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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

Quantlib supports multi-curve framework (to the best of my knowledge). By the way, there's a "newer" version of that paper (authored by Pallavicini & Brigo). http://arxiv.org/abs/1304.1397 This paper might also be useful for you, very practical and basically answers any question you could have. Also see this discussion about multi-curve discounting ...


6

Yes. Although sometimes people mean the Euro/Dollar currency pair which can cause confusion. Besides the daily mark-to-market, the counter-party risk is also removed through the clearing house for the futures. No. Eurodollar and FRA are not the same as swaps. A Eurodollar fixes an interest rate for a three month period in the future whereas a swap represents ...


5

You are asking about the term structure of lognormal implied volatilities for European swaptions, which is a two dimensional function (expiration and tenor). First expiration: typically (but not always), implied volatilities are increasing in the 0 to 6 month sector, because the immediate future is often more predictable than the medium term. At some ...


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 - ...


3

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)}-...


3

Delta is a linear approximation of the change in price due to a small move of the relevant interest rate. Typically a parallel move of the whole interest curve is assumed here. This applies to all kind of fixed income instruments, in particular IRS. Interest rates can be given as coupon rates (these are the so called par rates, based on prices observable in ...


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 ...


2

Libor is indeed usually fixed in advance (and paid in arrears). Thus, in your example the first fixing date will be 2 business days before March 5th, and the second fixing date will be 2 business days before June 5th. Usually, therefore, the first fixing is already known when the swap is traded. You say that the Libor leg is paid semi-annually - that's not ...


2

Going backwards 2 days with qlCalendarAdvance(..., "-2D", ...) works in this particular case. To be more robust, and to take into account the number of fixing days and the conventions of the index you're using, you can use the qlInterestRateIndexFixingDate function. It takes the interest-rate index and a value date (that is, the start of your coupon) and ...


2

A corporate that has an ISDA master agreement to trade Interest Rate Rwaps (IRSs) with a bank will undoubtedly be capable of also trading Overnight Indexed Swaps (OISs), as will any type of counterparty for that matter. A corporate whose loan is tied to floating LIBOR will hedge using an IRS to convert to fixed. Hedging with an OIS would introduce ...


1

What you need is the convexity adjustment for 3 month libor when the payment is made 1 month after the reset date (ie 2 months before the natural date). As an approximation, this will be approximately 2/3 of the convexity adjustment for an arrears swap (paid 3 months before the natural date) and it will be approximately 4/3 of the convexity adjustment for ...


1

This seems to be a (short term, only 3 months) CMS swap. I wrote a paper about the different approaches to price them, available here. You can pick the one best fitted for your needs.


1

The link you posted does not contain the word "physical" in it, however with respect to the Brazilian interest rate swaps it does mention "non-deliverable currency." An interest rate swap is a defined series of coupons or cashflows so the only question remaining is then how to settle those cashflows, with respect to currencies that may be lesser liquid or ...


1

The pre-crisis concept of a risk-free rate was either government securities or LIBOR-based swap rates. As LIBOR is unsecured bank borrowing-lending rate, this was clearly an approximation too far. Counterparty credit adjustments for a bank, and post-crisis discounting: The value is derived by discounting at the overnight (OIS) rate, and then apply xVA ...


1

1. Discount Yes, usually, people discount using the risk free rate, and then adjust for the counterparty credit risk (CVA), funding cost (FVA), and so on. 2. Collateral The Margin period of risk: In the case of default, the counterparty will usually stop posting collateral for a given period of time before being closed-out. This period is called the ...


1

Two counterparties can agree any date they choose as the maturity date. IRS, being bilateral over the counter derivatives, are completely customizable. Having said that, on any given day the most heavily traded IRS are those with a standard maturity such as 2yr, 5yr, 10yr.


1

It looks like you should use a different convention for the zero rates. I tried the following: $$\left(1+r_{0;t_{0}}\frac{t_{0}}{360}\right) \times \left(1+r_{t_{0};t_{0}+t{u}}\frac{t_{u}}{360}\right) = \left(1+r_{0;t_{0}+t{u}}\right)^{\frac{t_{u}+t_{0}}{360}}$$ Solving with the same input gives $r_{t_{0};t_{0}+t{u}}=0.00756843$, in agreement with ...


1

I will attempt to summarise the content included in this book, which has a specific chapter dealing with carry and roll-down. There, two concepts are made completely separate. Costs-of-carry are defined as costs relating to holding a trade that are not directly related to market movements. For example, funding a margin requirement for an IRS facing a ...


1

In basic instruments, one can ignore the past fixings and price purely on the future cashflows. Hence the term Net Present Value. With more exotic stuff such as range accruals, the past fixings are used to calculate the future payoff. In this case, to find the NPV at an intermediate date between the start date and expiry, you typically need to enter the ...


1

The idea of considering past cash flows into an NPV calculation is rather adventurous, in my opinion. If an investor wants to invest money into a financial instrument that has already generated positive cash flows before making his investment (e.g. investing into a bond when some interest payment dates have already passed), the investor would not consider ...


1

Under the Ho-lee model, \begin{align*} dr_t = \theta_t dt + \sigma dW_t. \end{align*} Then, the price at time $t$ of a zero-coupon bond with maturity $T$ and unit notional is given by \begin{align*} P(t, T) = E\left(e^{-\int_t^T r_s ds} \mid \mathcal{F}_t \right), \end{align*} where $\mathcal{F}_t$ is the information set at time $t$. Note that, for any $s\ge ...


1

from a practitioner perspective, i can say there's no such thing as a 0 year swap (obviously). The shortest tenor that you could trade would be a contract on one month LIBOR or more likely 3 month LIBOR. Then the instrument you are asking about is a 5 year expiration caplet (payoff in 5 years = max (0, LIBOR- strike).)


1

Obviously a perfect forecast for interest rates is a bit hard to come by, such a thing would make the inventor quite a tidy sum. Broadly, the task you're seeking to accomplish falls under the banner of yield curve modeling, and there is a very substantial body of research in this area, including several good books. There are some canonical examples of ...


1

There is a new book about this new topic: http://www.amazon.com/Interest-Rate-Modelling-Multi-Curve-Framework/dp/1137374659 The author is a leading developer in Opengamma. Opengamma does have support for multi-curve building.


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