Hi,
I'm programming a forward price of a bond and I have a doubt.
According the 'usual' formula (hp: no accrual in t_0 and no accrual in t_n)
F = S* e^(rt_n )-∑_(i=0:n) [C_t_i *e^(r(t_n - t_i))]
where:
F=forward price
t_n= forward date;
r= repo rate;
C_t_i=coupon in t_i;
S= spot price
According this formula the forward price is the spot price capitalized by the repo rate minus the coupons between today and the forward rate capitalized at the same repo rate.
In my opinion this formula is 'aged' because it assume that the coupons are certainly payed; in a risky world is more correct to discount the coupons at t_0 with a risky curve and the whole difference
(S-∑_Discounted_coupon(with_risky_rate))
Should be capitalized with a repo rate to the forward date.
The difference is not very high but, according to me, in the second formula the risk premium of the coupons is payed to the owner of the risk, while in the other the premium is (uncorrectly) payed to the counterpart.
What do you think about it?
I'm programming a forward price of a bond and I have a doubt.
According the 'usual' formula (hp: no accrual in t_0 and no accrual in t_n)
F = S* e^(rt_n )-∑_(i=0:n) [C_t_i *e^(r(t_n - t_i))]
where:
F=forward price
t_n= forward date;
r= repo rate;
C_t_i=coupon in t_i;
S= spot price
According this formula the forward price is the spot price capitalized by the repo rate minus the coupons between today and the forward rate capitalized at the same repo rate.
In my opinion this formula is 'aged' because it assume that the coupons are certainly payed; in a risky world is more correct to discount the coupons at t_0 with a risky curve and the whole difference
(S-∑_Discounted_coupon(with_risky_rate))
Should be capitalized with a repo rate to the forward date.
The difference is not very high but, according to me, in the second formula the risk premium of the coupons is payed to the owner of the risk, while in the other the premium is (uncorrectly) payed to the counterpart.
What do you think about it?
