The Black–Scholes–Merton Model
Using the no-arbitrage approach to replicate a put option payoff for the buyer of a put option, you would:
Not quite.
The shares should be represented by _N_(-_d_1).
No.
In order to replicate a put option, you'd need to sell the shares of stock to be short the stock's performance, just like a put.
Yes!
To replicate a put option, you'd need to sell shares short _N_(-_d_1) and invest the proceeds in zero-coupon bonds _N_(-_d_2). So a put position is an overleveraged stock position.
sell short _N_(-_d_1) shares of stock and buy _N_(-_d_2) shares of zero-coupon bonds.
sell short _N_(-_d_2) shares of stock and buy _N_(-_d_1) shares of zero-coupon bonds.
buy _N_(-_d_1) shares of stock partially financed with _N_(-_d_2) shares of zero-coupon bonds.
