How would one price European Options using Trading days for Volatility and Theta; and Calendar days for calculating forwards and Cost of carry, Rho. In other words I want a trading day model for Volatility and Theta and use calendar days for cost of carry.In black scholes model, when calculating d1 and d2, and call and put prices where would I use trading days and calendar days for T for sqrt (T). Additionally when I calculate Vega, it would give me a option price sensitivity w.r.t changing trading day vol.Any help would be highly appreciated.Thanks in advance

With Tbus = Tenor Business Days and Tcal = Tenor Calendar Days and sig the business day vol in BS:d1 = [ ln(s/k) + (r-q)*Tcal + sig^2 / 2 * Tbus] / [sig * sqrt(Tbus)d2 = d1 - sig * sqrt(Tbus)More interestingly, I'd like to know how to deal with this reality for american options. And to be more correct, European should be priced with Discrete/Proportional divs like amercian.

Great, thanks for your prompt response. Will try this approach, and hopefully should work well in the practical world. Is this the only theoretically correct way of solving this?So when I calculate Vega I should use Tbus or TCal or use combination of both?Vega = S * exp(q*Tcal) * n?(d1)*sqrt(Tbus)Call Theta = (-S*exp(-q*Tcal) * n?(d1) * sig)/(2*sqrt (TBus)) + q*S*exp(-q*TCal) * N(d1) ? r*X*exp(-r*Tcal) * N(d2)Additionally I would also be using Tcal for calculation Call and Put prices right?Call = S*exp(-q*tcal)*N(d1) ? X*exp(-r*Tcal)*N(d2)Interesting, I was also going to ask later about applying this reality to American Options, but I haven?t started pricing pricing American options with discrete dividends as yet, if you have an insight, please let me know.Thanks a ton.

Put the interest components together with the spot and use the forward on the d1 and d2 formulas; the time left is always together with vol (in fact, they should be always thought of as one thing - vol Sqrt[t]).

Is this typically what practitioners also do, use trading days for volatility and theta; and use calendar days for cost of carry or do practitioners do something different. M Carreira thanks, will IM you if I have anymore questions.BestD

The trading time calendar can be adapted for events (weighting days differently), and this can deal with weekends and holidays, so one solution deals with it all.

So, why not just use calendar time -- save yourself a big headache -- and weight those if you want? After all, money never sleeps

Sometimes in Brazil people will express the vol in business days (our local interest rate is in business days); this is still an heritage of our hiperinflation days.But Alan is correct; treat time as one variable and weigh it outside the formula.Worst case scenario your theta is going to be dependent on your weights.

Thanks MCarreira and Alan.I dont know how would I weight calendar time, but someone messaged me this link from Espen Haug's book and it seems like a good enough solution.http://books.google.com/books?id=FU7gam ... &f=falseIf you could just give me an example of how would I weight calendar time, then that would be great.Regards

weight[date]=0, all weekendsweight[date]=0.1, all holidaysweight[date]=1.5, all FOMC meetingsweight[date]=1, all other dates