Question

What is the option delta? Delta = Spread of Option Price / Spread of Stock price Spread of Option Price = (40 * 1.2) – 40 = 8 Spread of Stock price = (40 * 1.2) – (40 * 0.833) = 14.7 Delta = 8 / 14.7 Delta = 0.544 What is (1,2) and (0.833) it this calculation?

Answer 1

The factors of 1.2 and 0.833 are the upward and downward price movement factors for the stock price, In simpler words, in a risk-neutral two state setup, any upward price movement will be equal to 1.2 times the existing price and any downward price move will be equal to 0.833 times the existing price.

The upward price factor u can be calculated using the following formula:

u = e^[Standard Deviation x (Time)^(1/2)] where standard deviation is the deviation of the returns of the underlying asset and time is the time to maturity of the option.

The downward price factor d equals the reciprocal of u or d = 1/u

As is observable in the example given above: u = 1.2 and d = 1/u = 1/1.2 ~ 0.833