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Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 120, 9/1/7 Author of a study manual for exam FM available at: http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic) Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary If you find these exercises valuable, please consider buying the manual or attending the seminar, and if you can’t, please consider making a donation to the Actuarial Program at Illinois State University: https://www.math.ilstu.edu/actuary/giving/ Donations will be used for scholarships for actuarial students. Donations are taxdeductible to the extent allowed by law. Questions about these exercises? E-mail: [email protected] Study Note FM-09-07, Problem No. 2 You are given the following information: • The current price to buy one share of XYZ stock is 500. • The stock does not pay dividends. • The risk-free interest rate, compounded continuously, is 6%. • A European call option on one share of XYZ stock with a strike price of K that expires in one year costs 66.59. • A European put option on one share of XYZ stock with a strike price of K that expires in one year costs 18.64. Using put-call parity, determine the strike price, K. A. 449 B. 452 C. 480 D. 559 E. 582 Solution. Using put-call parity, we have C ! P = 66.59 ! 18.64 = S ! PV ( K ) = 500 ! Ke!0.06 . Therefore, K = ( 500 ! ( 66.59 ! 18.64 )) " e0.06 # 480.0032. Answer C. © Copyright 2007 by Krzysztof Ostaszewski. All rights reserved. Reproduction in whole or in part without express written permission from the author is strictly prohibited. Exercises from the past actuarial examinations are copyrighted by the Society of Actuaries and/or Casualty Actuarial Society and are used here with permission.