A risk-free portfolio can be created by buying the stock and simultaneously selling the call option on the stock. If the stock price rises, the value of the call option will be negative for the seller. This negative value will cancel the profits earned from a rise in the price of the stock. If stock prices fall, the gain on the sale of the call option will counter the loss on stock. An investor can create a risk-free portfolio with such an arrangement.
A risk-free portfolio must, in equilibrium, yield the risk-free rate. If the rate offered is higher than the risk-free rate, arbitrageurs will buy it and bring the rate down, and vice versa.
In a risk-free situation, the ending value of the portfolio is the same regardless of the change in the share price. The ending portfolio value discounted at the risk-free rate is what the investor has hedged for. Thus, assuming there is only one stock in the portfolio, the cost of acquisition of stock minus the present value of the ending value of the portfolio discounted at the risk-free rate should be equal to the price of the call option.
To create a risk-free portfolio, buy a stock and simultaneously sell a call option on the stock.
The price of a call option can be determined by subtracting the present value of the portfolio, discounted at the risk free rate, from the cost of the stock.