Call Option and Price

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ACT 4000, FINAL EXAMINATION
ADVANCED ACTUARIAL TOPICS
APRIL 24, 2007
9:00AM - 11:OOAM
University Centre RM 210- 224 (Seats 266- 304)
Instructor: Hal W. Pedersen

You have 120 minutes to complete this examination. When the invigilator instructs you to stop writing you must do so immediately. If you do not abide by this instruction you will be penalised.
Each question is worth 10 points. If the question has multiple parts, the parts are equally weighted unless indicated to the contrary: Provide sufficient reasoning to back up your answer but do not write more than necessary.
This examination consists of 12 questions. Answer each question on a separate page of the exam book. Write your name and student number on each exam book that you use to answer the questions. Good luck!

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Suppose call and put prices are given by
Strike
Call premium
Put premium

80
22
4

100
9
21

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Find the convexity violations.

(1.-)

What spread would you use to effect arbitrage?

105
5
24.80

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I A New York finn is offering a new financial instrument called a "happy calL" It has a payoff function at time T equal to max(.5S, S - K), where S is the price of a stock and K is a fixed strike price. You always get something with a happy call. Let
P be the price of the stock at time t
0 and let C, and C2 be the prices of ordinary calIs with strike prices K and 2K, respectively. The fair price of the happy call is of the fonn

=

CH

Find the constants ex, fJ, and y.

y

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= exP + fJC. + yC2.

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You are interested in stock that will either gain 30% this year or lose 20% this year. The one-year annual effective rate of interest is 10%. The stock is currently selling for $10.
(1) (4 points) Compute the price of a European call option on this stock with a strike price of $11.50