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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 ...


23

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, ...


15

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 ...


14

There are two parts to your question and I'd like to answer them separately. Curve Construction On a daily basis, you can observe prices on a large variety of instruments, whose prices are driven by news and trading flows. Based on market prices of these instruments, there are a number of ways to create discount curves/forward curves. At a very high level (...


11

CMS adjustments in single curve context can be roughly explained if you consider a CMS swaplet by the fact that there is a single payment at the CMS rate at a single date and not on the whole strip of the underlying CMS tenor schedule. So if you are trying to hedge a CMS swaplet with the corresponding swap of CMS tenor length (with correct naïve nominal ...


10

Derman et al has a long note on this from 1999. Variance swaps are actually the more natural choice. It has nothing to do with leverage. From the linked article: Although options market participants talk of volatility, it is variance, or volatility squared, that has more fundamental theoretical significance. This is so because the correct way to ...


10

(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 ...


9

Assume you have an USD-EUR Cross Currency Swap (3M-FloatUSD+SpreadUSD vs 3M-FloatEUR+SpreadEUR) (spread on USD side is usually zero), collateralized by USD-OIS (Fed Fund) I assume you know the USD-OIS discount curve, then you know the discount curve for USD cash flows. I further assume that you know the USD-3M forwards collateralized w.r.t. USD-OIS (from ...


9

Var and vol swaps are very similar products, with the leverage (convexity) being the biggest theoretical difference, yes. In the actual market however they are very different. After the 2008 debacle var swaps in the single stock space are not too common, whereas single stock vol swaps are regularly quoted. One interesting perspective is trading one versus ...


9

Why does USD based security valuation have to give a thing about what London Banks think? Your question is based on false premises: the USD Libor is not determined by polling London based banks as you seem to believe, but banks on the London money market. The difference is important, as there are—of course—banks which are not based in London and active on ...


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 ...


8

As you know both var swap & vol swap are traded on vol. The difference comes in convexity. Although variance swap payoffs are linear with variance they are convex with volatility. Because of the convexity, a variance swap will always outperform a contract linear in volatility of the same strike. This convexity is the reason that variance swaps strikes ...


8

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^{-...


8

Firstly, understand that the 1y Libor is not useful here; the swap is 2 6-month periods, which will each fix on 6m Libor. These days, the *ibor fixings at different tenors are essentially separate, and 0x6 & 6x12 do not compound up to 0x12. So we have 6m fixing at 0.63006%, and a 1y swap at 0.645% mid. To do this properly, we would need a discounting ...


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 $T_{n}$,...


7

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 ...


7

The short answer is that Libor swap rates come from the market. They represent a series of cashflows in the future whose value is determined by the fixing, which the market participants have their own valuations of. Since the actual cash flows are now discounted using a separate funding curve, the swap prices embed both a prediction of future fixings and a ...


7

A swap does not require a model because its price can be derived from the yield curve without any assumptions about how the yield curve may move in the future. The PFE however is an indication of by how much the swap's mark-to-market may move between now and a moment in the future. It is of course influenced by how volatile rates are. The more volatile ...


7

First of all it is not clear what exactly you mean by right number, you definitely do not adjust forward swap rate. You probably mean adjusting euro dollar futures contract rates so that you can later use these values to fit the swap/forward libor curve. Reason for adjustment is simple. If you are short ED futures and rates go higher futures price drops ...


7

As I've mentioned in a comment, it would be wrong to think that entering a variance swap specifically amounts to being "long skew". What you can say however is that, in the absence of jumps (i.e. in a pure diffusion framework, see here and here for further info), the fair variance strike $K_{var}$ at which a variance swap with notional $N$ and payoff $$ N ...


7

If you take Quantuple's stuff a little further, you can really see whether you're long skew. You can pretty easily see the dependence on convexity too (though it should be obvious that you're long convexity). So first off, we need some smile parametrisation that lets us easily control convexity and skew. I just went with a made up one; $$\mathrm{convexity} ...


7

An FX Swap can be described as "borrowing in one currency and lending in another". When put this way it is clear that it has something to do with interest rates in the two currencies. You will be very happy if the i.r. in the currency borrowed rises and the i.r. in the currency lent falls the day after you do the deal, because you will have locked in more ...


6

I have a little more informations, so let me share it with you. Even though I think that the frameworks I presented in my question are both corrects (i.e. aribtrage free), it happens to be the case that the market seems to have more "structure". Here is a methodology that allows to retreive market quotes and which is the same as BBG (which is the best ...


6

There are several ways to understand how to price a swap. One way is to see it as a sum of Forward Rate Agreements that you can price individually. This is more or less what Probilitator explained. A simpler way imho is this: if you are receiver of floatting leg the value of the swap at $t\leq T_0$ $$ Swap_t = Leg_{Float,t} - Leg_{Fixed,t} $$ I think ...


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

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

The problem here is that your market is not arbitrage-free: JPY OIS = 10% per day, flat USD OIS = 0% per day, flat USDJPY spot = 100 USDJPY Forward for tomorrow = 100 A quick sense check is that, if you have an interest rate differential, you cannot have the FX forward equal to the spot FX. I would take advantage of the arbitrage as follows: I ...


6

fixedLegBPS is the basis-point sensitivity of the fixed leg, that is, how much its NPV changes when the fixed rate changes by one basis point: it's calculated as the NPV corresponding to a fixed rate of 1 bps. Since the NPV of the fixed leg is linearly proportional to the fixed rate, you can write the equation targetNPV : fixedRate = BPS : 1 basis point ...


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

Better yet, don't use LIBOR for discounting at all. Since LIBOR involves credit spread over the risk free rate, using LIBOR for discounting would adjust the deal's market value to reflect some amount of credit risk. Hull and White argue it's not generally the best idea, since it would mean double-counting, as one also normally computes the CVA to handle ...


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