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Answer: $2.12 million
The bank is **receiving fixed** and **paying floating**, so when rates fall, the swap becomes **more valuable** to the bank. At \(T+0.5\) years, the current exposure is the positive market value of the swap: \[ \text{Exposure} = \max(V,0) \] Using the remaining 2.5 years and the new flat swap rate of **4.1%**, the swap value is approximately: \[ V \approx N (K - S) A \] where: - \(N = 100\) million - \(K = 5.0\%\) - \(S = 4.1\%\) - \(A \approx 2.35\) (present value of the remaining fixed-leg annuity) So: \[ V \approx 100{,}000{,}000 \times 0.009 \times 2.35 \approx 2.12\text{ million} \] Therefore, the current exposure is approximately **$2.12 million**.
Author: Manit Arora
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Q-177.1. Assume that today (T0), a bank enters into a fairly priced (i.e., initial value equals zero) interest rate swap where the bank receives a fixed rate of 5.0% per annum compounded semi-annually in exchange for paying six-month LIBOR. The notional amount is USD $100 million, and the tenor is three years. When the bank enters the swap, the LIBOR/swap rate curve is flat at 5.0%. Six months later, the LIBOR/swap rate shifts down by 90 basis points. At this time (T + 0.5 years), the current exposure of the bank will be nearest to what?
A
Zero
B
$440,000
C
$2.12 million
D
$102.12 million
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