msk2222's version from 2018-02-18 17:47

## Section 1

The Lognormal Distributionwidely used for modeling the probability distribution of share and other asset prices. For example, the lognormal appears in the Black–Scholes–Merton option pricing model
Black–Scholes–Merton assumes that the price of the asset underlying the option is lognormally distributed.
most noteworthy observations about the lognormal distributionthat it is bounded below by 0 and it is skewed to the right (it has a long right tail)
price relative, S1/S0, is an ending price, S1, over a beginning price, S0; it is equal to 1 plus the holding period return on the stock from t = 0 to t = 1:
The continuously compounded returnassociated with a holding period is the natural logarithm of 1 plus that holding period return, or equivalently, the natural logarithm of the ending price over the beginning price (the price relative)
continuously compounded return from t to t + 1rt,t+1 = ln(St+1/St) = ln(1 + Rt,t+1)
We can also express ST/S0 as the product of price relatives:ST/S0 = (ST/ST–1)(ST–1/ST–2)…(S1/S0)
E(r0,T) = E(rT–1,T) + E(rT–2,T–1) + … + E(r0,1) = μT   (we add up μ for a total of T times) andσ2(r0,T) = σ2T