# PRMIA 8007 Exam II: Mathematical Foundations of Risk Measurement – 2015 Edition Online Training

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1. The class intervals should be large enough so that they not obscure interesting variation within the group

2. An underlying asset price is at 100, its annual volatility is 25% and the risk free interest rate is 5%. A European call option has a strike of 85 and a maturity of 40 days. Its Black-Scholes price is 15.52. The options sensitivities are: delta = 0.98; gamma = 0.006 and vega = 1.55 .

What is the delta-gamma-vega approximation to the new option price when the underlying asset price changes to 105 and the volatility changes to 28%?

3. What is the maximum value for f(x)= 8-(x+3)(x-3)?

4. What is a Hessian?

5. You are investigating the relationship between weather and stock market performance. To do this, you pick 100 stock market locations all over the world. For each location, you collect yesterday's mean temperature and humidity and yesterday's local index return. Performing a regression analysis on this data is an example of…

6. The fundamental theorem of analysis establishes a relation between

7. If the annual volatility of returns is 25% what is the variance of the quarterly returns?

8. A 2-step binomial tree is used to value an American put option with strike 104, given that the underlying price is currently 100. At each step the underlying price can move up by 20% or down by 20% and the risk-neutral probability of an up move is 0.55. There are no dividends paid on the underlying and the discretely compounded risk free interest rate over each time step is 2% .

What is the value of the option in this model?

9. A typical leptokurtotic distribution can be described as a distribution that is relative to a normal distribution

10. In a portfolio there are 7 bonds: 2 AAA Corporate bonds, 2 AAA Agency bonds, 1 AA Corporate and 2 AA Agency bonds. By an unexplained characteristic the probability of any specific AAA bond outperforming the others is twice the probability of any specific AA bond outperforming the others .

What is the probability that an AA bond or a Corporate bond outperforms all of the others?

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