FIN 4650 Financial Derivatives Exam 2
Questions and Complete Solutions
Graded A+
S0 = $30 (non-dividend-paying stock), over the next 6 months, it is expected to rise to $36 or fall to $26.
R = 0%. An investor is interested in six-month call options with a strike price of $32.
What is the value of the option at the end of six-months if the stock price ends up being $36? - Answer:
$4
bought at $32, ends up being $36, value = $4
What is the value of the option at the end of six-months if the stock price ends up being $26? - Answer:
$0
bought at $32, ends up being $26 so lost $6 which means value expires worthless
Use No Arbitrage Argument approach-
What is the delta of the option above? - Answer: I took it steps too far and solved for f value as well but
if you stop after setting up the upward and downward states of the economy equal to each other you
can solve for delta
36(delta)-4=26(delta)-0
delta = 0.4
How will you create the risk-less portfolio? - Answer: Once you see which outcome has greater value
(and especially does not expire worthless), you would long these shares (hence buying)
Long 0.4 shares for each call option sold (what is our delta value)
, What is the value of the call option today using the no-arbitrage argument approach? R still is = 0% -
Answer: $1.60
CHECK THIS FROM 5A ANSWER KEY!
Using the risk-neutral (pseudo) probability approach, what is the up movement factor, u? - Answer:
30u=36 means u=1.2
Using the risk-neutral (pseudo) probability approach, what is the down movement factor, d? - Answer:
30d=26 means d=0.866
What is the growth factor, a?
a = e^rt - Answer: a = e^(0.00)(0.5) = 1
What is the risk-neutral (pseudo) probability that the stock price will be $36? - Answer: For this just use
the u and d you just computed to insert into p = e^(r)(t) - d / u - d
p = 0.4
Compute the value of the call option using the risk-neutral (pseudo-probability) approach? - Answer:
$1.60 because
f = (p-value x option price of the non-worthless state of the economy)e^(-r)(t)
The current price of a non-dividend paying stock is $30. You are interested in using a two-step tree to
value a European call option on the stock with a strike price of $28 that expires in 6 months. Each step is
3 months, the risk free rate is 8% per annum with continuous compounding. The up-movement factor, u
= 1.1 and the down-movement factor, d = 0.9
What can you say about the current money-ness of the option? - Answer: in-the-money
Questions and Complete Solutions
Graded A+
S0 = $30 (non-dividend-paying stock), over the next 6 months, it is expected to rise to $36 or fall to $26.
R = 0%. An investor is interested in six-month call options with a strike price of $32.
What is the value of the option at the end of six-months if the stock price ends up being $36? - Answer:
$4
bought at $32, ends up being $36, value = $4
What is the value of the option at the end of six-months if the stock price ends up being $26? - Answer:
$0
bought at $32, ends up being $26 so lost $6 which means value expires worthless
Use No Arbitrage Argument approach-
What is the delta of the option above? - Answer: I took it steps too far and solved for f value as well but
if you stop after setting up the upward and downward states of the economy equal to each other you
can solve for delta
36(delta)-4=26(delta)-0
delta = 0.4
How will you create the risk-less portfolio? - Answer: Once you see which outcome has greater value
(and especially does not expire worthless), you would long these shares (hence buying)
Long 0.4 shares for each call option sold (what is our delta value)
, What is the value of the call option today using the no-arbitrage argument approach? R still is = 0% -
Answer: $1.60
CHECK THIS FROM 5A ANSWER KEY!
Using the risk-neutral (pseudo) probability approach, what is the up movement factor, u? - Answer:
30u=36 means u=1.2
Using the risk-neutral (pseudo) probability approach, what is the down movement factor, d? - Answer:
30d=26 means d=0.866
What is the growth factor, a?
a = e^rt - Answer: a = e^(0.00)(0.5) = 1
What is the risk-neutral (pseudo) probability that the stock price will be $36? - Answer: For this just use
the u and d you just computed to insert into p = e^(r)(t) - d / u - d
p = 0.4
Compute the value of the call option using the risk-neutral (pseudo-probability) approach? - Answer:
$1.60 because
f = (p-value x option price of the non-worthless state of the economy)e^(-r)(t)
The current price of a non-dividend paying stock is $30. You are interested in using a two-step tree to
value a European call option on the stock with a strike price of $28 that expires in 6 months. Each step is
3 months, the risk free rate is 8% per annum with continuous compounding. The up-movement factor, u
= 1.1 and the down-movement factor, d = 0.9
What can you say about the current money-ness of the option? - Answer: in-the-money
