Option Payoffs

Payoffs for interest rate options function are similar to other options. The main difference is that the interest rate options take the days to maturity attached to the agreement into account. Also, the payoff from the option is not made until the end of the number of days attached to the rate. For example, if an interest rate option expires in 60 days and is based on 180-day LIBOR, the holder will not be paid for 180 days.

Interest rate option payoffs
Interest rate call option payoffs are determined by the following formula:

Max {(underlying asset – exercise rate) (days in rate/360) , 0 }

Interest rate put option payoffs are determined by the following formula:

Max {( Exercise rate - underlying asset –) (days in rate/360) , 0 }

Intrinsic Value - Intrinsic value in options is the in-the-money portion of the option's premium. It is the value that any given option would have if it were exercised today.

Intrinsic value of a call = Min {0, CP –X}
Where CP - stock's current price (CP), X - option's strike price (X)

Intrinsic value of a put = Min {0, X-CP}

Time Value - The time value is any value of an option other than its intrinsic value, basically as the risk premium. Fundamentally, time value is related to a stock's beta or volatility. If the market does not expect the stock to move much (if it has a low beta), then the option's time value will be relatively low. Conversely, the option's time value will be high if the stock is expected to fluctuate significantly.

Option	Min. Value	Max. Value
European call	ct ³ Max{0, St-X/(1+RFR)T-t}	St
American call	Ct ³ Max{St-X/(1+RFR)T-t}	St
European put	pt ³ Max{0, X/(1+RFR) T-t - St}	X/(1+RFR) T-t
American put	Pt ³ Max{0, X - St}	X