Uses the Black-Scholes model to calculate the "gamma" of a European option struck at @strike on an asset with price @price.
(The gamma of an option is the second derivative of its price with respect to the price of the underlying asset, and is the same for calls and puts.)
@volatility is the annualized volatility, in percent, of the asset for the period through to the exercise date. @days_to_maturity the number of days to exercise, and @rate is the risk-free interest rate to the exercise date, in percent.
The returned value will be expressed as the rate of change of delta per unit change in @price.
opt_bs_call, opt_bs_put, opt_bs_call_deltaopt_bs_put_delta, opt_bs_call_rho, opt_bs_put_rho, opt_bs_call_theta, opt_bs_put_rho, opt_bs_vega.