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Results tagged with bond
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user 7788
A bond is a fixed-income instrument generating cash flows at some specific dates in the futures. These cash-flows depend on the interest rate of the bond, which can either be fixed or variable. It is a debt instrument acting as a loan made from the buyer to the seller.
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Yield to Maturity
I think $t_n$ is the time the nth coupon is paid and $t_n$-t is the time difference between the time the coupon is paid at the time the bond is issued. … So if a bond is issued on May 10 and coupons are paid on June 10, July 10 and August 10, then the $t_n$ - t's are 1/12, 2/12 and 3/12.
Y cannot be solved directly. It's like Internal Rate of Return. …
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If we modify duration, should we modify bond price? Options Futures and Other Derivatives
The claim is that if bond yield increases from 12% to 12.1%, then the bond price will decrease from 94.213 to 93.963. … Shouldn't we recompute the bond price using semiannual compounding? …
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If we modify duration, should we modify bond price? Options Futures and Other Derivatives
Recomputing the bond price would just give the same bond price XD …
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answer
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Differential equation involving bond price and forward rate
Given forward rate f(t,T) and bond price P(t,T) where
$f(t,T) = - \frac{\partial}{\partial T} \ln P(t,T)$,
$P(T,T) = 1 = P(t,t)$,
T>0 and
$t \in [0,T]$
Does it follow that $P(t,T) = exp(-\int_{t}^ …
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Differential equation involving bond price and forward rate
The negative solution does not satisfy $P(T,T)=P(t,t)=1$
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Differential of stochastic term
ki3i:
A less heuristic proof is the following. Define the function $Y(t,T,\mathcal{P})$ such that, for each partition $\mathcal{P}$ (of size $n$) of the interval $[t,T]$, we have
$$
Y(t,T,\mathcal{P …
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answer
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Girsanov theorem and default rates in bond credit rating
Default rates are kind of probabilities, right?
Is it possible to use the Girsanov theorem in that context? For example if we have a table of real world probabilities, could we use the Girsanov theor …
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How can we have negative probabilities in finance? Can we have negative payments in bonds? I...
In Half of a Coin: Negative Probabilities, the author mentions bond duration. … Then the bond value today is given by
$$B = \sum_{t=1}^{n} R_tv^t$$
The bond duration is
$$D = \frac{\sum_{t=1}^{n} tR_tv^t}{\sum_{t=1}^{n} R_tv^t}$$
It can be seen that $$D = E[T]$$
where
$T$ is …
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2
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Incorrect characterization of spot rate?
Is the t in the red boxed $R(t,T)$ supposed to be the same as the S in the green boxed $R(S,T)$?
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2
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Differential of stochastic term
Question 1:
How does one come up with the equation in the red box below?
It looks like some kind product rule, but I'm not sure how to apply Ito's lemma here.
Bjork doesn't seem to explain it ful …
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Differential of stochastic term
Note that Bjork says the fundamental theorem of integral calculus. ki3i proves it rigorously, but we can also guess based on analogy with integral calculus specifically the general form of the Leibniz …
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