Kean University Introduction to Derivatives Second Exam

This document presents solutions to a second exam in an Introduction to Derivatives course. The exam covers core concepts such as American and European options, option delta, and bullish market indicators. It includes multiple-choice questions, definitions, and problem-solving scenarios. The solutions address topics like calculating gains and losses on options, break-even points, and the impact of stock dividends. Furthermore, the document explores strategies such as protective puts and covered calls, analyzing potential profits and losses. The document also includes a detailed analysis of option pricing using the Black-Scholes model and binomial trees. The solutions are comprehensive and provide a thorough understanding of the subject matter, making it a valuable resource for students preparing for derivatives exams.

Second Exam Spring
Concept
Answer 1
Which of the following is a valid completion of the sentence—“An American
option ...”?
(a) Reflects the higher impatience of Americans relative to Europeans.
(b) Is traded in America and Europe, whereas European options are only traded
in Europe.
(c) Is exercisable prior to maturity whereas European options are not.
(d) All of the above.
Answer
(d)
Ans 2
(b)
Ans 3
Delta measures how the value of an option changes with change in underlying security. It
helps to measure the change in the value of option based on directional change of the
underlying.
Ans 4
The term bullish means that the market is going to go up and the prices of securities shall
rise. Thus, majority of options in the market are call and investors believe that future is good.
Problems
1 (a)
Strike Price = 30$
Premium=3$
Closing price : 25
Call option is written it wont be exercised, gain shall be premium amount i.e. $3.
1 (b)
Break even point in terms of closing price shall be $ 30+ $3=$33;
1(c)
Maximum gain by writing the call option shall be the premium of call which is $3.
1(d)
Maximum loss is infinite as the prices of securities may go any farther in upward movement.
Ans 2

European Put option Value : 4.8$
Strike Price; 40
Expiry 2 Months
Current stock price 42
Risk free interest: 5%
Considering call put parity
C+PV(X)=P+S
C=Price of Call
PV(X)=Present value of Strike Price
P=Put
S=Spot Price
Accordingly = C+40/(1.05)^(2/12)=42+4.8
6.473
Ans 3
Call option Exchange traded
Strike Price: 60
Number of Shares =100
Maturity : 4 Months
Part a
When a 5% stock dividend is declared, it generally results in increase in price of the
underlying which shall cause an increase in the price of call option in the short term.
Part b
When a 5% cash dividend is declared and paid it shall result in fall of price of security which
shall result in fall of call price of the option on such security. Thus, dividend shall create
decrease in the value of call option most likely. Further, the price falls depends on the price
fall of security.
Part c
No impact happens on the call options when the share is split as the number of shares on
which the call has been exercised shall increase and price shall be adjusted accordingly.
There shall be no increase or decrease in price of underlying which shall not cause any
change in price of call option.
Ans 4
Stock Selling Price: $35

Put option : $3
Cost total : $ 38
When price ends at $ 0
Stock price: 0
Put option value : $35
Total Value : $35
Loss: $ 38-$35=$3
When price ends at $ 30
Stock price: $30
Put option value : $5
Total Value : $35
Loss: $ 38-$35=$3
When price ends at $ 49
Stock price: $49
Put option value : 0
Total Value : $49
Profit: $ 49-$35=$14
When price ends at $ 500
Stock price: $500
Put option value : 0
Total Value : $500
Profit: $ 500-$35=$465
Ans b
Maximum gain is unlimited under protective put
Ans c
Maximum loss is premium of put option i.e. $3
Ans d
Break even stock price is $ 35+ $3= $38
Ans 5
Current Selling price : $52

Call Strike Price: 50
Selling price : 5
Another call strike price : $ 55
Selling Price : 1.5
Ans a
Purchase call at 50 and sell at 55
Net outflow:$5-$1.5=$3.5
Sl. No.
Price of
Security
Value of Call
$50
Value of Call
$55
Initial
Pay
Total
Pay
1 45 0 0 3.5 -3.5
2 46 0 0 3.5 -3.5
3 47 0 0 3.5 -3.5
4 48 0 0 3.5 -3.5
5 49 0 0 3.5 -3.5
6 50 0 0 3.5 -3.5
7 51 1 0 3.5 -2.5
8 52 2 0 3.5 -1.5
9 53 3 0 3.5 -0.5
10 54 4 0 3.5 0.5
11 55 5 0 3.5 1.5
12 56 6 -1 3.5 1.5
13 57 7 -2 3.5 1.5
14 58 8 -3 3.5 1.5
15 59 9 -4 3.5 1.5
16 60 10 -5 3.5 1.5
17 61 11 -6 3.5 1.5
18 62 12 -7 3.5 1.5
19 63 13 -8 3.5 1.5
Ans b
Break even stock price shall be $ 53.5
Ans c
The most that can be lost in this strategy is $ 53.5 which is premium paid
Ans d

Most that can be made out of this strategy is $ 5-$3.5=$1.5
Anse
Graph is provided as under:
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63
-4
-3
-2
-1
0
1
2
Total Pay
Ans 6
Current stock price $70
Up: 1.2
Low: 0.8
European put strike: 67.2
Maturity : 1 Year
Current risk free rate: 6%