Hi, I'm confused by the solution to Q1 ii) in the mock exam. First we calculate F_0 from the current price B_0 = 64.39%. I understand this (although I forgot to do it!). Then we assume yields fall by 0.25%, so we calculate the new price of the 10 year bond as 65.954%, and use this as F_0. But isn't this the new B_0? Can anyone explain why we don't then use this 65.954% to calculate a new F_0? Thanks
We don't use the "new" bond price of 65.954% to calculate F(0) (the forward price in Black's formula), because F(0) is based on the current bond price, which is still B(0) = 64.39%. In other words, 65.954% isn't the current price of the bond. It merely represents what the current price will move to if bond yields exactly move as the investor anticipates - which they are unlikely to do so. To sum up, Black's bond option formula gives the current price of the option in terms of the current price of the bond. It is then up to the investor how he or she thinks bond and option prices may subsequently change in the future.
I'm still confused! Why do we use the 65.954% in Black's formula? You're saying (in the first paragraph) that 65.954% is not the current price of the bond, but in the second paragraph you say that Black's formula gives the current option price in terms of the current bond price. I thought that: F_0 = the expected value of the underlying at maturity (ie at time 1 here) 65.954% = price of the bond at time 0 if yields fall immediately by 0.25%. These two aren't equal, so why do we use the 65.954% in Black's formula in place of F_0?
Sorry Cathy, I may have misunderstood what you were saying. Black's formula always uses the current forward price of the bond, ie the price we would agree now to buy the bond at the forward date (which here is in 6 months' time, at the strike date of the option). So, initially, the current bond price is 64.39% and the current forward price is 64.39% x 1.042 = 67.09%. which is what we use in the formula to work out the initial price of the option as 3.659. And then, if yields did change, the current bond price would rise to 65.954%, the corresponding forward price would then be: 65.954% x 1.0395 = 68.559% which is what we then use in the formula to work out the new price of the option to be 4.629.
