Page 8 - Study Notes of Hull Chapter 13: Binomial Trees

[Dr. Jayanthi Sankaran]

Hi David,

Wanted to bring to your attention some errors in the referenced above.

Hull's Example 12.8

Two-step European put option, with up and down simply given as inputs. In this way,
volatility does not inform up and down and, consequently, this model does not
implicitly assume lognormal prices. Here the assumption is simply that the jump is+/-
20%:

1=call, 0=put 0 PUT
Asset $50.00 Solved:
Strike $52.00 u 1.2000 << magnitude of up jump
Time (yrs) 1.0 d 0.8000 << magnitude of down jump
Volatility 30% a 1.0513
Riskless 5.0% p 0.6282 << probability of up jump
Div Yield 0.0% 1-p 0.3718 << probability of down jump

I get an option price of 9.462 at node 1 on the down jump (intrinsic value = $12). Hull gets $9.4636 and finally,
I get an option price of $4.189 at node 0. Hull gets $4.1923. Your node 0 option price is $5.09.

Don't know whether this is a rounding error. Nevertheless, thought I would bring it to your attention!

Thanks!
Jayanthi

 

[Dr. Jayanthi Sankaran]

Hi David,

Sorry about my first comment above - it so happens that Page 8 of the Study Notes talks about valuing American call or put options as a header. However, the problem stated above is about a European put option, which threw me off. I also notice that you have used inputs from Hull's Figure 6-8 on Page 114. This was kind of confusing because Hull's Figure 6-7 on page 114, also had the same inputs for a European put.

Happy that the dilemma has been resolved

Thanks!
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran

Yes, exactly, agreed!

• The header of page 8 ("Calculate value of an American call or put option using a two‐step binomial model") is correct but the text contains a typo ("Hull’s Example 12.8: Two-step European put option, with up and down simply given as inputs.") as the example concerns an American-style put
• You are right, my inputs are borrowed from Hull (Figure 13.7, page 284 in the 9th Edition) but he assumes a European style put to arrive at a value of 4.1923 (as does my spreadsheet, if I assume European). FWIW, if European assumption, I get $9.4639 for node [1,0]. Thanks!