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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,...


5

The piece you are missing is an approximation via the Taylor formula of the logarithm: $$\ln(1+x) \approx x-\frac{x^2}{2} \; .$$ Apply this to the first term in the final formula of the technical paper: $$\frac{2}{T}\ln\frac{F_{0}}{S^{*}} = \frac{2}{T}\ln\left(1+\left(\frac{F_{0}}{S^{*}}-1\right)\right) \approx \frac{2}{T}\left(\left(\frac{F_{0}}{S^{*}}-1\...


4

Let’s say the settlement period is T+2, and you made a deal on the 8/10/2018. The spot date would be 10/10/2018 (assuming no holidays!), that’s when the physical exchange would happen. Now if you don’t want physical delivery, then tomorrow (9/10/18) you can use T/N (tommorow/next) swap to delay the physical delivery by one day, T/N is essentially swap ...


4

In an Asian-style swap, instead of using the last price quote of the underlying (such as commodity price), they take an average, such as the average closing price over the last month. This is fairly common in commodity swaps. As for pricing, a good start is this paper on pricing Asian-style interest rate swaps (where the floating leg uses the average of an ...


4

I would not say that this is universally acknowledged but here is my view: Instead of considering par rates, i.e. 10Y and 20Y, consider forward rates, such as 10y and 10y10y. The useful difference here is that forwards do not 'overlap' and therefore incorporate aspects of each other into the price. A 20Y is >50% directly dependent upon the 10Y price for ...


4

Suppose 40yr bond and 30yr bond have the same yield. It is a mathematical fact as @attack68 has pointed out, that the convexity of the 40yr is greater than the convexity of the 30yr bond. So consider the following strategy ; long the 40 yr bond and short the 30yr bond with the same dv01. Then every time the market moves, you make money (get longer when ...


4

It's an interesting question. The fundamentally devout macro wannabe-strategist within cries out for a long-term growth/inflation expectation narrative. However, the cynical realist within reminds that although the market does make long-term predictions thus because it has to create prices then, there is no latent consensus that the world will really look so ...


3

Look at the infinitesimal version of the change in variance: $$ d\sigma^2 = 2\sigma d\sigma + (d \sigma)^2 $$ The Ito term $(d\sigma)^2$ is non-zero for stochastic processes, and is of order $dt$, but if we ignore that then we get the approximate relation $$ d\sigma^2 \approx 2 \sigma d\sigma $$ which is where the factor $2 \sigma$ comes from in the ...


3

Yes that’s pretty simple : for the purposes of defining the swap spread, we assume that the libor leg of the swap is at libor flat.


3

To trade a swap counterparties must have an ISDA Master Agreement drawn up and signed between themselves. If collateral is to be exchanged that agreement will also contain a section called a CSA: a Credit Support Annex. That documentation defines the types of collateral available to post as the liability holder: and the banks choice of discount curve will ...


3

Just my 2cts' worth: With commodity swaps exchanging typically a daily spot price (i,e, immediate delivery price) vs a fixed rate payable in regular intervals, the only difference to a truly Asian product is that discount factors are not perfectly equal to unity. So while rates are not high or tenors very long, regular commodity swaps would be pretty close ...


3

Let's look at a much smaller piece of the puzzle: What is the value of a 3m loan at Libor? Cashflows: t0 -P t3 +P(1+r.f) Where f is the year fraction for t0-t3 and r is the rate on the loan. If r is the funding rate, then the discount factor (price of a ZCB maturing at t3) is 1/(1+r.f): dt cf df pv t0 -P 1 -P t3 ...


3

So my question is how do I prove that the use of 2y, 5y, 10y and 30y is justified for risk bucketing and not other alternate buckets? Ok so just to pose a second viewpoint but why do you have to necessarily use PCA to do this? You are basically trying to show that given any underlying swap portfolio $P$ you can find a set of trades / risk exposures in ...


3

To justify the use of tenors 2Y, 5Y, 10Y, 30Y for risk bucketing, you could analyse up to the first four principal components and examine which variables summarize better the information displayed on each axis using the factor score. For example, if the first four pc contains 90% of the available information (let's say 1st pc: 40%, 2nd pc: 30%, 3rd pc: 15% ...


3

A plethora of instruments, a menagerie of curves Different instruments are traded in different ways, and relate to a collection of curves. Floating rate instruments depend on some index in order to calculate the cashflows, and so trading instruments which depend on different indices is implicitly trading the expectations of those indices in the future. Fed ...


2

The curve Bloomberg EUR swaps curve (YCSW0045 Index) is indeed the euro equivalent of the Bloomberg USD swaps curve (YCSW0023 Index). By equivalent I mean that each curves are constructed in the same manner : using sames types of instruments (deposits, FRAs, futures, swaps) with the same bootstrapping/implying method (exact fit vs best fit). For each you ...


2

To add to the above on a more practical note: In general, SP desks make money on the individual product when the underlying declines. Dividends make the underlying decline, hence they are naturally long dividends. Take an auto-callable product which is exercised if the spot is above a pre-determined strike each year and say the SP desk sells this ...


2

I suppose it depends on the context, i.e. what the trader is trying to do. But arguably this is one of the thing swaps were invented for: If you are long a bond you receive fixed payments from the bond (the coupons). By entering a swap where you pay fixed and receive floating you can largely get rid of the interest rate risk. Essentially you have turned ...


2

On the technical side of things, make sure that your actual PCA analysis is correct. A reasonable check here is to plot the loadings of all tenors (not just the few you are interested in) for the first 3 factors and see if you recover level, slope and curveature components. Now if your results are correct, the reasoning goes something like: the first three ...


2

It may be a different from a buyside perspective, than from a sellside perspective. Off course, I must add a caveat that this is based on my rather limited role and experience in this domain. The sellside would have access to the complete dataset comprising the asset pool (to each single loan and mortgage). The buyside would have a prospectus containing a ...


2

Which swap curve are you trying to interpolate? And what swap are you trying to price? The 60d to 1y60d swap (1y long, starting at 60d), or now to 1y60d (not a usual length)? Really by interpolating the swap rates, easy though it seems, you are implicitly building a curve of forward rates. You are also ignoring the structure of the market where the fixing ...


1

We note $A$ the annuity, so that $V^{swap} = A(s - K)$ so that $\frac{\partial V^{swap}}{\partial s} = A$. As the chain rule gives $$\frac{\partial V^{swap}}{\partial r} = \frac{\partial s}{\partial r} \frac{\partial V^{swap}}{\partial s}$$ we get that $$\frac{\partial s}{\partial r} = \frac{1}{A} \frac{\partial V^{swap}}{\partial r}$$ and as the chain rule ...


1

My understanding is as follows - you pay 100 at $T=0$, receive LIBOR+40bp annually, and get back 100 at the end of the deal. This is actually a cash outflow of 100, plus a floating rate note (FRN). The FRN with a 40bp spread (i.e. the one that pays LIBOR + 40bp) can be decomposed into a LIBOR flat FRN (priced at 100), plus a 40bp annuity paid out at $T=1,2,.....


1

I have only traded a few FX swaps and not in a while so do correct me if my understanding of their technical product specification is not correct: A Purchase of an FX Swap with say, a 3M tenor, at an initially struck spot rate and forward rate demands the spot receipt of a nominal amount of domestic currency and the payment of rate equivalent foreign ...


1

Market Impact I was asked this question numerous times, often by clearing houses as a measure to gauge their initial margins and concentration fees. As a market maker you may have limited information about the volumes traded, i.e. you know your own volumes. Our strategy was to first infer expectations about the market as a whole, and ask brokers to ...


1

Quarterly-Quarterly Swaps (normal rolls) start on a specific date, say 20th March 2018 and have roll dates on the 20th of each Mar, Jun, Sep and Dec, meaning the fixing and accrual start date will be as close as possible to the 20th (but rolled forward if the 20th falls on a holiday). E.g. Normal QQ 20th Rolls Swap: PaymentDate Fixing Date Accrual Start ...


1

This is not exactly an answer to your question, but I have found that for practical purpose it is best to use directly the discount factors (last column on the screen), which you can export to Excel and interpolate according to your prefered method for specific maturities. Beware that the curve reference date (the date for which the discount factor is 1) ...


1

Only just saw this. Commodity swaps are very simple products. For each averaging period, they will pay off the notional for the period multiplied with the difference between the strike and the average of some reference contract. The thing that's a little hard is knowing what the conventions are for how the reference price is determined. For example, for WTI ...


1

There is no CNY LIBOR to speak of. The CNY swap curve is OIS (don't know the index off the top of my head) and the compounding is weekly.


1

First, I am assuming that the bond trader has a long position in bonds and therefore is concerned that if interest rates go up the price of the bonds will go down. The problem here might be that he/she bought 20 years bonds when he/she should have bought 5 year bonds. One way to hedge against a rise in interest rates would be options on interest rates. For ...


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