0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 Time to Expiration (months)

Recall from our earlier chapter on options that the intrinsic value of an option is:

Call intrinsic value = Max[S - E, 0] Put intrinsic value = Max[E - S, 0]

where "Max[S - E, 0]" just means S - E or 0, whichever is bigger. American-style options can never sell for less than their intrinsic value because, if one did, there would be an arbitrage opportunity. For example, suppose a stock sells for $60. A three-month call option with a $50 strike price sells for $8. What do you think?

You think you are going to be rich because you can buy the option for $8, exercise it for $50, then sell the stock for $60 for a $2 riskless profit. To prevent this type of simple arbitrage, the option has to sell for at least its intrinsic value of $60 - 50 = $10. In reality, the option might sell for $11. The extra $1 in value over the intrinsic value is called the "time premium." In other words, an option's value can be written as:

Option value = Intrinsic value + Time premium

It is the time premium that wastes away or decays as time goes by. The reason is that the day an option expires, it is worth exactly its intrinsic value because, on that day, it must be exercised or torn up. The existence of the time premium also explains our earlier observation that a call option is always worth more alive than dead. If you exercise an option, you receive the intrinsic value. If you sell it, you get the intrinsic value plus any remaining time premium.

EXAMPLE 24.7 |

Time Premiums

At the end of September 2001, shares in Microsoft were going for about $51.20. A call option expiring in January of 2002 with a $55 strike was quoted at $3.70. A put with the same strike was quoted at $7.90. For both options, what are the intrinsic value and time premium?

24. Option Valuation

Beginning with the call option, we see that it is out of the money because the $55 strike price is higher than the $51.20 stock price. The intrinsic value is zero, and the entire $3.70 is therefore time premium. The put is in the money, and its intrinsic value is $55 - 51.20 = $3.80. The put's value is $7.90, so the time premium is $7.90 - 3.80 = $4.10.

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