It's show incorrect after I received expert answer of $13\mathrm{.}48\%$

Previous

Question $4$

Bookmark this page

Homework due Aug $6,202416$:$36$ CDT Question $4$

Completed

$\frac{6\mathrm{.}0}{20\mathrm{.}0}$ points $($graded$)$

Consider two European call options on the stock of $xYZ.$ Both options mature one year from now. The first option $($Option #$1)$ has a strike price of $$20\mathrm{.}0$ and trades at $$21\mathrm{.}6$ today; the second option $($Option #$2)$ has a strike price of $$40\mathrm{.}0.$ Currently, the stock price is equal to $$40\mathrm{.}4,$ and the one$-$year continuously$-$compounded risk$-$free rate is $4\%.$ The stock does not pay dividends.

What is the lowest price of the second option $($Option #$2)$ consistent with absence of arbitrage?

That's a good first step, but the answer is not correct yet because there is a higher bound. Hint: Try to construct a portfolio consisting of Option #$2$ and a discount bond that provides at least as high payoff at expiration as Option #$1.$ The price of this portfolio should be at least as high as the price of Option #$1,$ which would give you the lower bound on the price of Option #$2.$

You have used $2$ of $15$ attempts

Save