Question

Replicate a long call option using only linear securities.

Answer 1

Let is assume,

For the portfolio to replicate the call, we must have:

∆c · (110) + B · (1.02) = 10
∆c · (90) + B · (1.02) = 0

Solving, we obtain:

∆C = 0.50 B = −44.12.

In words, the following portfolio perfectly replicates the call

option: A long position in 0.50 units of the stock.
Borrowing of 44.12.

Cost of this portfolio:

(0.50) · (100) − (44.12)(1) = 5.88.

Since ,the portfolio perfectly replicates the call,

we must have

C = 5.88.

Any other price leads to arbitrage:

If C > 5.88, we can sell the call and buy the replicating portfolio.

&

If C < 5.88, we can buy the call and sell the replicating portfolio.