# Why a European call option (no div.) costs more than spot minus strike

Posted 12-29-2008 at 12:52 AM by Marid Audran

I think the discussion and formula derivations in McDonald (pp. 294-95) are not as simple as they could be.*

"Spot minus strike" is the same thing as "exercise value," in the case of an American option. But I want to focus on European options, about which put-call parity says

The assumption of no dividends implies PV(F)=S, today's spot price. Applying this equality and adding P to both sides yields

The inequality C >= S-PV(K) is what is illustrated in Table 9.4 in the textbook. The inequality C>S-K is Formula 9.11.

* With that said, the breakdown in Formula 9.11 for a European option,

seems important. Furthermore, in discussing American options at the top of P. 296, McDonald writes:

This seems especially important, as well as being related to the "time value of money" term in Formula 9.11. I need to think about it more.

"Spot minus strike" is the same thing as "exercise value," in the case of an American option. But I want to focus on European options, about which put-call parity says

C - P = PV(F) - PV(K).

The assumption of no dividends implies PV(F)=S, today's spot price. Applying this equality and adding P to both sides yields

C = S - PV(K) + P >= S - PV(K) > S - K.

The inequality C >= S-PV(K) is what is illustrated in Table 9.4 in the textbook. The inequality C>S-K is Formula 9.11.

* With that said, the breakdown in Formula 9.11 for a European option,

Call price = (Exercise value) plus (the insurance of a "put") plus (time value of money on strike price),

seems important. Furthermore, in discussing American options at the top of P. 296, McDonald writes:

Quote:

That is, if interest on the strike price (which induces us to delay exercise) exceeds the present value of dividends (which induces us to exercise), then we will for certain never early-exercise at that time.

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