Question

Suppose the short rate $r$ is $4 \%$ and its real-world process is $d r=0.1(0.05-r) d t+0.01 d z$, while the risk-neutral process is $d r=0.1(0.11-r) d t+0.01 d z$ : (a) What is the market price of interest rate risk? (b) What is the expected return and volatility for a 5 -year zero-coupon bond in the riskneutral world? (c) What is the expected return and volatility for a 5 -year zero-coupon bond in the real world?

   Suppose the short rate $r$ is $4 \%$ and its real-world process is $d r=0.1(0.05-r) d t+0.01 d z$, while the risk-neutral process is $d r=0.1(0.11-r) d t+0.01 d z$ :
(a) What is the market price of interest rate risk?
(b) What is the expected return and volatility for a 5 -year zero-coupon bond in the riskneutral world?
(c) What is the expected return and volatility for a 5 -year zero-coupon bond in the real world?

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 31, Problem 10

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Step 1

1(0.11-r) and the real-world drift is 0.1(0.05-r). The volatility is 0.01. Market price of interest rate risk = (0.1(0.11-r) - 0.1(0.05-r)) / 0.01 Simplifying the equation, we get: Market price of interest rate risk = (0.011 - 0.005r - 0.005 + 0.001r) / Show more…

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Suppose the short rate $r$ is $4 \%$ and its real-world process is $d r=0.1(0.05-r) d t+0.01 d z$, while the risk-neutral process is $d r=0.1(0.11-r) d t+0.01 d z$ : (a) What is the market price of interest rate risk? (b) What is the expected return and volatility for a 5 -year zero-coupon bond in the riskneutral world? (c) What is the expected return and volatility for a 5 -year zero-coupon bond in the real world?

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