Referring to chap 13 & Q8, Apr' 2003, Subject 109 (part iv ) How do we estimate delta? One of the threads say that delta is just the amount of shares we hold at the start. Is that true? If yes, Why is the initial amt of shares called "delta"?
Delta is the rate of change of the derivative price with respect to the underlying share price. It tells us how the derivative price changes when the underlying share price changes. It can be estimated from a binomial tree by taking the difference in the derivative value at two nodes (at the same time) and dividing by the difference in the share prices associated with those nodes, ie difference in derivative value/difference in share price. The "formula" for this appears on page 7 of Ch13 - it's the expression for phi, the number of shares held at time 0 in the replicating portfolio. So, yes, delta is the amount of shares we hold in an initial replicating portfolio. In the Examiners Report for the question you refer to, this is the approach taken to the calculation for delta. Although they have an exp(-qt) term in the denominator that I can't work out at all - I think it's an error.
