33

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 ...


14

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 ...


9

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 ...


9

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 ...


8

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 $T_{n}$,...


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 ...


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

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 ...


5

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,...


4

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 Overnight fixings, called Sonia, Eonia and -ahem-...


4

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 ...


4

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 ...


4

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 - ...


4

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


3

First of all, it seems that you are solely concerned about the Funding Valuation Adjustment (FVA) here, and not CVA; Sovereigns have credit risk which should also be valued here given they would not be posting any collateral as mitigant when the market moves in your favour. But let's focus on FVA: It is important to think about FVA (and all other VAs also) ...


3

An interest rate swap (IRS) can have a vega component if it is not a standard IRS. If you are familiar with the convexity adjustment for FRAs (and single period IRSs) compared with their respective short term interest rate (STIR) future, you will be aware that it is the different gamma components of these products that result in profit-and-loss (PnL) over ...


3

Instrument 2 looks to me like the standard regular definition of a 3x6 FRA. This is a relatively liquid instrument, so that forward rate r2 is just the price of the FRA and is available on Bloomberg, etc. If you have a yield curve model and associated suite of functions there will certainly be a function to return that forward rate, because it's vanilla. ...


3

You're thinking of a "cross-currency basis swap", not a CCS. A CCS is a floating-for-floating swap that would, for example, let you switch 3m SHIBOR into 3m USD Libor. A cross-currency basis swap, on the other hand, is a swap of funding spreads (loosely speaking, LIBOR - OIS equivalent). It's essentially the liquid way of exchanging currency for long ...


3

Consider a payer swaption with maturity $T_0$ and strike $K$. Here the strike $K$ is the fixed rate paid on the fixed leg of the underlying 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 payments $L(T_{i-1}; T_{i-1}, T_i)\Delta ...


3

Firstly, some instruments: FX Swap, also known as an FX Forward: exchange of principals at start, and exchange back at end. The back exchange is at an adjusted FX rate, which differs from the spot rate by the quoted number of forward points. Non-Deliverable Forward FX (NDF): much the same as an FX Forward above, but delivery is of the USD (usually) ...


3

The answer is that it depends of the Zero Curve you're looking to build and the precision and maturity of it. For example, for the Libor3M curve, you might need indeed to use futures if you want to obtain a clean smooth curve for maturites close to 1Y. But again, if you're planing on using longer contracts, you can just bootstrap that part of the curve. It ...


3

There are two items that must be clarified with respect to your question: Are you assuming an interest rate swap (IRS) at mid-market, i.e. at-the-money (ATM) or an off-market IRS with some unknown net present value (PV)? Are you interested in a risk approximation or a more accurate formula that reflects the truest risk sense of a market curve shifted up or ...


3

Since the 10 year and 30 year swap spreads are frequently traded and have time series available, think of this as a 2 variable problem. You then have a simple "spread of spreads" trade which is easily analysed using PCA type methodology. You should find a high correlation between these two spreads, so the variability of the spread of spreads is quite low.


3

You can only infer forward vol by pairing a mid-curve option with a spot option. It's easier to go through an example (I'll use 5y x 5y vol since I have the sketch below handy...) One decomposition of the 5y5y spot vol is as follows: 1y forward 4y x 5y vol: this is the implied vol of an option starting in 1 year, expiring 4 years thereafter, and eventually ...


3

Hedging with futures Calculate DV01 of your corporate bond Calculate DV01 of the cheapest to deliver of the future contact that is closest to the maturity of your bond Ratio between DV01 of Cheapest to Deliver and DV01 of your corporate will give you a number of future contract that you will have to sell in order to be hedged. I.e. if you are long 5 ...


3

The price of a swap is the rate on the fixed leg that puts the market value to zero. Swaps are typically quoted this way, so in your example it would be the fixed rate of a swap with the same dates and floating leg as your previous one. However, if you wish to sell the swap you could also ask for a quote in absolute currency terms (could be negative or ...


3

There are 3 main books: Hulls: Options Futures and Other Derivatives - This is a generalist introduction. It doesn't have a rates focus and less a focus on trading or risk management or interest rate swaps. But you should read it and own it anyway. Everyone in finance is basically expected to know this. Corb - Interest Rate Swaps and Other Derivatives - To ...


3

Forget for a moment that your option is delivering the immediate entrance in a swap (if the swaption is physically settled) or the cash amount of the swap (if the swaption is cash-settled), as your question doesn't depend on this fact, and take a "general" 1Y option. Your today's (date $t_0$) cube loses the "swap tenor dimension" and becomes a today's ...


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