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A zero-coupon bond promises to pay $1000 in three years. However, there is a 20% probability that the bond issuer defaults and investors are only able to get $700. There is a further 10% probability that the bond issuer defaults and investors get nothing ($0). To clarify, there is a 70% probability that the bond pays off the full $1000 and a 30% total probability that the bond defaults and the investors get less than $1000. Assume that investors are risk neutral and that time-equivalent treasuries offer an interest rate of 8% per year. The bond is zero-coupon, so makes no intermediate payments. Part 1 What is the expected payoff (in dollars) of the bond in three years? Part 2 What is the current traded price of the bond today? (Remember that the bond pays off or defaults in three years.)

A zero-coupon bond promises to pay $1000 in three years. However, there is a 20% probability that the bond issuer defaults and investors are only able to get $700. There is a further 10% probability that the bond issuer defaults and investors get nothing ($0). To clarify, there is a 70% probability that the bond pays off the full $1000 and a 30% total probability that the bond defaults and the investors get less than $1000. Assume that investors are risk neutral and that time-equivalent treasuries offer an interest rate of 8% per year. The bond is zero-coupon, so makes no intermediate payments. Part 1 What is the expected payoff (in dollars) of the bond in three years? Part 2 What is the current traded price of the bond today? (Remember that the bond pays off or defaults in three years.)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 39E: The following problem submitted by Daniel Hahn of Blairstown, Iowa, appeared in the Ask Marilyn...
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A zero-coupon bond promises to pay $1000 in three years. However, there is a 20% probability that the bond issuer defaults and investors are only able to get $700. There is a further 10% probability that the bond issuer defaults and investors get nothing ($0). To clarify, there is a 70% probability that the bond pays off the full $1000 and a 30% total probability that the bond defaults and the investors get less than $1000. Assume that investors are risk neutral and that time-equivalent treasuries offer an interest rate of 8% per year. The bond is zero-coupon, so makes no intermediate payments.

Part 1 What is the expected payoff (in dollars) of the bond in three years?

Part 2 What is the current traded price of the bond today? (Remember that the bond pays off or defaults in three years.) 

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