I am using the QuantLib library to determine the historical simulation prices of a fixed rate bond. The idea behind my simulation is to use the spot curve as driver of the bond price. Let $\{y^{j}(t)\}_{t=1}^T$ be the historical series of node $j$ of the spot curve. In general I consider a number $n$ of nodes (for example 1-month node, 3-months node, 1-year node and so on) and an annual historical series for each node. I then calculate the simulated scenarios of the curve according to the canonical formula

$ySim^j(t) = y^j(T)(y^j(t) - y^j(t-1))$

where $y^j(T)$ is the value of the spot rate at the calculation date. However, I observe that the simulated scenarios differ little from the initial value $y^j(T)$ for each node $j$ and, for this reason, I get a bond price that does not differ much from the original value.

How can I amplify the simulated scenarios on the spot rate nodes? Is there a method that allows me to amplify the values of the simulated rates?

Thanks for your help


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