Continuous compounding question

[stunnerrunner]

When there is continuous compounding in forward contracts, how do you know when to use a negative sign in S0e^-rt versus S0e^rt? In the answers there are mixed uses of a negative sign and no negative sign (reading 48 Eoc #s8b and 7a)

 

[ryzhiy]

You should use the negative sign to discount for the future dividend payments. That is not the Rfree that you are using, but the dividend yield.
The formula for for the equity future (for equities you use the continious IR, for other discret) is:
F = S0 * exp(Rfree*t)*exp(-DY*t)

 

[S2000magician]

ryzhiy wrote:You should use the negative sign to discount for the future dividend payments. That is not the Rfree that you are using, but the dividend yield.
The formula for for the equity future (for equities you use the continious IR, for other discret) is:
F = S0 * exp(Rfree*t)*exp(-DY*t)

= S0 × exp((Rfree – DY) × t)

 

[breadmaker]

General rule for continuous compounding: exponent is negative (positive) when discounting (accumulating).
It’s very much analogous to accumulating with (1+i)^t or discounting with (1+i)^(-t).

 

[CMLSML]

breadmaker wrote:
General rule for continuous compounding: exponent is negative (positive) when discounting (accumulating).
It’s very much analogous to accumulating with (1+i)^t or discounting with (1+i)^(-t).

Nice!