And in case you're wondering,

we haven't said anything about the true probabilities in this section.

We've discussed fixing con derivatives up to to now, and

we've completely ignored true probabilities.

We've only discussed risk-neutral probabilities, Q and one minus Q,

and in fact in the binomial model, we set them equal to a half.

So, does that mean that the derivative prices and

practise don't depend on true probabilities?

Well that is not true.

Of course they depend on practise and

the dependence actually enters into the calibration process because the true

probabilities will enter the market's perception.

Of market conditions, economic conditions, political conditions and so on.

And so, the markets perception of the two probabilities will certainly enter in here

into the market prices of these securities.

So, implicitly when we do this calibration we're actually Including

the market's views, the market's probabilities,

the market's level of risk aversion, into the entire derivative's pricing exercise.