OPT_BINOMIAL(amer_euro_flag,call_put_flag,num_time_steps, spot, strike, time, rate, volatility, cost_of_carry)
OPT_ models the theoretical price of either an American or European style option using a binomial tree.
amer_euro_flag is either 'a' or 'e' to indicate whether the option being valued is an American or European style option respectively.
call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
num_time_steps is the number of time steps used in the valuation, a greater number of time steps yields greater accuracy however is slower to calculate.
spot is the spot price of the underlying asset.
strike is the strike price at which the option is struck.
time is the initial maturity of the option in years.
rate is the annualized risk-free rate of interest.
volatility is the annualized volatility in price of the underlying asset.
cost_of_carry is the leakage in value of the underlying asset.
OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA.