Chapter 7 - Fixed Income Securities = The Science of Term Structure Models

[Northshore]

Hi David,
May I ask on this. ( Page 201, of Market Risk Measurement and Management 2015 ). I noticed the answers for the face value of the bonds of six months and one year of -613.3866 and 630.2521 is different from the excel sheet of -612.5000 and 629.3437. I agree with your answer after working out on excel.

Upon reading on the same page 201, I noticed that equation of 12.5 in Tuckman that solves for price of the call option does not provide the answer of the call option at 0.5818 ( as per your answer and I also agree). May I know whether equation 12.5 in Tuckman's book is correct ( as I would be more interested to know ) and hope you could share some light on this ? I mean does equation 12.5 is an alternative to solve for the price of the call option apart from using the risk neutral probabilities method as equation 12.9 on page 203

Appreciate very much for your kind inputs.
Ong

 

[David Harper CFA FRM]

Hi @Northshore

sorry for the delay

• That is merely rounding. My XLS is exact, while Tuckman's text rounded the bond prices from 973.2360 and 977.9951 to 973.24 and 978.00; ie., if you hard-code those rounded numbers into the bond prices, you'll see the solved values match! so this doesn't implicate anything ...
• Yes, 12.5 formula is correct. There is a similar rounding effect in play. But you make a good point: there are two different formulas that solve for the risk-neutral option price of $0.58. It's a tough concept, but it's really the point of the text. The point is that there is a sequence, only one of them comes first. And that's 12.5 because 12.5 gives us the cost of the replicating portfolio. The subsequent 12.9 is more of a "confirming" reconciliation: it needs to work given the procedure (i.e., "The fact that the arbitrage price of the option equals its expected discounted value under the risk-neutral probabilities is not a coincidence. In general, to value contingent claims by risk-neutral pricing, proceed as follows. First, find the risk-neutral probabilities that equate the prices of the underlying securities with their expected discounted"). I hope that helps!