j******g
发帖数: 175 | 1 A bond has a one year term and one cash flow at year end, with face value $
100 and coupon 6.5%. The 1yr yield for a zero coupon bond is y=5%, with
continuous compounding.
a. What is the price of the 6.5% bond.
b. If the bond duration is defined as Dur = -[p(y+dy) – p(y)] * 100/(P*dy).
c. Assume y has a (risk neutral) Gaussian distribution. Draw the price
distribution of the 6.5% bond with sigma = 1.5% and sigma=2%. [Hint: the 1yr
yield for zero coupon bond is y0=5%].
d. If the bond has a call option embedded, i.e. whenever y<6%, the bond
holder will get $100 back instead of $106.5. What is the price of the bond
when sigma=1.5% and 2%.
e. What is the approximate duration for sigma=2%, if you use dy=0.25. | j******g
发帖数: 175 | 2
这个应该是: 106.5*exp(-0.05)
).
1yr
【在 j******g 的大作中提到】
: A bond has a one year term and one cash flow at year end, with face value $
: 100 and coupon 6.5%. The 1yr yield for a zero coupon bond is y=5%, with
: continuous compounding.
: a. What is the price of the 6.5% bond.
: b. If the bond duration is defined as Dur = -[p(y+dy) – p(y)] * 100/(P*dy).
: c. Assume y has a (risk neutral) Gaussian distribution. Draw the price
: distribution of the 6.5% bond with sigma = 1.5% and sigma=2%. [Hint: the 1yr
: yield for zero coupon bond is y0=5%].
: d. If the bond has a call option embedded, i.e. whenever y<6%, the bond
: holder will get $100 back instead of $106.5. What is the price of the bond
| j******g
发帖数: 175 | 3
).
1yr
P(0,T)*106.5?
P(0,T) is the one year bond price based on the Vasicek model with a=0?
【在 j******g 的大作中提到】
: A bond has a one year term and one cash flow at year end, with face value $
: 100 and coupon 6.5%. The 1yr yield for a zero coupon bond is y=5%, with
: continuous compounding.
: a. What is the price of the 6.5% bond.
: b. If the bond duration is defined as Dur = -[p(y+dy) – p(y)] * 100/(P*dy).
: c. Assume y has a (risk neutral) Gaussian distribution. Draw the price
: distribution of the 6.5% bond with sigma = 1.5% and sigma=2%. [Hint: the 1yr
: yield for zero coupon bond is y0=5%].
: d. If the bond has a call option embedded, i.e. whenever y<6%, the bond
: holder will get $100 back instead of $106.5. What is the price of the bond
| j******g
发帖数: 175 | 4
这样就没有distibution了。有谁可以解答一下么
【在 j******g 的大作中提到】
:
: ).
: 1yr
: P(0,T)*106.5?
: P(0,T) is the one year bond price based on the Vasicek model with a=0?
| j******g
发帖数: 175 | 5 有谁可以解答一下么?
).
1yr
【在 j******g 的大作中提到】
: A bond has a one year term and one cash flow at year end, with face value $
: 100 and coupon 6.5%. The 1yr yield for a zero coupon bond is y=5%, with
: continuous compounding.
: a. What is the price of the 6.5% bond.
: b. If the bond duration is defined as Dur = -[p(y+dy) – p(y)] * 100/(P*dy).
: c. Assume y has a (risk neutral) Gaussian distribution. Draw the price
: distribution of the 6.5% bond with sigma = 1.5% and sigma=2%. [Hint: the 1yr
: yield for zero coupon bond is y0=5%].
: d. If the bond has a call option embedded, i.e. whenever y<6%, the bond
: holder will get $100 back instead of $106.5. What is the price of the bond
| x********9
发帖数: 31 | 6 1. Straightforward , discount the cash at one-year horizon, your answer is
right
2. Why multiply by 100? Duration of an zero coupon bond should always be
equal to its maturity, so it is 1 year.
3. The distribution of price is a lognormal, with mean 0 and variance =
sigma^2
4. Use black-scholes
5. Do it numerically, I dunt know |
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