Dec
3

## Zero coupon CIR bond price

A simple Matlab code to calculate a zero-coupon bond price under the Cox-Ingersoll-Ross (CIR) Interest Rate Model, where r0 is the current interest rate, alpha, kappa, sigma are CIR parameters standing for mean reversion speed, long term mean rate, and volatility of interest rate, T is the maturity of bond.

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Calibrating the Ornstein-Uhlenbeck model

h = sqrt(kappa^2 + 2*sigma^2);

A = (2*h*exp((kappa+h)*T/2)/(2*h + (kappa+h)*(exp(T*h)-1)))^((2*kappa*alpha)/sigma^2);

B = 2*(exp(T*h)-1)/(2*h + (kappa+h)*(exp(T*h)-1));

P = A*exp(-B*r0); % bond price at 0

A = (2*h*exp((kappa+h)*T/2)/(2*h + (kappa+h)*(exp(T*h)-1)))^((2*kappa*alpha)/sigma^2);

B = 2*(exp(T*h)-1)/(2*h + (kappa+h)*(exp(T*h)-1));

P = A*exp(-B*r0); % bond price at 0

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