Question

1 year call option on a stock with a strike price of $30 costs $3 - a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option.What will be the breakeven stock price, above which the trader makes a profit?What will be the breakeven stock price below which the trader makes a profit

Answer 1

Solution:

a. Breakeven stock price, above which the trader makes a profit $35    

Working Notes:    

Put option is right to sell at strike price.  

Call option is right to Buy at strike price.  

As the trader buy two call options & one put option, then his cost of the strategy  

$=2 * call premium +1 * premium on put option$

$=2 * \ 3+1 * \ 4$  

=$6 + $4    

=$10    

Under call option we got right to receive difference between Stock price above strike price at expiry & Strike price, means call option is beneficial when expiry stock price is above strike price of the call option.

And break even stock price is the price of the share at which it recover its all cost of strategy.

Hence, stock price above strike price , cost of strategy is recover will be the trader breakeven price.

$cost of strategy = no. of Call option * (Break even stock price - Strike price)$

$\ 10=2 * \text { (Break even stock price }-\ 30)$

$Break even stock price =(\ 10+\ 60) / 2$

Break even stock price =$35

Above $35 of stock price the trader will start making profit , hence , its Breakeven stock price, above which the trader makes a profit is $35

b. Breakeven stock price below which the trader makes a profit $20   Working Notes:

Under put option we got right to receive difference between Strike price & below strike price (stock price at expiry) . Our Breakeven stock price below which the trader makes a profit will be the price below strike price up to which cost of strategy would have been recovered

As the trader buy two call options & one put option, then his cost of the strategy  

= $2* call premium +1 * premium on the put option$

$=2 * \ 3+1 * \ 4$  

=$6 + $4    

=$10    

And now Computation of break even stock price. Cost of strategy = no. of Put option x (Strike price - Break even Stock price)

$\ 10=1 \times(\ 30-\text { Break even Stock price })$

Break even Stock price) = $30 -$10

Break even Stock price) = $20

Hence, Breakeven stock price below which the trader makes a profit $20