The sensitivity profile like (delta, vega, gamma etc.) of an option contract is quite established if the valuation model follow log-normal model like the Black-Scholes pricing.

I am wondering what could be the Delta, Gamma profile if the valuation model follow a normal model like Bachelier process.

Any internet reference or research insight will be very helpful.

Thanks and regards,

  • $\begingroup$ First a small remark: in trading lingo we define "Delta, Gamma profile" just as "The Greeks". That makes it for everyone easier what you are after. Furthermore, yes I can derive that if you want them but why? The lower bound of an asset is zero so a normal underlying can't model it. $\endgroup$
    – simsalabim
    Mar 26 at 5:36
  • $\begingroup$ @wecandothis I cant agree with your statement that a normal underlying cant model it. There are many spread options particularly calendar spread on commodities (look at CME etc), which are best candidates for this modelling. $\endgroup$
    – Bogaso
    Mar 26 at 9:08
  • $\begingroup$ That was true; before oil prices turned negative. It's not a black swan event anymore. Furthermore; from an oil trader at one of the biggest oil firms: MR with GBM nowadays ;). $\endgroup$
    – simsalabim
    Mar 29 at 14:23

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