— Here are some pointers to myself —
log(PR) (known as r) is normally distributed.
random walk — Brownian motion
BS started with a (diffusion) differential equation describing how instantaneous stock movement depends on exponential drift + geometric Brownian motion
** parametrized with sigma and r, assumed constant.
assumption : constant vol assumption — biggest shortcoming
** no skew no term structure
**** seriously underestimates vol at low strikes – tail risk
** due to this shortcoming, BS is good for price quoting/inversion only, not valuations
assumption : zero-dividend assumption — later addressed by Merton
Applies to European style only
Applies to stocks only, not FX with 2 interest rates
Requires integration of normal pdf, so the valuation formula is based on the N() function i.e. the cummulative function