Question

) Consider a 4-year, 5% annual coupon bond with a face value of $10,000, which was issued three years ago. The bond just paid the coupon. Therefore, this bond has one year to maturity, and the next payment of the face and coupon will be made in exactly one year, after which the bond will cease to exist. If the bond defaults before next year, it will pay total of $8,000 in one year. The effective 1-year risk-free rate is 3.55%. If the bond is currently selling at $9,501.50, compute the risk-neutral probability that the bond will default within one year.

Answer 1

If bond default next year receipts is 8000

If bond do not default then next year receipts is 10000

Risk free rate is 3.55%

Let probability of default is 1-P

Let probability of non default P

In risk neutral probability the payoff should be equal to current price deposited at risk free rate

P(1000)+(1-P)8000=9501(1.0355)

P(2000)+8000= 9838.28

P(2000)= 1838.28

P = 91.94%

So probability of default is 100-91.94% = 8.08%

So risk neutral probability of default is 8.08%