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