Why European call options (no div.) with greater time to expiration tend to cost more
Posted 12-29-2008 at 12:26 AM by Marid Audran
Updated 12-29-2008 at 12:27 AM by Marid Audran (adding category)
Updated 12-29-2008 at 12:27 AM by Marid Audran (adding category)
McDonald (p. 297) points out that American call option premiums tend to increase with time to expiration. This fact is not hard to see.
McDonald then says that the same is true for European call options
I found this explanation nonintuitive. The following explanation by example makes more sense to me:
Let S_t be the spot price of the underlying asset (which pays no dividends) at time t. Suppose that today you buy a two-year European call option with strike price K. After one year (i.e., at time t=1), you could sell this option as a one-year European call, whose price (according to Formula 9.11 on Page 294) must be greater than
But S_1 - K (if positive) is precisely the payoff you would get from purchasing a one-year call with strike price K today. So the two-year call will be more valuable a year from now, and therefore (in order to avoid arbitrage) it must be more valuable today.
McDonald then says that the same is true for European call options
Quote:
because, with no dividends, a European call has the same price as an otherwise identical American call.
Let S_t be the spot price of the underlying asset (which pays no dividends) at time t. Suppose that today you buy a two-year European call option with strike price K. After one year (i.e., at time t=1), you could sell this option as a one-year European call, whose price (according to Formula 9.11 on Page 294) must be greater than
S_1 - K.
But S_1 - K (if positive) is precisely the payoff you would get from purchasing a one-year call with strike price K today. So the two-year call will be more valuable a year from now, and therefore (in order to avoid arbitrage) it must be more valuable today.
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