Hull Derivatives Probability Density

Question

I am using option data to calculate the implied probability density; essentially copying the Appendix: Determining Implied Risk-Neutral Distributions from Volatility Smiles from Hull's book.

My question is his about his example:

Using the code math.exp(0.03*0.25)*(((4.045+3.055)-(2*3.549))/(0.5^2)) gives the answer 0.00806 not 0.0057.

Am I doing something wrong?

Answer 1

Hull is not wrong. The difference is due to rounding.

The option values below, calculated with Black-Scholes, will give Hull's result of 0.005695928, rounded to 0.0057

BS VALUES

$4.0449121994898

$3.0546354450165

$3.549067151214