Country : | Australia |
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Task:
Question 1
Dell options expiring in November 2020 are traded on CBOE. Today is 15 November 2020. Dell’s last stock price was $66.56. Using 10-step binomial tree estimate:
a) The option premiums (per 1 share) for the ATM call and put options, assuming that option minimum strike step is $0.50. Estimate the volatility for the remaining life of the option using GARCH(1,1) model. [4 points]
b) What is the expected average daily volatility (annualized) for the remaining life of the option according to your GARCH estimate? [2 points]
c) What are the deltas of these options at t=0? [1 point]
d) What are the gammas of these options at t=0? [1 point]
e) What are the vegas (per 1% change) of these options at t=0? [1 point]
f) What are the thetas (per calendar day) of these options at t=0? [1 point]
g) What are the rhos (per 1% change) of these options at t=0? [1 point]
Question 2
For this question, use data from 03 March 2017 to 03 December 2018. On 03 December 2018, after the market close, your portfolio consisted of 5 different stocks: CGC (Nasdaq), KHC (Nasdaq), PFE (NYSE), MSFT (Nasdaq), and SNAP (NYSE). Here is the number of stocks of each company that you hold in your portfolio:
a) Using historical simulation approach, calculate 10-day 99% VaR and C-VaR [3 points]
b) What would be your 10-day 99% VaR estimate if you incorporate a jump component of -5% for your portfolio return every 2% of the time? [3 points]
c) Back-test your estimate in b): how many times did your daily portfolio return was worse than your 1- day 99% VaR estimate from b)? [2 points]
d) Using EWMA approach, estimate daily annualized volatility of your portfolio return for tomorrow? [3 points]
Question 3
You are a financial manager at a pharmaceutical company producing insulin. You consider building a new plant to produce insulin in Brazil. Production of insulin is done in 2 stages. First you need to create a formula and put it into a specific lab environment (i). After the insulin is produced, you need to put it into the prefilled insulin pens and assemble them into boxes for final distribution (ii). Each stage requires different investments. Constructions required for each stage take 1 year. In this period (t = 0), you invest in stage (ii) production. But you need to consider an option to build everything needed for stage (i) in 1 or 2 years in case the demand for your insulin is high enough. The business planning department in your company made a forecast of potential future scenarios for the demand for your insulin depending on economic conditions, competitive environment, and other concerns. Below you can see the factors by which the current demand for your insulin may be multiplied in different possible scenarios (and risk-neutral probabilities of those scenarios) for the next 4 years.
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