Question

# The following prices are available for call and put options on a stock priced at \$50....

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?

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.