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The derivative of the bond prices is very sensitive to the interpolation mode. actually, if you use a linear interpolation mode, you will have some cases for which the right derivative is different from the left derivative at a given point.


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There is a way, although you will have to code the logic. I'm assuming you want the tenor DV01 (change of market value for a shift of 1 bp in the market rate for a given tenor) and not the PV01 (present value of 1 bp). Also, bear in mind Luigi's warning on the interpolation between the curve tenor points in one of the posts you mentioned. import QuantLib ...


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Already answered, but... from scipy.optimize import root def pv(r): return 2000 / (1+r)**2 + 3000 / (1+r)**4 rate = root(lambda x: pv(x) - 4000, 0.)['x'][0] print(f"Rate is {rate*100:.5f}%") print(f"Present Value is {pv(rate):,.2f}") Rate is 7.30274% Present Value is 4,000.00


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try this : 4000= 2000/(1+r)^2 + 3000/(1+r)^4 solving this equation for r you'll find equals 7.30274083178438%.


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I believe the duration constraint and the proceeds constraint are not self consistent. You cannot satisfy both. The duration constraint alone fixes $N_1/N_2$ and $N_3/N_2$, so you cannot also satisfy the proceeds constraint.


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While the answer seems to be clear, the reason why this correlation to interest rates was important is due to the posting of margin. The book you're reading was written prior to Dodd-Frank, Swaps clearinghouses and collateral collection for all forward contracts. Today, presuming both products are collateralized via margin, there will be no difference in ...


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You are obviously using a local-optimizer ( here Nelder-Mead method). One should expect different results for different initial guesses as it will get stuck to a local minima ( or just a "solution" for Nelder-Mead, as it is a heuristic optimizer). In practice, play around and collect the different solutions and their errors, the smaller the error , the ...


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The easiest way to understand this issue is to consider a basket holding opposite positions in the two derivatives. tl;dr: The futures have a linear profile whereas the forward is convex due to discounting, so there is a bias priced in by the market Building a simple, par basket So we are long some interest rate futures and short some Forward Rate ...


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For your first doubt: the futures price is proportional to the asset price, so they are perfectly correlated. For your second doubt: if futures price is positively correlated to interest rates, the buyer of a futures contract will (tend to) make a gain when interest rates are higher. The gain is immediately realised through margin calls, and invested at ...


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It all depends on how you want to represent your yield curve internally. If you choose to use compounded rates as internal yield curve then yes you would need to convert. All you care about in curve bootstrap is that you want to reprice exactly the instruments you use as input (usually being Libor deposit rates, forward rates, futures, swaps, OIS, basis ...


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Assume the (annualised, continuously compounded) forward rate between two nodes, say $t_{10}$ and $t_{12}$, is constant, say $ f_{10,12}$, then the discount factors of the two consecutive knots will be linked as follows: $D_{12}=D_{10}e^{-f_{10,12} \left(t_{12}-t_{10}\right)}=D_{10}e^{-2f_{10,12}}$ From which is then easy to infer the formula for $t_{11}$, ...


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