What is the forward pricing model
Hi, it's William Jiamin here. In the previous video, we discussed forward rates and how they can be used in the forward pricing model to calculate prices. In this video, I'll be sharing with you guys the forward pricing model.
Let's start by drawing a timeline. We'll start at time zero and go all the way up to a certain time, let's say T equals to M. Then, at time T, which is M plus N, we have two investors, Investor A and Investor B.
Investor A buys a zero coupon bond at time zero, which matures at time M plus N. The price of this bond at maturity is denoted as P(M+N).
On the other hand, Investor B enters into a forward contract at time zero, agreeing to purchase a certain bond at time M. During the period from time zero to time M, Investor B holds the forward contract, but does not actually buy the bond. The bond in question is also a zero coupon bond, but it starts at time M and matures at time M plus N. Therefore, its maturity period is N instead of M plus N. We represent the price of this bond as P(N).
Investor B pays a certain price to enter into the forward contract, which we represent as F(M,N). We calculate the present value of this forward contract by discounting it back to time zero.
Now, these two investments should have the same price, even though Investor B's situation may seem more complex. If you buy the bond right now and hold it until maturity at M plus N, you will receive the face value of the bond, as there are no coupon payments in a zero coupon bond. The only cash flow you will receive is at time M plus N.
Similarly, in Investor B's case, even though they enter into a forward contract to buy a bond that matures in N years, they also receive the face value of the bond at time M plus N, as it is a zero coupon bond.
So, we have an equation: P(M+N) = Present Value of the Forward Contract (M,N). Rearranging this equation, we get: P(M+N) = Discount Factor M * F(M,N).
The present value can also be represented as the discount factor, which is essentially 1 plus a certain rate raised to the power of the period M. We use the multiplication symbol instead of division because, well, we don't like division in finance or computer science.
Thus, we have the formula: P(M+N) / Discount Factor M = F(M,N). This formula is known as the forward pricing model. It allows us to calculate the forward price starting at time M and ending at time N by dividing the current price of the bond by the discount factor of that period.
That's it for the forward pricing model.