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3

The present value of a Vanilla Swap (the word Vanilla is used since I am considering the simplest swap, i.e., notional equal to one, contiguous time intervals, constant rate, etc) is given by: \begin{align} V_s(t) &= \mathbb{E}_t^Q \left[ \sum_{i=1}^N D(t, T_{i+1}) \cdot \tau_i \cdot (L(T_i, T_i, T_{i+1}) - k) \right] \end{align} where $T$ describes the ...


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This is a Structured Product. Desks issuing these products make money by selling the product for X when it is really worth X-Y (where X is usually 100%, and Y will be some number of the order 1%, depending on the complexity and maturity of the product). In the case you reference, you can see from the link that Y was 1.75%. This means that, unhedged, the ...


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Discretisation schemes If you want to simulate the path, then common practice is to sample from the exact distribution, as for the CIR process this is known. The distribution can be found from the original CIR process (1985). However, this requires sampling from a non-central $\chi^2$-distribution, which can be very expensive, and a bit more difficult to ...


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