Question

Suppose that in a risk-neutral world the CIR parameters are $a=0.1, b=0.03$, and $\sigma=0.07$. The market price of interest rate risk is -1 times the square root of the short rate. What are the risk-neutral and real-world processes for (a) the short rate and (b) a zerocoupon bond with a current maturity of 4 years.

   Suppose that in a risk-neutral world the CIR parameters are $a=0.1, b=0.03$, and $\sigma=0.07$. The market price of interest rate risk is -1 times the square root of the short rate. What are the risk-neutral and real-world processes for (a) the short rate and (b) a zerocoupon bond with a current maturity of 4 years.

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Options, Futures, and Other Derivatives

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 31, Problem 5

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Step 1

The CIR model is given by the following stochastic differential equation: dr(t) = a(b - r(t))dt + σ√r(t)dW(t) where r(t) is the short rate at time t, a is the speed of mean reversion, b is the long-term mean of the short rate, σ is the volatility of the short Show more…

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Suppose that in a risk-neutral world the CIR parameters are $a=0.1, b=0.03$, and $\sigma=0.07$. The market price of interest rate risk is -1 times the square root of the short rate. What are the risk-neutral and real-world processes for (a) the short rate and (b) a zerocoupon bond with a current maturity of 4 years.

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