Session 1, 2021 Assessment task: Assignment

Structure

This is an individual assignment with 100% of the marks allocated to individual performance. The assignment requires each student to submit an Excel spreadsheet that contains all necessary computations and explanations. You should use the template provided; each task should be performed on a separate worksheet; you may create more worksheets if necessary.

Submission

The individual Excel spreadsheets are to be submitted online using the relevant link on iLearn no later than 16 May 2021 11:55pm AEST. Make sure that your name and student number are on every worksheet of the Excel file. The names of the submitted files should follow the format AFIN3028- LastName.FirstName, e.g., AFIN3028-Shi.Lei.

No extensions will be granted. Students who have not submitted the task prior to the deadline will be awarded a mark of 0 for the task, except for cases in which an application for special consideration is made and approved.

Assignment data

You are to download assignment-data.xlsx from iLearn. This Excel spreadsheet comprises three worksheets, one for each question. Data and other relevant information for each question are provided on each of the worksheets. You may insert more worksheets if necessary.

Important: You must use assignment-data.xlsx as a template for completing the assignment. Complete each task on a separate worksheet in the template.

Assignment questions

Suppose a FI has written and sold an option to a client on 10,000 shares of a listed stock. The current share price S0 = 24, expected return μ = 0.02, volatility σ = 0.80. Moreover, the put option has a strike price of K = 24 and a maturity of 1 year. The FI has decided to charge the client 10% more than theoretical no-arbitrage price of the option, and then delta-hedge its risk exposure on a daily basis by trading the underlying stock and the risk-free asset. For simplicity, assume the risk-free interest rate r = 0. The FI wants to be informed about the potential profit and loss of this trade. As a result, you are required to perform the following tasks.

Assume the stock price follows a geometric Brownian motion, simulate two trajectories of daily prices for the next year (assume 252 trading days per year). One of the price trajectories should have ST > S0, and the other should have ST < S0 at maturity. Plot the two price trajectories together in a graph. Label x-axis as t (number of years) and y-axis as St (stock price at time t).

(2 marks)

• Suppose the option is a call option. For each of the price trajectories simulated in Part (a), perform a dynamic delta-hedging strategy similar to that in Table 8.2 of the textbook. Compute the profit/loss of the FI for each price trajectory.

(3 marks)

• Suppose the option is a put option. Repeat the exercise in Part (b).

(3 marks)

• Does the profit/loss in Part (b) and Part (c) depend on the difference between the two price trajectories? Why or why not?

(2 marks)

• An investor has an index portfolio tracking the All Ordinaries Equity Index (AORD). The investor wants to estimate the daily 99% value at risk (VaR) and evaluate its accuracy.
  • Using the data provided for the 2019/20 financial year, estimate the EWMA model for the daily volatilities. You should estimate the parameter λ using maximum likelihood and produce a table like Table 10.4 in the textbook. You may use an initial value of λ = 0.94 with Excel Solver. Plot the estimated daily volatilities. Based on the estimated daily volatilities, calculate the 99% VaR for each trading day in the 2019/20 financial year.

(3 marks)

• Repeat Part (a) by replacing the EWMA model with the GARCH (1,1) model for estimating the daily volatilities. You may use initial values of ω = 0.000001347, α = 0.08339 and β = 0.9101 with Excel Solver. Plot the estimated volatilities by EWMA and GARCH together for comparison.

(3 marks)

• Test the accuracy of each of the VaR estimates in Part (a) and (b), in how many days were the percentage loss in the portfolio larger than the VaR estimates. Compare accuracies between the EWMA and GARCH (1,1) models.

(3 marks)

• Comment on the accuracies of the VaR estimates in Part (a) and Part (b). What do you think is the main reason for the difference in accuracies?

(1 mark)

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