed interest-rate swap will have the daily overnight index compounded throughout the accrual period. A vanilla IRS will not compound during the accrual, being a term rate. 6 It depends on what you want to do with the interpolated 9M rate. For example, I encountered this practical problem once. Desk loaned some money to an agricultural firm that, for liquidity reasons, wanted to pay interest like this: a coupon with 9 months worth of interest, reset from 9M USD LIBOR + spread 3 monthly coupons reset from 1M USD LIBOR + spread ... 5 Vol_smile. The sentence as you quote it doesn't make much sense, but my guess as to what they mean is this: OIS stands for Overnight Index Swap. In the US the overnight rate is called Fed Funds as 'experequite' mentioned (in the Euro-zone it is Eonia). The bank is borrowing at 3m Libor, which in this example is currently 2.10%. If 3m Fed Funds OIS is at 2%, ... 5 I recenlty worked on a similar problem and solved it with the help of Quantlib library. Assuming you are working with EUR and USD: get cross currency (xccy) swap data EUR / USD. You want to know how the xccy is collateralized and if Mark-to-Market resets apply to the USD leg. get interest rates swaps fixed vs ois / 3m / 6m in EUR and USD build USD/FedFunds ... 5 The ois curves were (and still are) primarily build from adding together (a) interest rate swap rates and (b) Fed Funds/Libor basis swaps. For example, if 10yr swaps are 2.0%, and 10yr fF/libor is -35bp, the 10yr ois is 1.65%. The basis swaps have been liquid for decades, so this calculation has always been possible. However, participants didn't ... 5 It turns out that the two things are the same, appropriately scaled. Proof: we can construct a 5 year swap using 3 month libor combined with a 3mo-4.75yr forward swap, weighted by the dv01s of each part. Thus, ignoring discounting, we have 5yr swap rate = (0.25*3mo libor + 4.75*forward rate)/5. This can be rewritten as 0.25*(5yr swap rate - ... 5 are you using the same volatility 20% for both black76 and Bachelier? The black76 is a lognormal model, where volatilities are quoted as relative price changes. The bachelier/normal model quotes volatilities as absolute changes. That might be what you're missing? Kind regards 5 A forward rate agreement is an agreement to exchange a fixed for a floating rate over one period, with the payment being made at the start of the period. A zero coupon swap (with both legs paid at maturity) is an agreement to exchange a fixed for floating rate over one or more periods, with the payments being made at the end of the final period. So the two ... 5 If L and Z curves are identical, you are in a single curve frame work. A swap can be seen as a long position in a fixed rate bond and a short position in a floating rate bond. (I'll use yearly payments 30/360 in order to be able to ignore the \tau =1 and simplify the notation)DF_1 \times C^{fixed} + ... + DF_n \times C^{fixed} + DF_n - (DF_1 \...

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A multi-curve meants that you observe the discounting instruments (such as fed funds) and projection (libor, swap curve) and solve for all of them simultaneously; as opposed to bootstrapping separately a projection curve and a discounting curve. A simple paper with examples is Numerix Model Calibration: The Multiple Curve Approach. A more detailed intro is ...

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I think I understand the question, but maybe not. In USD market, the most liquid IR swaps have floating leg reset quarterly from 3Mo LIBOR. (The fixed leg is semi-annual. Ths will change when LIBOR is discountinued; it looks like the most common SOFR floaters will have annual frequency both for fixed and floating legs). (Market conventions differ for other ...

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