P2 MR Tuckman Ch. 7 - Replication of option portfolio

[MissJaguar]

Dear David,

Refering to p. 17 in Tuckman's notes, ch. 7 and slide 9 in the video (Tuckam ch. 7).

What is teh formulae used pleased to get these prices?

Thanks,

 

[David Harper CFA FRM]

Hi @MissJaguar

I assume you are referring to Tuckman's replicating portfolio, which he explains in Chapter 7. The main idea is to use two bonds to match the payoff of the option; i.e., zero or $3.0.

As Tuckman writes" To price the option by arbitrage, construct a portfolio on date 0 of underlying securities, namely six-month and one-year zero coupon bonds, that will be worth $0 in the up state on date 1 and $3 in the down state. To solve this problem, let and F1 be the face values of six-month and one-year zeros in the replicating portfolio, respectively. Then, these values must satisfy the following two equations:

(7.3) F(0.5) + 0.97324*F(1) = $0
(7.4) F(0.5) +0.97800*F(1) = $3

So the key step is solving for these two unknowns in two equations. You can see my specific math in the tab "29.7 Replicate Port (option)" of this worksheet @ https://www.dropbox.com/s/r6m5ogryvg31kfl/T5.29.7_Term_Structure.xlsx?dl=0 . I hope that helps!