sol06

# 90 084 and 077 forward rates are 202 303 513 and

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: .77 Forward rates are: 2.02%, 3.03%, 5.13%, and 7.37%. and 9.79% for t=0,1,2,3,4 (b) Let be the zero prices of Argentina Bond. Similar to part (a), we have: the zero prices for t=1, 2, 3, 4, 5 are 0.97, 0.90, 0.78, 0.60, 0.37 respectively. And Forward rates are: 3.03%, 7.25%, 15.45%, 30.35%, and 62.87% (c) Let be the default rate at time t. We get the implied probability of default for Argentine bonds are 0.98%, 3.93%, 8.94%, 17.64%, 32.59% respectively. 6. Use the bond spread sheet to find the prices of zero bonds paying \$100 at maturities 1, 2, 9, 10, 99, 100, 199, and 200 years, assuming a starting interest rate of 8% and a rate volatility of 60%. What is happening to the forward rate? Solution: Use the callable bond spread sheet, although the interest rate is volatile in this case, we can still use backward induction to solve the price of the bond at each state. At state s, ( ) [ ( )] [ ( )] where c=0 for zero coupon bonds. Hence, we can get all zero bonds prices by changing maturities in the spread sheet. We see that the zero prices decreases when maturity increases, as we discount more when we have longer maturity. Use the formula , we can get the forward rates. Maturities 1 2 9 10 99 100 199 200 Zero Bonds Prices 92.59 84.75 43.23 40.02 7.87 7.82 5.28 5.26 Forward Rate 9.25% 8.02% 0.64% 0.38% When interest rate follows a stochastic process with positive volatility, the forward rate goes down as maturity increases. Forward rate is always positive but goes to 0 when maturity is big enough....
View Full Document

## This note was uploaded on 01/20/2013 for the course ECON 251 taught by Professor Geanakoplos,john during the Spring '09 term at Yale.

Ask a homework question - tutors are online