The Lower Bound of a European Call
The price of a
European call must be at least equal to the greater of zero or the stock price minus
the present value of the exercise price:
Ce(S0, T, X) = Max(0, S0 - X(1+r)-T)
The following
figure shows this result. The curved line is the call price, which must lie above the lower bound. As expiration approaches,
the time to expiration decreases such that the lower bound moves to the right
with the call price following it. At expiration,
the lower bound and price curves
converge with the Max(0, S0 - X) curve.
When we showed that the intrinsic value of an American call
is Max(0, S0 - X), we noted that the inability to
exercise early prevents this result holding for a European call. Now we can see that this limitation is of no
consequence. Because the present value of the exercise price is less than the
exercise price itself, the lower bound of a European call is greater than the intrinsic value of an American call.
Finally we
should note that if the stock pays dividends such that the stock price minus the
present value of the dividends is 
then the
lower bound is:
Ce(S0, T, X) = Max(0, S0
- X(1+r)-T)
No comments:
Post a Comment