risk-neutral pricing

CFA Level I Derivatives
#1

Hello,

I’m studying pricing derivatives part and I have a question about risk-neutral pricing. Actually, I can’t understand below paragraph.

As an example of replication and risk-neutral pricing, consider a long position in a stock and a short position in a forward contract at 50 on the stock. Regardless of the price of the stock at the settlement of the forward contract, the stock will be delivered for the forward price of 50. As 50 will be received at the forward settlement date, the value today is 50 discounted at the risk-free rate for the time until settlement of the forward contract. For a share of stock and a short forward at 50 with six months until settlement, we can write:

S – F(50) = 50/(1 + Rf)0.5

My question is what S and F(50) stand for? I guess F(50) is forward price of 50 and S is a share of stock. But I don’t understand the logic under the equation.

#2

Where did you find this formula?

It makes no sense.

#3

I found it in Schweser… I can’t understand logic

#4

Neither can I.

Because it doesn’t make sense.

#5

After the above contents,

and replicate a long forward position as: F(50) = S – 50/(1 + Rf)0.5. That is, we can replicate the long forward position by purchasing a share of stock and borrowing the present value of 50 at the risk-free rate so the value at the maturity of the loan will be the stock price minus 50. Alternatively, we could replicate a short forward position by selling a share of stock short and lending the present value of 50 at the risk-free rate.

I also don’t have any ideas of that

#6

OK, I get it.

By S they mean the spot price of the stock.

By F(50) they mean the value of a forward contract with a price of 50 that expires in half-a-year.

I hate that CFA Institute keeps changing the notation.

#7

Thank you so much!

Could you explain the logic behind the equation S – F(50) = 50/(1 + Rf)0.5 ? I don’t understand the equation. I mean how S – F(50) equal to 50/(1 + Rf)0.5

#8

I think he mentioned that it was from Schweser.

The official textbook still uses V(T) for value of forward contract.