# FIN4750 HW1 MT1 Review

```FIN4750
Options
Department of Economics and Finance
Baruch College
FIN 4750
Midterm (Practice) Exam I
09/29/2023 (due on Friday 6 PM)
Name
___________________________________
ID Number
___________________________________
Signature
___________________________________
1. The exam is closed book and closed notes. You can bring in one page, double-sided, 8&times;11
formula sheet.
2. You can (and probably have to) use a calculator.
3. You have a total of 90 minutes for the exam.
4. The whole exam has a total of 60 points. It will count 30% for your final course grade.
5. Do not separate the exam book. Turn in the entire exam at the end.
7. Good luck.
Page 1
Q1. You believe stock price by year end will have the following multinomial distribution (15 points):
Price Probability
60
10%
80
20%
100
40%
120
20%
140
10%
Q1a. What should be the stock price TODAY? (3 points)
Q1b. what is the prob that a 110 strike CALL will expire ITM? (3 points)
Q1c. what is the conditional average price of underlying stock when 110 strike CALL expires ITM? (3
points)
Q1d. what is the conditional average payment from the 110 strike CALL option when the CALL expires
ITM? (3 points)
Q1e. based on Q1b-Q1d, how much should the 110 CALL be priced at? (3 points)
Page 2
Q2a. What is the probability of option expiring ITM for a 160 CALL? (3 points)
Q2b. What is the average underlying price when CALL expires ITM? (3 points)
Q2c. How much should the 160 CALL be priced at? (3 points)
Q2d. Out of the price in Q2c, how much of that is intrinsic value and how much is time value? (3
points) Hint: intrinsic value is the value of option if option expires NOW. Time value is the remaining.
Page 3
Q3. Implied MAD with Uniform Distribution
Underlying price currently at 200, and follows a uniform distribution with mean of 200. You
observed 80 strike PUT priced at \$5.00. What is the implied MAD? (10 points)
A: put price equation
Which one to choose? Or need to keep one
A: need to double check to make sure strike price X stays inside the uniform form distribution
boundaries. We throw away the smaller solution and keep the larger one.
Page 4
Q4. Current underlying price at 100, and you expect price at expiration follows uniform distribution
with mean absolute deviation of 20.
You short 10 PUTs with strike at 90.
Q4a. What is the TOTAL delta of your 10 short PUT position? (2 points)
Q4b. How many shares do you need in order to offset PUT delta from Q4a? Do you long or short the
underlying shares (2 points)?
Q4c. What is the total gamma value of your hedged PUT positions from Q4a and Q4b? (2 points)
Q4d. For the hedged put position (short 10 puts, hedged with shares), what is the PnL from
(starting) delta, and from gamma when underlying moves from 100 to 80, respectively? (4 points)
Page 5
Q4e. Calculate option price when stock moves \$80. How much of the total PnL of Q4d is from option
position, and how much is from the stock position? (2 points)
Q4f. If underlying moves down from 100 to 80, what is the new delta at stock price of 80 for your
overall position based on gamma? If you need to re-hedge to flatten delta with underlying shares,
what trade do you need to do in the shares to flatten the delta? (2 points)
Q4g. What is the PnL from the delta and gamma when underlying moves from 100 to 120,
respectively? (2 points)
Q4h. For Q4g, how much of the total PnL is from option position, and how much is stocks, when
underlying moves from 100 to 120? (2 points)
Q4i. If underlying moves up from 100 to 120, If you need to re-hedge to flatten delta with
underlying shares, what trade do you need to do in the shares? (2 points)
Page 6
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