1
$\begingroup$

I'm studying for a test and am stuck on this practice question:

With interest rates equal to 0, two different stocks $S_1$ and $S_2$, both valued at \$1 today, can be worth \$2 or \$0.50 at some point in the future. If the option that pays \$1 when both $S_1 = S_2 = \$2$ is traded in the market and is worth \$0.125, calculate the price and replicating portfolio of the option that pays \$1 when $S_1 = \$2$ but $S_2 = \$0.5$. You may leave your answer in matricial form.

$\endgroup$
0
$\begingroup$

Hint The future world has 4 states: $(0.5,0.5), (2,0.5), (0.5,2), (2,2)$. You have 4 instruments - cash, each stock, and an option they are both \$2 which is traded. Take $x,y,z,w$ of each and match the portfolio to the price of the option in each market state.

You get 4 equations and 4 unknowns, solve, and supposedly you get a unique solution, which immediately yields the replicating portfolio.

$\endgroup$
1
  • $\begingroup$ Got it. Didn't think to use the given option as the 4th instrument. Thanks! $\endgroup$ – user108 Feb 25 '14 at 14:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.