Assume the Black-Scholes framework. Consider European call and put options on a stock that pays dividends continuously at a rate
proportional to its price.
Determine the signs of the following twelve Greeks:
Call delta, call gamma, call theta, call vega, call rho, call psi,
put delta, put gamma, put theta, put vega, put rho, and put psi.
That is, for each of these Greeks, answer “Always positive,” “Always negative,” or “Sometimes positive and sometimes negative.” Explain your answers briefly