Let the stock price be $50. We are given the following information on the BSM prices of three European call options with 3 months to expiration:

K	45	50	55
C	6.86	3.60	1.61
	.83	.60	.35
	.034	.052	.049

(a) Write down the equations which one needs to solve to make a zero-cost, delta-neutral portfolio with a convexity of 0.05 by using the three types of calls. Do not solve these equations.

(b) Graph the value of this portfolio as a function of the stock price. (You only need to illustrate the functional form and you need not do any serious numerical calculations.)