OPT_ON_OPTIONS(type_flag,spot,strike1,strike2,time1,time2,rate,cost_of_carry,volatility)
OPT_ON_OPTIONS models the theoretical price of options on options.
type_flag is 'cc' for calls on calls, 'cp' for calls on puts, and so on for 'pc', and 'pp'.
spot is the spot price of the underlying asset.
strike1 is the strike price at which the option being valued is struck.
strike2 is the strike price at which the underlying option is struck.
time1 is the time in years to maturity of the option.
time2 is the time in years to the maturity of the underlying option.
(time2 >= time1).
rate is the annualized risk-free rate of interest.
cost_of_carry is the leakage in value of the underlying asset of the underlying option.for common stocks, this would be the dividend yield.
volatility is the annualized volatility in price of the underlying asset of the underlying option.
OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA.