OPT_TIME_SWITCH(call_put_flag,spot,strike,a,time,m,dt,rate,cost_of_carry,volatility)
OPT_TIME_SWITCH models the theoretical price of time switch options. (Pechtl 1995)
The holder receives a * dt for each period dt that the asset price was greater than the strike price (for a call) or below it (for a put).
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.
strike is the strike price at which the option is struck.
a is the amount received for each time period as discussed above.
time is the maturity of the option in years.
m is the number of time units the option has already met the condition.
dt is the agreed upon discrete time period (often a day) expressed as a fraction of a year.
rate is the annualized risk-free rate of interest.
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.