Question

Consider:

(a) Stock trades for $100;

(b) Calls with exercise prices of $90, $100, and $110 trade at prices of $17.78, $11.06, and $6.74 respectively.

If a person buys a $90 call and writes a $110 call, what is her profit if the stock price is 92.63 at maturity? The answer is 8.41, how do you solve this?

Answer 1

A call option gives the owner the right to buy stock at a specified exercise price on or before specified maturity date.

Consider initial cash flows:

The person buys a $90 call, so he would have to pay $17.78 to buy the call option. So, his cash flow is -$17.78

The person writes a $110 call, this means that he sells this call option, and would receive $6.74 from selling this call option. So, his cash flow is +$6.74

Now, the stock price is $92.63. So, Which call options should get exercised? Only those call options whose exercise price is below $92.63. Why? Because you can get a stock at a price which is cheaper than the price it is available in the market. So the $90 call will get exercised.

Cash flow from exercising the call, $92.63-$90= +$2.63 (We assume here that you bought the stock from the call option at $90 and sell it in the market at $92.63)

So, Net cash flow= -$17.78+$6.74+$2.63=-$8.41 i.e. a loss of $8.41