Chapter 5: Option Pricing Models: The Black-Scholes-Merton Model

variables in the BSM model

- delta - gammma - rho - vega - theta

Nobel formula

- the black-scholes-merton model gives the correct formula for European call under these assumptions - the model is derived with complex mathematics but it is easily understandable

calculation steps

1. compute d1 2. compute d2 3. look up N(d1) 4. look up N(d2) 5. plug into formula for C

buy call

expected volatility is greater than implied volatility

sell call

expected volatility is less than implied volatility

gamma

is the change in delta for a given (again very small) change in the stock price

delta

is the change in the call price for a given change in the stock price

theta

is the relationship between the option price and the time to expiration

vega

measures the change in the option price for a change in the volatility

rho

measures the change in the option price when the risk-free rate changes