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

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 13 (Version 2.0)

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. See an index all sections by following the link in the previous sentence.

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 ESQPCP1.

Similar to Question 1 from the Society of Actuaries' Sample MFE Questions and Solutions:

Subterranean, Inc., pays no dividends on its stock, which currently trades for $123 per share. You know that the European call option on Subterranean, Inc., stock is $3 more expensive than the European put option with the same strike price and time to expiration. The strike price of the options is $145. The options expire in 9 years. Calculate the annual continuously compounded risk-free interest rate.

Note: The test will give you five multiple-choice possibilities for answers to this kind of problem. See if you can do without them. I will only include multiple-choice possibilities when they are necessary to answering the question or would make doing so more difficult rather than less.

Solution ESQPCP1. 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.

Here, T = 9, C(K, T) - P(K, T) = 3, S₀ = 123, K = 145, and we want to find r.

So 3 = 123 - 145e^-9r

Thus, 145e^-9r = 120 and -9r = ln(120/145).

Hence -ln(120/145)/9 = r = 0.0210268888

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

Problem ESQPCP2.

Similar to Question 13 from the Casualty Actuarial Society's Fall 2007 Exam 3: