# Problem solving using the put-call parity

I am self-studying for an actuarial exam on financial economics. I encountered this problem, and I am having difficulty seeing why the statement underlined is true:

How do we know that $P(60) - C(60) + P(50) - C(50) = 110e^{-rT} - 2Se^{-\delta T} = (2/3)(15)$?

The part with (2/3) confuses me. We are using 2 out of the 3 equations, but I don't see why that would necessarily imply that the value of adding 2 of the 3 equations is (2/3) the value of adding the three equations together.

• where did you find these problems? I am also looking for such practice – grayQuant Nov 7 '15 at 21:38

What a difficult problem. The first line gave $165 e^{-rt} -3 S e^{-dt} = 15$ [since 50+55+60 = 165]. In the second line we want to evaluate $110 e^{-rt} -2 S e^{-dt}$. We notice that this is exactly two thirds of the left side of the above, because 110 is two thirds of 165 and 2 is two thirds of 3. So we take two thirds of the right hand side of the first eqn. i.e. (2/3)*15, which is 10.