More Exam-Style Questions on Put-Call Parity and Arbitrage

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 14

This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.

This is Section 14 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here. See Section 5 here. See Section 6 here. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10

here. See Section 11 here. See Section 12 here. See Section 13 here.

The problems in this section were designed to be similar to problems from past versions of Exam 3F / Exam MFE. They use original exam questions as their inspiration - and the specific inspiration for each problem is cited so as to give students a chance to see the original. All of the original problems are publicly available, and students are encouraged to refer to them. But all of the values, names, conditions, and calculations in the problems here are the original work of Mr. Stolyarov.

Problem MESQPCPA1.

Similar to Question 16 from the Casualty Actuarial Society's Fall 2007 Exam 3:

The stock of Precarious Co. does not pay any dividends. It currently trades at $565 per share, and the annual continuously compounded interest rate is 20%. European call and put options on Precarious Co. stock are available with strike price of $596, expiring in 3 years. There are no arbitrage opportunities in the pricing of these options. Digtammar decides to purchase 782 call options and sell 782 put options on Precarious Co. stock. What is the net cost of this transaction?

Solution MESQPCPA1. We use the put-call parity formula

C(K, T) - P(K, T) = [S₀ - PV_0,T(Div)] - e^-rTK, which, with no dividends, simplifies to

C(K, T) - P(K, T) = S₀ - e^-rTK.

We note that Digtammar will pay 782[C(K, T) - P(K, T)] for this transaction, which is the same as 782[S₀ - e^-rTK] = 782[565 - e^-0.2*3596] = 186044.2631. So the net cost of the transaction to Digtammar is $186,044.2631 (i.e., this is the amount he pays).

Now try the corresponding test question, if you have not done so already. Do this after you do each of the problems here.

Problem MESQPCPA2.

Similar to Question 3 from the Casualty Actuarial Society's Spring 2007 Exam 3: