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2

You tell me. The IR parity is a statement of an arbitrage: that if can exchange my amount in currency A into another currency B, invest it and enter a forward spot trade to get back my currency A at a greater effective rate than the rate in currency A, then I have an arbitrage. The trades for the arbitrage, therefore, are a Spot FX trade, lend currency B, ...

1

I recenlty wokred on a similar problem and solved it with the help of Quantlib library. Assuming you are working with EUR and USD: get cross currency (xccy) swap data EUR / USD. You want to know how the xccy is collateralized and if Mark-to-Market resets apply to the USD leg. get interest rates swaps fixed vs ois / 3m / 6m in EUR and USD build USD/...

1

Alex's post hits the main point: leverage amplifies returns (either positive or negative). In this case, it is not interest rate but loan constant that we should be focusing on. For a \$5.68MM loan (80% of \$7.1MM), the loan constant is 7.55%. In excel, I used the function: $$PMT(5.75\%/12,30\times12,5680000)\times12$$ to come up with annual debt service ...

0

The Black 76 swaption formula works for all these cases. The expiration time T= 1mo, 2mo or 3mo but the forward rate of the swap is the same in each case. The market will place different implied volatilities on these 3 options, according to the expectations of realized volatility in these 3 time periods.

2

By the usual integrating factor method, \begin{align*} r_t = r_0e^{-\beta t} + \int_0^t \alpha(s) e^{-\beta(t-s)}ds +\sigma \int_0^t e^{-\beta(t-s)}dW_s. \end{align*} Let \begin{align*} x_t &=\sigma \int_0^t e^{-\beta(t-s)}dW_s, \textrm { and}\\ y_t &=r_0e^{-\beta t} + \int_0^t \alpha(s) e^{-\beta(t-s)}ds. \end{align*} Then $r_t = x_t + y_t$, ...

6

Let $$Y_t = \int_0^t N_u du$$ where $(N_t)_{t \geq 0}$ figures a Poisson process with intensity $\lambda$. Using the stochastic Fubini theorem we have that: \begin{align} Y_T &= \int_0^T N_t dt \\ &= \int_0^T \int_0^t dN_u dt \\ &\color{lightgray}{= \int_0^T \int_0^T \mathbf{1}\{u \in [0,t]\} dN_u\ dt} \\ &\color{lightgray}{= \int_0^T \...

-1

If I have understand right what you are looking for, I think that Nelson–Siegel Model can halp you, google it. Hear some readng: Nelson-Siegel model

0

Does the link below help? It's free and has daily 3 month rates. https://fred.stlouisfed.org/search?st=Libor+3+month+daily

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