My recap of the replicating portfolio:

Where does the idea that

*“you need the cash to buy the shares”*show up?That’s the source of the minus sign in Drake's representation:

**The Motion Animating The Equation**

**Portfolio component:**

**cash loan**

In the model, how do you borrow money to buy shares?

*You sell a T-bill (zero coupon bond) with a face value of the probability-weighted strike.*

The

*probability-weighted strike*is the amount of cash we expect to receive at maturity from the shares we sell.Strike * N(d2)

$125 * 28.8% = $36

If we sell a 1 year T-bill with a face of $36, then today we receive the present value of $36:

**$36e^(-.10%) =**

**$32.57****Portfolio component:**

**shares**

The delta-weighted share quantity tells us how much stock we need to own today to hedge the value of the stock conditional upon the strike being in-the-money:

S* N(d1)

$100 * .397 = $39.77

**We need to own**

**$39.77**

**worth of stock to be hedged against the possibility of the stock going in the money.****The value of the call option emerges**

We borrow $32.57 today

We invest it in the stock.

We need more stock to cover the contingency that the call gets assigned. On average we need:

$39.77 - $32.57 =

**$7.20**

**The value of the call option is therefore the price that reflects the full cost to replicate its payoff!****Decompose the p/l:**

The loan cost the interest on the T-Bill:

**$32.57 - $36=**($3.43)

In expectancy terms, I will be selling you $39.77 worth of shares for only $36:

$36 - $39.77 = ($3.77)

**Net P/L =**

**($7.20)**

The replicating portfolio will cost you

**$7.20**in expectancy, therefore that must be the value of the call option!The recap table: