A financial institution has written 50 put options on stock with a strike price of $45 and maturity 100 days. The current stock price is $55. The institution decides to hedge this position using two other options and the money market account (to borrow or lend at risk-free rate) such the hedged portfolio is delta-gamma neutral. Relevant pricing details are given below.

	Option to be hedged European put	Option 1 European put	Option 2 European call
Strike price	$45	$55	$60
Maturity	100 days	45 days	16 days
Volatility	25%	25%	25%
Discount rate	5.30%	5.20%	5.05%
Price	$0.1341	$1.7457	$0.0667
Delta	-0.0434	-0.4530	0.0556
Gamma	0.0128	0.0821	0.0389
Theta	-0.0029	-0.0174	-0.0105
Vega	2.6513	7.6507	1.2911

a) Determine the composition of the delta-gamma neutral portfolio. The contract size for each option is 100 shares. Round off your position in Options 1 and 2 to the nearest integer.

b) What is the theta of the hedged portfolio? What is the theoretically expected change in the value of the hedged portfolio if volatility increases by 1%?