1. A barrel of oil is currently valued at $54.00. Its ATMF is $54.50. Given the following available derivatives, form the requested synthetic positions. Specify the traded positions you will take for each synthetic position. Also, for each synthetic position, calculate the (i) trading cost/premium, (ii) Delta, (iii) Gamma and (iv) Vega. (30 points)

Derivative	Contract Price	Premium	Delta (for long position)	Gamma (for long position)	Vega (for long position)
Forward	$54.50	NA	1.0000	0.0000	0.0000
	54.00	NA	1.0000	0.0000	0.0000
Call option	54.50	$3.04	0.5281	0.0522	0.1153
	54.00	3.28	0.5540	0.0518	0.1145
Put option	54.50	3.04	-0.4719	0.0522	0.1153
	54.00	2.79	-0.4460	0.0518	0.1145

1. Synthetic short forward
2. Synthetic long call
3. You notice that a traded call option on oil with a $54.50 strike price has a $2.87 premium. Given the premium you calculate for the put option in b., is there an option arbitrage opportunity? If so, what traded positions would you take to profit from this opportunity? If not, explain why not?