Some software plot the tplus21 graph for option position. How does the software derive the tplus21 graph
Typically, the T+n has many assumptions, the most important (IMO) is the value to "assume" for the IV 21 days from now (for the T+21 case). The standard practice is to then use an option pricing model, such as BSM, and plug in the parameters (Interest, yield, IV, Time to expiration (This is set to Time to expiry 21 days from now for the T_21 case), strike, and then sweep the underlying price input across the entire range of interest. Do this for all option positions, long and short, and merely sum the results for each underlying price point. The above is a bit simplified, typical implementations have some extra moving parts.
Possible to use greeks to derive the t21 graph? Use some option spread like vertical on t29 and the theta is really very little at 0.003 and a week of theta also little but the t21graph after a week has change beyond the amount of theta for the week. Definitely the shape changes is not entirely due to theta. What exactly make the tgraph change shape?
If you think about it, the graph of the T+n Y-axis is the P&L, which is merely the summation effect of the option(s) estimated prices at that time. If one uses B&S model, then most information to derive that option price is known, except for the volatility input (which is typically supplied by the current implied volatility for each option, with the assumption the volatility will be the same at that time which is known to be inaccurate, but some estimate is needed and that one is available and may be the best guess for now). -- So, greeks are not the proper way to derive the PnL graph for future time spots. If you have access to some tool such as TOS, you can create the position in the Analyze Tab under Risk Profile, and alter the "Day Step" to observe the PnL at differing dates in the future. Other tools such as ONE and OV can provide this information with less manual effort. I do not understand what you mean by a vertical on T29! I assumed your original post relates to the Risk or P&L graph. If not, then if you can post an example graph, I can try again! I'm likely not describing things well. Perhaps I'll try to supply graphs next. Perhaps a graph of some position showing All n for T+n will help to understand how the graph morphs with passage of time. -- Since I typically use BWB's (Broken Wing Butterflies), I can easily show graphs of one of those.
Yes, it will be theta... because at t=now that's the only known fact.... ceteris paribus we know what the time decay is over 21 or 29 days.
stepandfetchit why is the peak of your graph at the furtherest dte? How do you guard against spike is volaility for your trades?
clarodina: That is the expiration graph. The peak is at the short strike of the Butterfly. The short strike is your liability on the butters, and when short strike at expiration is spot on with the underlying price, you have no liability and you cash your lotto ticket! Note: probability of underlying price being precisely same as the short strike at expiration is near nil! This graph can be called the P&L or the Risk graph. If you note the curves approaching expiration, if price is in general vicinity of the short strikes, the PnL moves positive, but the curves have more curvature, signifying increased Gamma.
stepandfetchit your trade vega is quite negative how do you handle large increase in volaility? What sofware do you use to create the 3d graph?
clarodina: This is the standard RTT trade, referenced on CapitalDiscussions. I coded this in Perl and use Gnuplot for the graph. Gnuplot has 3-D capability, unlike Excel, and is free.