Question

The following prices are available for call and put options on a stock priced at $50. The risk-free rate is 6 percent and the volatility is 0.35. The March options have 90 days remaining and the June options have 180 days remaining. The Black-Scholes model was used to obtain the prices.

	Calls		Puts
Strike	March	June	March	June
45	6.84	8.41	1.18	2.09
50	3.82	5.58	3.08	4.13
55	1.89	3.54	6.08	6.93

. Use the June/March 50 call spread. Assume one contract of each. What will be the profit if the spread is held 90 days and the stock price is $45?

              

Answer 1

Call option means right to exercise but not the obligation to buy an option.

If we take June/March 50 call spread, the profit will be:

One contract generally consist of 100 shares.

As the spread is for 90 days we will consider premium of $3.82

The amount of premium paid is $3.82*100= $382

If the stock price is $45 then trader will not exercise its call option as it is priced at $50 and it is available for less amount in market at $45.

So, the loss in this option will be the amount of premium that is $382.

Put option means right to exercise but not the obligation to sell an option.

in this case premium paid is $3.08*100= $308

If the stock price is $45 then trader will exercise its put option as it is priced at $50 and market value is $45.

so the gain will be ($50-$45)=$500,

reduced by amount of premium paid i.e. $500-$308= $192.

Ans: Call option holder will bear loss to the amt of premium i.e. $382 and

Put option holder will gain from the contract with $ 192.