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An interest rate swap is a financial derivative where two parties exchange interest payments on a specified notional principal over a set period. One party pays a fixed rate, while the other pays a floating rate tied to a reference rate (e.g., LIBOR). These swaps help manage interest rate risk, hedge against rate fluctuations, and enable speculation on future rate changes.
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EPE for interest rate swap
$$
\triangle \ \ \text{EPE}_{\text{swap}} (t) \triangleq E_t^\mathbb{Q} \Big[ \beta(t) \beta(T_k)^{-1} \Big( V_{\text{swap}} (T_k) \Big)^+ \Big] = E_t^\mathbb{Q} \Big[ \underbrace{\beta(t) \beta( …