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$$\frac{1}{(1+r_{02})^2} = E\left(\frac{1}{1+r_{12}}\right)\frac{1}{1+r_{01}}$$ Indeed, in the pricing measure, the distribution of $r_{12}$ has to be such that this relation holds. If you look at drift derivations for the LIBOR market model, a lot of work goes into making this sort of equation hold.


There is no conflict here. In the identity, \begin{align*} \frac{1}{(1+r_{02})^2} = E\left(\frac{1}{1+r_{12}}\right)\frac{1}{1+r_{01}}, \end{align*} the expectation is under the year-1 forward measure. However, in the identity \begin{align*} (1+r_{01})E(1+r_{12})=(1+r_{02})^2, \end{align*} the expectation is under the year-2 forward measure. For ...


You can create the data using the procedure described in the reference manual on pages 31 and 32. The necessary code is copied below: # The following code may be used to generate an empty data set, # which can then be filled with bond data: ISIN <- vector() MATURITYDATE <- vector() STARTDATE <- vector() COUPONRATE <- vector() PRICE <- ...


You are going to need to interpolate in some way shape or form.... Linear is the easiest and most basic, however it may not capture the curvature, you can use splines to better capture the curve. A nice guide to doing so is here: It's a guide to bootstrapping and it has all the components.


Yes. The map $R(\cdot;S,T):\mathbb{R}^{2}\to\mathbb{R}$ completely describes the forward rate/spot rate term interest rate structure for each $t\geq0$. (You can think of it as the market interest rate surface for the rate $R$ at time $t$). The notation $R(t;S,T)$ is meant to remind you that $R$ is a stochastic process for $t>0$, the periods of time ...


I am note $100\%$ sure that I understand the question. But yes. More formally one could write $R(t,S,T)$ for the rate from $S$ to $T$ observed at $t$ and $R(t,t,T)$ for the spot.


If you're bootstrapping and if there are bonds maturing on the same date, you should use only one. A good rule is to discard the older issue and keep the more recently issued securities. If you're building a spline, then it really doesn't matter since you're building a best fit curve that best approximates the prices of all bonds. Assuming the quotes you ...


I'm not expert on this field so may not able to answer your question precisely, but I can try the best to offer you some hints. According to the pure expectations hypothesis(PEH), forward rates provide unbiased predictions about future spot rates. Even if the PEH can be rejected, various scholars including Fama has provided evidence for the weaker form of ...


Assume we have $r(t)$ continuously compounded spot rate for maturity $t$. The price of the 2-year bond with semi-annual coupon $C$ is known to be $P$. We already have $r(0.5)$ and $r(1)$. We need $r(2)$ and $r(1.5) = f(r(1), r(2))$. Then $$ P = C [e^{-0.5 \times r(0.5)} + e^{-r(1)}+e^{-1.5 \times r(1.5)}] + (1+C)e^{-2 \times r(2)} $$ Using linear ...


It turned out to be more simple than I thought. First, be sure to replace "STARTDATE" with "ISSUEDATE" when building the list. Once the list is build simply reclassify it using the following command: class(mybonds)="couponbonds" That's it!

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