Page 7 - Study Notes - Hull Chapter 13 - Binomial Trees

[Dr. Jayanthi Sankaran]

Hi David,

Just needed to clarify that the volatility parameter in the following is extraneous to the problem:

Below is the two-step binomial for a European call option. Assumptions are: Current asset
price = $20, Strike = $21, Time = six months, Volatility = 19%, Riskless rate = 12%, and
Dividend Yield = 0%.

Hull’s Example 12.4,

Two-step European call 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+/-
10%:
1=call, 0=put 1 Call Option
Asset
$20.00 Solved:
Strike
$21.00 u 1.100 << magnitude of up jump
Time (yrs) 0.25 d 0.900 << magnitude of down jump
Volatility 19% a 1.030
Riskless 12.0% p 0.652 << probability of up jump
Div Yield 0.0% 1-p 0.348 << probability of down jump

Thanks!
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran Yes, that is correct. In this case, the up (u) = 1.10 and down (d) = 0.90 are given directly--i.e., +10% or -10% in arithmetic fashion--such that the volatility input is not used. Thanks!