Remember that we set the "price" of a forward such that at the time the forward is "purchased," it is equal to the risk-neutral pricing value of the contract. This will be expanded upon later
Once again, here is the short-rate lattice:
We decided to price a forward contract on a coupon-bearing bond.
The bond is delivered at time t=4, but is a 2-year bond with at 10% coupon rate. We assume that the delivery takes place after the coupon has been paid. We use the same method to compute the forward price as we did the option price, simply working backwards from the end. However, since the forward is not completely over the six periods, we must do this in two steps.
Before we continue with the steps we must find the equations we will need. Risk-neutral pricing implies that:
We can then rearrange this to find:
Recall that E(1/B(4)) is simply the time t=0 price of a zcb maturing at time t=4. This is 77.22/100, which we found in previous modules.
The first step is then to find the price of the bond that matures in 2 periods with a 10% coupon, but is purchased at time t=4. We can use a lattice to recreate this bond:
We choose a final price of 110 instead of 100 because there is a 10% coupon.
We use the old equation to find these prices:
We then work backwards using this same equation to finish computing the price of the bond:
So $79.83 is the price that we would pay at time t=0 to receive a 2 year 10% coupon-bearing bond at time t=4. However, this is not the price that we would pay for the forward, G(0). To find the price of the forward, we would use the equation from above:
In this example:
G(0) = 79.83/0.7722 = 103.38. This is the price of a forward contract in which we would receive a 2 year 10% coupon-bearing bond at time t=4
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