Risk Management Project Week 7

Instructions:
Be verbose. Explain clearly your reasoning, methods, and results in your written work. Write clear code
that is well documented. With 99% certainty, you cannot write too many code comments.
Written answers are worth 16 points. Code is worth 4 points. 20 points total.
1. When finished, respond to the questions in Sakai as “done.” We will record your grade there.
2. In your code repository, create a folder called “Week06.”
3. In that folder, include
a. a document (preferably a PDF) with your responses.
b. Slides for presenting your results.
c. All code
d. A README file with instructions for us to run your code
Everything must be checked into your repository by 8am Saturday 3/26. A pull will be done at that time.
Documents and code checked in after the instructors pull will not be graded.
Data for problems can be found in CSV files with this document in the class repository.
Problem 1
● Current Stock Price $165
● Strike Price $165
● Current Date 03/13/2022
● Options Expiration Date 04/15/2022
● Risk Free Rate of 0.25%
● Continuously Compounding Coupon of 0.53%
Implement the closed form greeks for GBSM. Implement a finite difference derivative calculation.
Compare the values between the two methods for both a call and a put.
Implement the binomial tree valuation for American options with and without discrete dividends. Assume
the stock above:
● Pays dividend on 4/11/2022 of $0.88
Calculate the value of the call and the put. Calculate the Greeks of each.
What is the sensitivity of the put and call to a change in the dividend amount?
Problem 2
Using the options portfolios from Problem3 last week (named problem2.csv in this week’s repo) and
assuming :
● American Options
● Current Date 02/25/2022
● Current AAPL price is 164.85
● Risk Free Rate of 0.25%
● Dividend Payment of $1.00 on 3/15/2022
Using DailyReturn.csv. Fit a Normal distribution to AAPL returns – assume 0 mean return. Simulate
AAPL returns 10 days ahead and apply those returns to the current AAPL price (above). Calculate Mean,
VaR and ES.
Calculate VaR and ES using Delta-Normal.
Present all VaR and ES values a $ loss, not percentages.
Compare these results to last week’s results.
Problem 3
Use the Fama French 3 factor return time series (F-F_Research_Data_Factors_daily.CSV) as well as the
Carhart Momentum time series (F-F_Momentum_Factor_daily.CSV) to fit a 4 factor model to the following
stocks.
AAPL FB UNH MA
MSFT NVDA HD PFE
AMZN BRK-B PG XOM
TSLA JPM V DIS
GOOGL JNJ BAC CSCO
Fama stores values as percentages, you will need to divide by 100 (or multiply the stock returns by 100)
to get like units.
Based on the past 10 years of factor returns, find the expected annual return of each stock.
Construct an annual covariance matrix for the 10 stocks.
Assume the risk free rate is 0.0025. Find the super efficient portfolio.