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# 银行风险管理代写 ECOM055代写 风险管理代写 金融经济代写

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## Final Exam 2021/22 Duration: 3 hours

THIS IS AN OPEN BOOK EXAMINATION TO BE CONDUCTED ONLINE. YOU MAY REFER TO ANY OF THE COURSE MATERIALS, OR ANY OTHER SOURCE OF INFORMATION. YOU MAY ALSO USE A SPREADSHEET OR CALCULATOR.

YOU CANNOT SUBMIT HANDWRITTEN ANSWERS

PLEASE ENSURE THAT YOUR WORKING IS CLEARLY SHOWN WITH ALL STEPS OF YOUR CALCULATION INCLUDED IN YOUR ANSWER DOCUMENT, INCLUDING ANY FORMULA USED.

When writing formulas, please note the following:

• It is acceptable to use the standard alphabet rather than Greek letters. The following are recommended: m for μ, s for σ, w for ω, r for ρ, d for Δ, b for β.
• For mathematical operators: add +, subtract -, multiply *, and divide /.
• Where appropriate, use an underscore to indicate a subscript, eg r_f for rf.
• Use the ^ character for power, eg x^2 for x2, x^0.5 for √x.
• As an alternative to x^.5 you may type sqrt(x).
• Use brackets as necessary. To make your answer clearer use different brackets where appropriate, eg [] {} ().

### Question 1银行风险管理代写

Answer the following unrelated qualitative items. You are not expected to implement any calculations in your answers.

a）There are 2 types of investors: pension funds and day-traders, the latter with an investment horizon of one day. How differently should these 2 types of investors approach VaR and ES in the following 2 scenarios: (i) when there is autocorrelation of returns AND (ii) (iwhen returns are normally distributed, independent with a mean of zero (you can assume they are independent and identically distributed) [13 marks]

b）Figure 1 below shows the Dow Jones Industrial Average (DJIA) index on May 6, 2010. This episode is known as the flash crash. Connect this episode to a mechanism you have learnt in our Risk Management for Banking module. Which type of traders were possibility involved in this episode? Could you envisage another episode such as the flash crash, but in reverse: one where prices would go up quite a lot and then go down back to normal levels in a matter of minutes? Explain in detail your answer. [12 marks] 银行风险管理代写

### Question 2

Answer the following unrelated qualitative items. You are not expected to implement any calculations in your answers.

a）Discuss the following statement in detail: “Life-insurance companies have a harder time in predicting their payouts than property-casualty insurance companies due to a higher level of moral hazard.” [12 marks]

b）Discuss the following statement in detail: “Historical hazard rates tend to be lower than hazard rates computed from credit default swaps. The higher the quality of the bond, the higher the difference. One of the reasons for this difference is that bond returns have negative excess kurtosis.” [13 marks]

### Question 3银行风险管理代写

Suppose that you are presented with 2 models: (i) an EWMA model with parameter l=0.91; and (ii) a GARCH(1,1) model with parameters a= 0.09, b= 0.90, and w = 0.000008.

a）What is the long-run average volatility in both models? [4 marks]

b）Assume that the most recent return un-1  is estimated at 2% and the most recent volatility sn-1 is estimated at 1%. Update the volatility estimate in both models. [4 marks]

For all the remaining items, consider only the GARCH(1,1) model:

c）If the current volatility is 0.5% per day, what is your estimate of the volatility in 5, 100, and 500 days. [4 marks]

d）What volatility should be used to price 5-, 100-, and 500-day options? [4 marks]

e）Suppose that there is an event that increases the volatility from 0.5% per day to 1.5% per day. Estimate the effect on the volatility in 5, 100, and 500 days. [4 marks]

f）Estimate by how much the event increases the volatilities used to price 5-, 100-, and 500-day options. [5 marks]

### Question 4银行风险管理代写

Consider the portfolio shown in Table 1 comprised of four over-the-counter options on the Tesco stock, that was trading at £2.77 at the close of the trading day 18th March 2022:

Table 1

a) Compute the delta, gamma and vega of the portfolio. What position is needed to make the portfolio delta neutral? [5 marks]

b) A new traded option (Option X1) is available on the market with a delta of 0.4, a gamma of 0.9, a vega of 0.6 and a theta of -0.3. Is it possible to make the portfolio gamma and delta neutral? If yes, what are the positions needed to make the portfolio gamma and delta neutral? If not, explain in detail why it is not possible. [6 marks] 银行风险管理代写

c) Suppose that a second traded option is available (Option X2). The option has a delta of -0.4, a gamma of -0.3, a vega of 0.8 and a theta of -0.2. Is it possible to make the portfolio vega, gamma and delta neutral by using options X1 and X2? If yes, what are the positions needed to make the portfolio vega, gamma and delta neutral? If not, explain in detail why it is not possible. [7 marks]

d) Is it possible to make the portfolio theta, gamma and delta neutral by using options X1 and X2? If yes, what are the positions needed to make the portfolio theta, gamma and delta neutral? If not, explain in detail why it is not possible. [7 marks]

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