Option valuation: Consider a call option with a strike price of $20, which expires in one year. The risk-free rate of interest is 5 per cent. The underlying share price is $30. Without arbitrage, which of the following is a possible price for the call option?

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Quizplus · Accepted Answer

The price of a call option can be calculated using the Black-Scholes formula. However, in this case, we can use a simpler method based on intuition. The call option has value only if the stock price is above the strike price of $20. If the stock price is at or below $20, the option has no value, and its price should be zero. 
If the stock price is above $20, the option will have some positive value. Intuitively, the option should be worth more the higher the stock price is above the strike price. The maximum possible value of the option is equal to the difference between the stock price and the strike price, since that is the intrinsic value of the option. In this case, that difference is $10 (since the stock price is $30 and the strike price is $20). However, the option does not have to be worth its maximum possible value due to the time value of money and risk. 
Therefore, a possible price for the option is between $0 and $10. We can eliminate option A since the stock price is above the strike price, so the option has some positive value. We can eliminate option B since it is too low, and the option should be worth at least some significant fraction of its maximum possible value. Therefore, option C ($15) is the only possible price.

Option Valuation: Consider a Call Option with a Strike Price