The current price of a non-dividend paying stock is 40 and the continuously comp

Question

The current price of a non-dividend paying stock is 40 and the continuously compounded risk-free rate of return is 4%. You enter into a short position on 4 Call options, each with 3 months to maturity, a strike price of 35, and initial premium of $6.13. Simultaneously, you enter into a long position on 5 Call options, each with 3 months to maturity, a strike price of 40, and an option premium of $2.78. Assuming all 9 options are held until maturity, what is

(i) the maximum possible profit?

(ii) the maximum loss for the entire option portfolio?

Could you draw a labeled profit diagram in order to support your answer.

Explanation / Answer

Formula: A = Pe rt

Spot price of stock after 3 months: => 40e0.04*0.25 = $40.4020

P = Current Price
E = 2.7183 (You can use exponential formula in excel)
r = 4% or 0.04
t = 3 Months / 12 Years = 0.25 years

Proceedings for Short Position: (You receive the premium)

As the strike price is less than the current market price, the buyer will exercise the option. So, proceedings from one option:

= $40.4020 - $35 + $6.13 = $0.728

Total Profit = $0.728 x 4 = $2.912 (Maximum Possible Profit)

Proceedings for Long Position: (You pay the premium)

= $40.4020 - $40 - $2.78 = -$2.378

Total Loss = -$11.89 (Maximum Possible Loss)

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