# Options with minimum rates

This lesson is part 2 of 6 in the course Option Valuation Lower Bound We know that the value of an option is equal to the sum of its intrinsic value and time value. Since an option cannot sell below its intrinsic value, its value cannot be negative, Therefore, the lower bound for both American and European options is zero.

Upper Bound Call Options A call option provides the option buyer the right to buy the asset. For the option to have value, its price at any time must be lower than the underlying stock price at any time.

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This is because if the option price were higher than the stock price, it would be cheaper to just buy the asset directly in the spot market. Therefore, the maximum price for an option is equal to the stock price at that time.

This applies to both American and European options. Put Options A put option provides the option buyer to sell the asset at the strike price.

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Since an American option can be exercised at any time, its maximum price can be equal to its strike price. However, for a European option, since it cannot be exercised options with minimum rates the expiry date, its maximum value will be equal to the present value of the strike price.

The following table summarizes the upper and lower bounds for these options. Minimum Value.

As a result, time value is often referred to as an option's extrinsic value since time value is the amount by which the price of an option exceeds the intrinsic value. Time value is essentially the risk premium the option seller requires to provide the option buyer the right to buy or sell the stock up to the date the option expires. Typically, stocks with high volatility have a higher probability for the option to be profitable or in-the-money by expiry. As a result, the time value—as a component of the option's premium—is typically higher to compensate for the increased chance that the stock's price could move beyond the strike price and expire in-the-money.