2019年4月英国精算师-金融数学真题

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  16 April 2019 (pm)

  

  Subject CM2A – Financial Mathematics and Loss Reserving Core Principles


  1 (i) Describe the three forms of the Effcient Markets Hypothesis.


  (ii) Describe the evidence against market effciency in relation to:


  (a) over-reaction of market prices to events


  (b) under-reaction of market prices to events.


  2 (i) Describe the frst order stochastic dominance theorem.


  (ii) Describe the second order stochastic dominance theorem.


  Consider two portfolios 1 and 2, which have normally distributed returns with parameters (m1, s1) and (m2, s2) respectively. Investors in this market meet the assumptions of the dominance theorems.


  (iii) Explain which portfolio, if any, dominates the other in the following situations,indicating whether any dominance is frst or second order and why:


  (a) m1 < m2 and s1 = s2


  (b) m1 = m2 and s1 < s2


  (c) m1 > m2 and s1>s2


  3 Consider a process St which follows a lognormal process with parameters m and s2.


  (i) State the mean and variance of St.


  The price of the security at time 0 is S0 = $1,000. The expected price at time 3 is $2,042 and the standard deviation is $1,290.


  (ii) Determine the parameter values for the corresponding lognormal model.


  (iii) Calculate the probability that the security price at time 5, S5, will fall between $2,000 and $2,500.


  (iv) Defne the following risk measures algebraically:


  (a) Value at Risk at the level p%


  (b) Expected shortfall below a benchmark level L.


  (v) Suggest why it can be diffcult to apply Value at Risk to real-world situations at higher percentage levels (for example at the 99% level).



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