VANILLA OPTIONS :   PAYOUT AT EXPIRATION

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OPTION PAYOUT:

The economic value of an option at expiration or exercise follows the definition of intrinsic value applied to the expiration or the exercise date. It is also the absolute value of the directional difference between the strike of an option and its underlying market value at expiration.

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If the option is cash settled at maturity, it is also the cash payment due from the option seller to the option buyer.

 

For a call option it is the underlying price minus the option strike, or zero if the underlying value is below the strike.

 

For a put option it is the strike minus the underlying market value, or zero.

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NOTE THAT THESE ARE THE SAME DEFINITIONS AS THOSE FOR INTRINSIC VALUE, AS THE OPTION PAYOUT IS THE REALIZED INTRINSIC VALUE OF THE CONTRACT AT MATURITY.

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Under most circumstances no rational person would exercise an option that has negative value (eg, that costs him money to exercise) so for valuation purposes the payout is always deemed to be a positive value. However exercise of puts on assets with storage or insurance costs might be efficient under certain circumstances.

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For a call option the payout can be expressed as MAX(0, underlying price minus the strike).

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For a put option the payout can be expressed as MAX (0, strike minus the underlying price).

Call option payouts can in theory be infinite (underlying prices have no upper bounds).

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For non-negative assets put option payouts are bounded at a value for the underlying of zero, at which the payout is equal to the strike.