Cox-Ingersoll-Ross CIR
Tags: #Financial #EconomicsEquation
$$\mathrm{d} r(t) = a[b - r(t)] \mathrm{d} t + \sigma \sqrt{r(t)} \mathrm{d} Z(t) \\ P(r, t, T) = A(T-t)e^{-rB(T-t)} \\ \gamma = \sqrt{(a-\bar{\phi})^{2} + 2 \sigma^{2}} \\ q(r, t, T) = \sigma \sqrt{r} B(T-t) \\ \text{yield to maturity} \\ \frac{2ab}{ a - \bar{\phi} + \gamma}$$Latex Code
\mathrm{d} r(t) = a[b - r(t)] \mathrm{d} t + \sigma \sqrt{r(t)} \mathrm{d} Z(t) \\
P(r, t, T) = A(T-t)e^{-rB(T-t)} \\
\gamma = \sqrt{(a-\bar{\phi})^{2} + 2 \sigma^{2}} \\
q(r, t, T) = \sigma \sqrt{r} B(T-t) \\
\text{yield to maturity} \\
\frac{2ab}{ a - \bar{\phi} + \gamma}
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Introduction
Equation
Latex Code
\mathrm{d} r(t) = a[b - r(t)] \mathrm{d} t + \sigma \sqrt{r(t)} \mathrm{d} Z(t) \\
P(r, t, T) = A(T-t)e^{-rB(T-t)} \\
\gamma = \sqrt{(a-\bar{\phi})^{2} + 2 \sigma^{2}} \\
q(r, t, T) = \sigma \sqrt{r} B(T-t) \\
\text{yield to maturity} \\
\frac{2ab}{ a - \bar{\phi} + \gamma}
Explanation
Latex code for the Cox-Ingersoll-Ross model.
: 1-year interest rate.
: 1-year bond price
: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.
: Observed year-1 price of a 1-year bond
Related Documents
- Cox-Ingersoll-Ross Model
- A THEORY OF THE TERM STRUCTURE OF INTEREST RATES
- Cox-Ingersoll-Ross (CIR) model-Mathworks
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