There are two screencasts on option pricing using binomial approach: the first one is 1-step binomial, the other 2-step.
It is not clear for me why the method of pricing is so different in both cases.

Any suggestions would be appreciated!

Thanks.

Hi Ened,

No essential difference. The one-step is but a template that is reused over a multiple-step binomial. Either one or two-step is unrealistic, both are (in John Hull) for learning purposes.

But one thing I would offer is that the one-step holds the key, i think, to understanding the elusive RISK-NEUTRAL VALUATION (try finding somewhere a good explain of this!). Here is snapshot of the slide that mimics John Hull’s example of a one-step, where the stock S = $10 and can go up (S)(U) to $12 or down (S)(D) to $8. This is similar to Hull’s 11.2 where S = $20, goes to $22 or $18:

The instructive point of this is (i) to show the approach is based on a riskless portfolio [i.e., long delta shares plus short the call option is indifferent to the outcome; so portfolio is riskless]. To understand this is to understand something counterintuitive: the probability (p) of an up step is irrelevant to the option price (but note: u and d are relevant, as volatility increases they will increase/decrease). The is the essence of the risk-neutral idea: (p) is irrelevant, so that the expected return on the stock does not matter to the value of the option. Why? A higher expected return must be met (i.e., offset by) with a higher discount rate.

David

Or explained like this:

12p + 8(1-p)=10*exp(0.25*0.12)

So p=0.58

So p the probability of an upward movement now the expected value is:

We assume a strike of 10 the down movement result in a value of 0

p * (12-10) + (1-p) * (0)

filling in results in 1.1523, this is the future value of the option, so we must discount it to get it to the present value

1.1523 * exp (-0.25*0.12) results in 1.1182.

John,

Thanks, that’s helpful. I posted a 9 min screencast just on risk neutral valuation:
http://www.bionicturtle.com/learn/article/risk_neutral_valuation_9_min_screencast/

David