A stock S that pays no dividends is currently trading at $30/share. Another stock Q which pays a onetime dividend of $0.5/share in 3 months from now is currently trading at $10/share. The relevant interest rate is 10% per annum continuously compounded. Furthermore, an exchange option which exchanges 3 shares of Q for 1 share of S after 6 months is currently trading at $5.

$35.37

Explanation:

This question is complete, the complete question is as follows;

A stock S that pays no dividends is currently trading at $30/share. Another stock Q which pays a onetime dividend of $0.5/share in 3 months from now is currently trading at $10/share. The relevant interest rate is 10% per annum continuously compounded. Furthermore, an exchange option which exchanges 3 shares of Q for 1 share of S after 6 months is currently trading at $5. Please calculate the price of an exchange option which exchange 10 shares of S for 30 shares of Q after 6 months.

Solution;

In this question, we are asked to calculate the price of an exchange option which is exchanging a number of shares of each type of shares in the question for a duration of six months

To solve this problem, we proceed as follows;

The prepaid forward price of S is $ 30. The time-0 prepaid forward price for the delivery of 1 share of Q after 6 months is = 10 – 0.5 e^-(0.1×0.25)= $ 9.512345

By generalized put-call parity,

c[S(0), Q(0), 0; 2, 0.5] – p[S(0), Q(0), 0; 3, 0.5] = 30 – 3 × 9.512345

p[S(0), Q(0), 0; 3, 0.5] = 5 – 30 + 3 × 9.512345 = $ 3.537035

Therefore the price of an option to exchange 10 shares of S for 30 shares of Q is $ 35.37035

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