Problem 1

Given the following data as of the close of trading on 10/26/18:

Quest Diagnostics (DGX): 91.47

T-bill: Asked 2.28, Days to Maturity 84

Options on DGX: expire January 18, 2019

c	X	p
23.7	70	0.35
17.5	75	0.55
12.9	80	1
8.7	85	1.95
5.2	90	3.4
2.55	95	6.1
1.1	100	9.7
0.45	105	14.2

Strike	Lower bound, call	Lower bound, put
70
75
80
85
90
95
100
105

From the T-bill data, calculate the discount factor.

Continue to assume that the call option struck at $80 trades at a premium of $11.00. This time, take the following positions: (1) buy the call; (2) short the stock; (3) invest in the T-bill at the risk-free rate. Show the value of these positions at expiration. Fill out the following table and show you make arbitrage profit.

Position	Cash Flow Today	Expiration, DGX < 80	Expiration, DGX > 80
Buy call	-11
Short DGX	+91.47
Invest in T-bill	-80.47
TOTAL	0

Calculate present value of the arbitrage profit made in part d and compare it to the arbitrage profit you made in part b. Which strategy do you choose: immediate exercise or holding positions until expiration?