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First question I downvoted David answer because $f(0,0) \neq 0$ (generally speaking). And that's because it's the instantaneous forward rate at time $t=0$, that is $f(0,0) = f(0, 0, \Delta t)= r(0)$ so it's the starting value of the short rate process. In practice, you can set $\Delta t$ as one day (in years) and compute the forward rate (continuously ...


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I suspect that your lecturer might be right; but for all the wrong reasons ;-) If a company uses derivatives to hedge its balance sheet, these assets/liabilities are effectively working capital. Its position with the CME/CBOE is no more (legally) senior or junior than its liabilities to John the plasterer, for doing up the Houston office last month. The ...


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Senior debt has the highest priority in bankruptcy and therefore the lowest risk. Thus, this type of debt typically carries or offers lower interest rates. Meanwhile, subordinated debt carries higher interest rates given its lower priority during payback. A borrower's credit credit evidences their ability to repay debt. A stronger borrower would have a ...


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You actually have more than one question here. First Question: Price of bond in Hull White model where t=0 The $t$ refers to start date of the bond and $T$ is the maturity of the bond. If $t=0$ you are valuing a bond that starts now (or spot) and the forward will $f(0,0)=r(0)$ and $P(0,0)=1$ (Thanks to LePiddu for pointing that out) Second Question: ...


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There is a simple way to find the number of rolls with the minimum of 4: the number of rolls with the minimum of 6 is 1. The number of rolls with the minimum of 5 is the number of rolls for which all outcomes are 5 or 6 minus the number of rolls with the minimum of 6: 2*2*2-1=7. The number of rolls with the minimum of 4 is the number of rolls for which ...


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This isn't really an option as it is an exercise in probability. How many rolls have a minimum of 6? 1 = 3C3 (6s) How many rolls have a minimum of 5? 7 = 3C3 (5s) + 3C2 (5s6s) + 3C1 (5s6s) How many rolls have a minimum of 4? 19 = 3C3 (4s) + 3C2 (4s5s) + 3C1 (4s5s) + 3C2 (4s6s) + 3C1 (4s6s) + 3P3 (4s5s6s) How many rolls have a minimum of 3? ...


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The last edition (10th, 2017) of Hull's book explains it fairly well. Basically, there is indeed a theoretical arbitrage within the dual curve framework: you could borrow at the overnight rate (Fed funds, SONIA, EONIA, etc.), lend at LIBOR and cash-in the spread in all your dynamic derivatives replication trades. However, such arbitrage is only theoretical : ...


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Your dynamics under the $T_{i-1}$-forward measure is wrong. Specifically, let $P_{i-1}$ and $P_i$ be, respectively, the $T_{i-1}$- and $T_i$-forward probability measures. Moreover, let $\Delta_i = T_i-T_{i-1}$. Then, for $0\le t \le T_{i-1}$, \begin{align*} \eta_t &\equiv \frac{dP_{i-1}}{dP_i}\big|_t \\ &= \frac{P_i(0, T_i)}{P_{i-1}(0, T_{i-1})}\...


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