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# Minyan Mailbag: Time Premiums and Options

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## Don't get caught up in time premium on an absolute basis.

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Prof Succo,

I look at Newmont (NEM) Feb 06 call options strike \$57.50. They sell for a time value of 80 cents. Then I look at NEM Feb 06 calls strike \$60. They sell for a time value of \$1.60.

I am puzzled on why the time value is so different for these options. In one case I pay up a bit more up front and get a better price. In the second case I pay a bit less but seem to have more time risk against me.

Again not for directional bias, but how would you value them in your models for whatever you can guide me here.

Thank you,

Minyan Suhas

MS,

Your numbers on time premium are approximately correct so no need to fiddle with them.

From a theoretical standpoint, one where we value options based on the volatility of a stock (an arbitrage point of view where the stock can go either up or down and direction is not a factor), the 60 strike calls are slightly less expensive. In other words, as a volatility vehicle, the 60 strike should produce more profits if the stock gets more volatile from here. I know this simply because the "implied volatility" of the 60 option is slightly lower (the 60 strike is priced so that the arbitrage buyer breaks even if the stock trades at a 35% volatility and the 57.5 strike if the stock trades at a 38% volatility).

But this does you, a person who is buying the calls speculating on an up direction, little good. So I will try to explain using few numbers.

First, don't get caught up in time premium on an absolute basis: It is comparing apples to oranges (although they are both fruits, so there is some good in comparing) when looking at time premiums of different strikes because the leverage is different in each (but as I allude to, don't abandon the comparison, just evaluate it indirectly).

If I think the stock is really going up, the 60 strike offers more leverage simply because it is a cheaper overall price. I can buy more of them. If I have \$2,000 to bet, I can buy 8 of the 60 strike calls, but only 4.7 of the 57.5 strike. If the stock goes to 65 I make \$2,000 profit by owning the 60's and only \$1,500 if I own the 57.5 strike.

The seller, if they are an arbitrage trader like me, knows this and will charge more time premium for the higher levered option (another way of saying the 60 strike is a better volatility vehicle). If the seller is an over-writer, they never target in the money options like the \$57.5 strike; they target more at the money options where the time premium is greater. This is why in general out of the money calls trade at cheaper theoretical prices than in the money calls (the 60 strike is relatively less in the money).

-Succo
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