0
$\begingroup$

Why when replicating a call option, the money market position (bond, risk free investment) is negative and when replicating a call option, the money market position is positive?

Please explain intuitively and with a simple proof.

$\endgroup$
  • 2
    $\begingroup$ When you replicate a Call you are long the stock (positive delta) and you finance that by borrowing, when you replicate a Put you short the stock to bring about negative delta, then you reinvest the proceeds by lending in the money market. $\endgroup$ – noob2 Mar 28 '16 at 13:05
  • $\begingroup$ Isn't that like arbitrage though? You make no initial investment. Please correct if wrong. $\endgroup$ – foshizzle Mar 28 '16 at 13:14
  • 1
    $\begingroup$ @noob2 I think that when you mention "the cost of the stock balances the amount you borrow/lend" OP interprets this as forming a replicating portfolio at zero cost. Yet since this portfolio should by definition replicate the option (instrument with positive payoff in all future states of the world), to the OP, this would represent an arbitrage opportunity (non zero probability of making money from nothing). To clarify things, I think it would be useful to distinguish between the initial wealth (= the option premium) from self-financing conditions (= rebalancing through zero net investment). $\endgroup$ – Quantuple Mar 28 '16 at 20:31
  • 2
    $\begingroup$ In other words what is a worth zero at inception is a portfolio composed of the option position minus its replicating portfolio (shares and bonds) and not the replicating portfolio on its own. $\endgroup$ – Quantuple Mar 28 '16 at 20:31
  • 1
    $\begingroup$ So, to clarify: when you initially sell a call-option and proceed to delta-hedge it, you do start with some money, namely the proceeds of the option sale $C$ but that is not enough to buy $\Delta * S$ worth of the stock because the BS formula shows $C < \Delta * S$ so you need to borrow some money on the first day to get started. $\endgroup$ – noob2 Mar 29 '16 at 17:25

Your Answer

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

Browse other questions tagged or ask your own question.