I have a bond with coupon rate 10% and annual coupon payments with maturity 3 years, face value 1000 and yield to maturity 8%. The bond pays the first coupon with 20% probability and nothing with 80% of probability. If it pays the first coupon, then with 75% probability it also pays the other coupons + face value and with 25% it does not. What is the price?

I tried to solve it this way:

annual coupon pmts: 100, face value + last coupon: 1100  
Present value of first coupon: 100/1.08 = 93  
Pres. value of the last 2 coupons (+face value): 100/1.08^2 + 1100/1.08^3 = 959

Price = 80% * 0 + 20% * (93 + 75% * 959) = 163

However, the solution differs from my result. Where is the mistake?

  • 3
    Is this a homework question? – JoeTaxpayer Jan 13 at 15:04
  • I would compute the expected value for each period by multiplying the probability with the payoff (coupon/notional) and then discount the results to get the present value, instead of starting with the present values. – 0xFEE1DEAD Jan 13 at 18:26

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.