资产定价两道计算题，可有会做的大神今晚就要。

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Part4 [8 Marks]: As the portfoliois currently levered, you are concerned that the positions are too risky andmay have to be liquidated in accordance with its guidelines. To reduce thepotential risk, you consider using a call or a put option written on A2M.

·        A2M 5 C8 – A2M call option with a strikeprice of $8.00 expiring on 20th May

·        A2M 5 P8 – A2M put option with a strikeprice of $8.00 expiring on 20th May

a)      Select an appropriate option from above(either call or put) to reduce the exposure of the portfolio. Using anappropriate methodology discussed in class suggest an appropriate amount toinvest in the option and recalculate the VaR of the portfolio (hint: You canignore gamma and just focus on a first order ‘delta’ approximation calculatedfrom your Black-Scholesspreadsheet. For your volatility input use either the GARCH forecast orhistorical vol and justify your choice).                                                                               (5marks)

Buy A2M 5 C8 to reduce the exposure of the portfolio.

b)      Comment on the effectiveness of the hedge(This is an open ended question – Did it work and reduce the VaR? How well? Whyor why not?).                                                   (3marks)

Part5 [18 Marks]: Given the recentvolatility, you are also concerned about the stability of estimatedcoefficients and distributional assumptions made in your analysis. For thisquestion, focus ONLY on your BTC and A2M positions (no option), with$100,000 invested into each security - i.e. for this question, you will beworking with a $200,000, two security portfolio.

a)      Stress test the correlations of theportfolio using the copula technique discussed in class.

First, map the empirical returns intoeither a Gaussian or a Student-t joint distribution on a percentile-to-percentile basis toestimate the correlation coefficient. Then simulate returns by sampling fromeither a Gaussian or a Student-t joint distribution using the copula parametersabove (degrees of freedom and/or correlation coefficient) and map the simulatedreturns back into their original empirical marginal distributions to calculateVaR and ES. (hint: you should end up with a similar result to your originalvalues. It won’t be exact due to the continuous → discrete mappings. This is a test tosee if your copula is set up correctly and the mappings are reversible)                                                                (5marks)

The correlation coefficient of empirical returns on apercentile-to-percentile basis is 0.1114.

b)      Carefully justify any decisionsregarding Copula selection and methodology in your report                                                                                                                          (3 marks)

c)       Discuss why detailed study ofcorrelations is relevant to your portfolio.                        (2 marks)

d)      Using appropriate justifications,estimate appropriate copula parameters across high and low correlation marketscenarios (hint: ‘stress test’ the correlations by examining how thecorrelation coefficient changes through time to find “high” and “low”periods).          (2 marks)

e)      Using the above copula parametersrepeat the second half of (a) and recalculate VaR and ES across these high andlow correlation market scenarios. What observations and conclusions can youdraw from your results?                                                                    (6 marks)

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关键词：资产定价 计算题 distribution correlations observations