kanukatchit
Member
Posts: 143
Joined: Dec 2003

Fri Jan 06, 06 12:17 AM


Quote
Originally posted by: NeedSomeHelp Hello: I was taking a look at CSCO's most recent filing. In their assumptions for Employee Stock Options, they provide a skewness and kurtosis assumption. They use a binomial tree model to value the options.
Now I understand that skewness and kurtosis describe the shape of the curve, but how are these practically used in pricing options? It seems that in Black Scholes, you could use a distribution that be normal but adjusted for the skewness and kurtosis. Is there anyway to do this in Excel? In building the binomial tree, how would this be implemented?
Much appreciated!
Ok this is a guess , but when a contstructing a binomial tree we usually determine u and d i.e the up and down stock moves using moment matching. This moment matching is done using the expected stock price and and the volatility or the variance of the stock. skewness and kurtosis are just the third and 4th moments of a rv.
The expected value of the stock is just given as p(S)u + (1p)Sd = S exp(mu*dt) and similarly for variance you can write an expression using var(X) = E(X^2)  E(X)^2 and the compute u and d from these two equations. And then there are the Cox RR and equal probability approximations.
I guess similarly you can write the equations for the 3rd and 4th moment and solve for u and d, though it would be an overdetermined system. You could impose some more conditions to solve it. somebody please correct me if I am wrong.
K.

