Payoff and profit/loss functions for call and put options

An option gives its buyer the right to buy (call option) or sell (put option) something in the future to the option seller at a predetermined price (exercise price). For example, if we buy a European call option to acquire a stock for X dollars, such as $30, at the end of three months our payoff on maturity day will be the one calculated using the following formula:

Here, is the stock price at the maturity date (T), the exercise price is X (X=30 in this case). Assume that three months later the stock price is $25. We would not exercise our call option to pay $30 in exchange for the stock since we could buy the same stock with $25 in the open market. On the other hand, if the stock price is $40, we will exercise our right to reap a payoff of $10, that is, buy the stock at $30 and sell it at $40. The following program presents the payoff function for a call:

>>>def payoff_call(sT,x):
        return (sT-x+abs(sT-x))/2

Applying...