Suppose the spot price on the underlying asset is $100 with a continuously compounded interest rate of 2% and a zero dividend yield. A one and three month put struck at 90 and call struck at 110 have the following information:

One mth. 90 put one mth. 110 call 3 mth. 90 put 3 mth. 110 call

Price	0.5337	0.0381	1.9051	0.7788
Delta	-0.1141	0.0225	-0.2088	0.1689
Gamma	0.0209	0.0116	0.0191	0.0280
Vega	5.5709	1.5435	14.3599	12.6010
Volga	23.3412	39.6638	25.6412	70.3471
Vanna	-0.6711	0.6855	-0.6325	1.4679
IV	0.32	0.16	0.30	0.18

Set up the equations to solve for designing a self-financed position for a prospective investor who would like to benefit by 50,000 from an increase in volatility of 2% percentage points accompanied by a 2% drop in the stock price. The position should be delta, gamma, vega and volga neutral as well.