The underlying asset (spot, not paying dividends) quotes 100, its volatility is 35%, the interest rate is 2%, and the expiry date of the considered options is 2 months. You live in Black- Scholes universe.

a) Show formally that a long condor made of 4 calls has exactly the same value and greeks as a long condor made of 4 puts.

b) Let one short strangle made of a call, strike 100, and a put, strike 90. Let another short strangle made of a call, strike 90, and a put, strike 100. You are given a Table reporting the value and greeks of both strangles but without stating which is which. How can you tell which is which at once? What do you notice about the greeks and why?