Your money: why option premiums can never be negative

Thus, both call options and put options, whether European or American, entail the payment of a positive premium at the outset, by the buyers.

By Sunil Parameswaran

Traders new to options may wonder why they have to pay a premium to buy an option, given that a premium is not required to buy a futures contract. The answer lies in the fact that the first is a contingent contract, while the second is a contract of engagement. In the case of a futures contract, once the position is taken, both long and short face the specter of negative cash flow.

However, in the case of options, once the contract is concluded, the long will have positive or no cash flow, while the short will have negative or no cash flow. This is the reason why options, both calls and puts, require longs to pay a premium to shorts at the start.

Buy and sell options
Option premiums can never be negative. A negative premium would imply that a trader is willing to pay you to buy an option. If so, buy it knowing full well that the subsequent cash flow will be either positive or zero. Therefore, this is a clear case or arbitration. Thus, both call options and put options, whether European or American, entail the payment of a positive premium at the outset, by the buyers.

The bonus consists of two components, intrinsic value and time value. Intrinsic value is what the holder would get if they were immediately exercised. It is therefore equal to the extent to which the option is in the money if it is in the money, or zero if the option is out of the money or in the money. Thus, intrinsic value cannot be negative.

The difference between the option premium and the intrinsic value is called the time value or speculative value of the option. This is the additional premium paid by the buyer for the waiting and subsequent exercise option. American options cannot have a negative time value, i.e. the premium must be greater than or equal to the intrinsic value.

European call
European calls on a non-dividend-paying share cannot have a negative time value either. However, European puts on a stock and European calls on a dividend-paying stock may have a negative time value. This can be appreciated as follows. Suppose the stock price is close to zero. The holder of a European put would like to exercise, but is constrained by the fact that the exercise date is later. This could result in a negative time value for the option. In the case of a European call for tenders on a share paying a dividend, the holder may wish to exercise and recover the dividend. However, the European character of the option prevents this. Therefore, the value of time can be negative.

The upper limit of the call premium is the share price. No one will pay more than the share price to acquire an option, resulting in the subsequent payout if an exercise price is exercised. If the stock is so appealing, you might as well buy it now. The upper limit for an American put is the strike price, while for a European put is the current value of the strike price. The lowest possible share price is zero. Thus, the upper bound for the first is the strike price. In the case of the latter, this cash flow will only be realized at maturity. Therefore, the upper limit is the present value of the strike price.

The author is CEO of Tarheel Consultancy Services

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