It would have a small positive or neutral Vega, depending on the strikes you choose and skew. Since equity options rarely expand without and up coming event or a down market, this is the best I could do with the question asked.
Is "pure arbitrage" an acceptable strategy? You can buy an option on one exchange and short-sell the same option on another exchange at a higher price....I believe it satisfies your desire for the positive vega and theta.....if you have the execution capability to trade in that manner.
I mined for it and can't rind any short backspreads with sufficient skew to net out a +vega. I found some flies, however.
There is only one situation that I can think of that will trade as the OP would like, and it would be a rare trade. Since the OP didn't give a ticker this trade would best be explained with a XYZ example and estimated option prices. I prefer real examples, but this will do for a quick demo. The stock would be a biotechnology stock XYZ at $20.00 Sell 1 contract of 21c/19p options. Credit $4.00 Buy 4 contracts of 25c/15p options. Debt $2.00 Total credit $2.00 Scenario one: XYZ trades flat, $2.00 profit. Scenario two: XYZ submits to FDA for drug approval, IV goes way up affecting the deeper OTM options the most.
The reason why I am looking for a positive vega, positive theta trade is to benefit from the increase in IV due to upcoming earnings. The objective is to construct vega positive trades that have at least theta decay as possible... The best would be to have it theta positive. Thanks! Regards, Samer