calculate bond price from spot rate
d = 1/(1 + r )3
find spot rate from discount factor, find r
(1 + r(3))3 = (1+r(2))2(1+f(2,1))
(1 + r(3))3 = (1+r(2))(1+f(1,2))2
find spot rate from forward rate, find r
Forward rate, is a rate that will make an investor indifferent between two scenarios. For example, 2 year forward rate 3 years from now, is a rate that make investor indifferent between investing in 5 year zero coupon bond or investing in 3 year zero coupon bond and reinvesting the proceeds for two more years after the 3 year instrument matures.
f(2,3) - three years forward rate, two years from today
F(2,3) =
2 = wait
3 = invest
total = 5
Convexity
The convexity of callable bond is negative when near the money. The convexity of putable bond is always positive when near the money.
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A bond with less convexity is more affected by interest rates than a bond with more convexity.
Bond A has more convexity than Bond B. When yield increase by large amount, Bond B price decrease more than Bond A.
The effective convexity of a putable bond cannot be less than that of an otherwise identical option free bond-->wrong
Callable Bond, Putable Bond
V(putable bond) = V(normal) + V(put option)
V(callable bond) = V(normal) - V(call option)
yield curve moves to upward sloping, the value of put option embed in bond increase
V(putable bond) = V(normal) +V(put option), so putable bond value increase
Pure expectation theory assume risk neutrality, investors unaffected by uncertainty, risk premiums do not exist
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