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@Philadelphia

I have 2 questions regarding probability of default and bond pricing, your inputs are welcome.

njwa(njwa)
本文发表在 rolia.net 枫下论坛I have the following 2 questions and your inputs are welcome:

1. This question is from John Hull’s bible book Options, Futures and Other Derivatives(6th edition). On page 510, there is a table of calculating probability of default. If the probability of default during first year conditional on no earlier default is 2%, then unconditional probability of survival during first year is 1-2%=98%.
Here comes my questions: the book further says that the probability of a default during the second year is 2%*98% and the probability of survival until end of the second year is 98%*98%=96.04%, why?

2. Suppose we have a 5 year bond that pays $6 yearly coupon, the yield to maturity is 7%. Which approach is correct in calculating the bond price in the third year, A or B?
A. Discount the remaining cash flows to the third year and you get the present value of the third year. This present value is the price in the third year.
B. Discount the remaining cash flows to the third year and you get the present value of the third year. Add the two coupon payments($12) in the first two years to the present value of the third year and this sum is the price in the third year.

Thank you very much.更多精彩文章及讨论，请光临枫下论坛 rolia.net
(#1713@52)
Last Updated: 2008-12-30
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Replies, comments and Discussions:

  • I have 2 questions regarding probability of default and bond pricing, your inputs are welcome. -njwa(njwa); 2008-12-30 {1200} (#1713@52)
    本文发表在 rolia.net 枫下论坛I have the following 2 questions and your inputs are welcome:

    1. This question is from John Hull’s bible book Options, Futures and Other Derivatives(6th edition). On page 510, there is a table of calculating probability of default. If the probability of default during first year conditional on no earlier default is 2%, then unconditional probability of survival during first year is 1-2%=98%.
    Here comes my questions: the book further says that the probability of a default during the second year is 2%*98% and the probability of survival until end of the second year is 98%*98%=96.04%, why?

    2. Suppose we have a 5 year bond that pays $6 yearly coupon, the yield to maturity is 7%. Which approach is correct in calculating the bond price in the third year, A or B?
    A. Discount the remaining cash flows to the third year and you get the present value of the third year. This present value is the price in the third year.
    B. Discount the remaining cash flows to the third year and you get the present value of the third year. Add the two coupon payments($12) in the first two years to the present value of the third year and this sum is the price in the third year.

    Thank you very much.更多精彩文章及讨论，请光临枫下论坛 rolia.net
    • too simple -xiaoshou(即然挥之不去,那就让); 2008-12-31 (#1715@52)
      • Why not share the answer you think? -buickregal(Motion - MoveOnFast); 2008-12-31 (#1720@52)
    • 2%possibility default in the first year,1.96%possibility default in the second year,96.04%not default in the first two years -nice_0209(浮木); 2009-1-1 (#1721@52)
    • answer of question 2 should be A -nice_0209(浮木); 2009-1-1 (#1722@52)
    • 1. for any given year with remaining x%, there will be x%*2% default and x%*98% survive. 2. A is right. If pricing on coupon date, just calculate the present value of future coupon; if not, you need to allocate the last coupon. -kevinchen(kevinchen); 2009-1-1 (#1723@52)
    • My 2 Cents -booyao(bobcat); 2009-1-1 {472} (#1724@52)
      Question 1: first year survival rate is 98%, sencond year survival rate is based on first year's 98%, and it's survival is 98% as well, so it will be (1x 98%) x 98%, not as first year's 1 x 98%， 因为第二年要刨掉第一年的default 部分，即2%.

      Question 2: A is correct. 第三年时，该Bond只是一个3Year to maturity 的Bond，其Price应该是将剩余的三个Coupon Price to 第三年（T＝0），加上Bond的本金在第三年时候的价格100/(1+7%)^3. 答案B将Bond的价格和实际买卖是应付的价格混淆。
    • Thanks everybody for the input! -buickregal(Motion - MoveOnFast); 2009-1-1 (#1726@52)

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