Question

Question 13 Assume that you purchase 2 call options and 1 put option in the German company Tegernsee & Augsburg GmbH with a time to maturity of 3 months. The exercise price on the call options is SEK 70 and the exercise price on the put option is SEK 75. If the stock's spot price at maturity is SEK 72, what is the total value of the portfolio at maturity? A. 7 B. 5 c. 9 E. 13 F. None of the above is correct.

hi how do i solve this

Answer 1

Answer is option A.

Explanation:

Let us first list down the information provided in the question.

i. The portfolio comprises of 2 long (i.e. buyer of option) call options and 1 long put option in Tegernsee & Augsburg GmbH.

ii. Exercise price of both the call options (Xc) = SEK 70

iii. Exercise price of the put option is (Xp) = SEK 75

iv. Stock's spot price at maturity (St) = SEK 72

v. Time to maturity = 3 months

Objective: To find the total value of portfolio at maturity.

In this case, the total value of portfolio at maturity = Value of 2 long call options at maturity + Value of 1 long put option at maturity  (equation 1). Hence, we have to first derive the value of our call positions and put position.

a. Value of call options

For a buyer of call option, if the stock's price at maturity is greater than the exercise price then the value of the option is positive and it is termed as in-the-money position. Mathematically the value of long call position is represented as Max of [(St-Xc),0].

We can calculate the value of the call options using the above formula and the information given in the question.

Value of 1 call option = Max of [(72-70),0]

= Max of [2,0]

= 2

Since we held two long call options in the portfolio, the total value of our call options position is (2 * 2) = 4

b. Value of put option

For a buyer of put option, if the stock's price at maturity is lower than the exercise price then the value of the option is positive and it is termed as in-the-money position. Mathematically the value of long put position is represented as Max of [(Xp-St),0].

We can calculate the value of the put option using the above formula and the information given in the question.

Value of put option = Max of [(75-72),0]

= Max of [3,0]

= 3

Let's use the values we derived in (a) and (b) in equation 1.

Total value of portfolio at maturity = Value of 2 long call options at maturity + Value of 1 long put option at maturity

Hence, the total Value of portfolio = 4 + 3 = 7