OPT_FORWARD_START(call_put_flag,spot,alpha,time1,time,rate,volatility,cost_of_carry)
OPT_FORWARD_START models the theoretical price of forward start options
call_put_flag is 'c' or 'p' to indicate whether the option is a call or a put.
spot is the spot price of the underlying asset.
alpha is a fraction that set the strike price the future date time1.
time1 is the number of days until the option starts.
time is the number of days to maturity of the option.
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, for common stocks, this would be the dividend yield.
OPT_BS, OPT_BS_DELTA, OPT_BS_RHO, OPT_BS_THETA, OPT_BS_GAMMA.