PRMIA 8007 Exam II: Mathematical Foundations of Risk Measurement – 2015 Edition Online Training
PRMIA 8007 Online Training
The questions for 8007 were last updated at Dec 24,2024.
- Exam Code: 8007
- Exam Name: Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition
- Certification Provider: PRMIA
- Latest update: Dec 24,2024
Which of the following are true:
I. A interest rate cap is effectively a call option on an underlying interest rate
II. The premium on a cap is determined by the volatility of the underlying rate
III. A collar is more expensive than a cap or a floor
IV. A floor is effectively a put option on an underlying interest rate
- A . I, II, III and IV
- B . I, II and III
- C . III and IV
- D . I, II and IV
Which of the following are true:
I. A interest rate cap is effectively a call option on an underlying interest rate
II. The premium on a cap is determined by the volatility of the underlying rate
III. A collar is more expensive than a cap or a floor
IV. A floor is effectively a put option on an underlying interest rate
- A . I, II, III and IV
- B . I, II and III
- C . III and IV
- D . I, II and IV
The class intervals should be large enough so that they not obscure interesting variation within the group
- A . Statements 2 and 3 are correct
- B . Statements 1 and 2 are correct
- C . All three statements are correct
- D . Statements 1 and 3 are correct
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%?
- A . 17.33
- B . 18.75
- C . 19.23
- D . 20.54
What is the maximum value for f(x)= 8-(x+3)(x-3)?
- A . 8
- B . -1
- C . 17
- D . None of these
What is a Hessian?
- A . Correlation matrix of market indices
- B . The vector of partial derivatives of a contingent claim
- C . A matrix of second derivatives of a function
- D . The point at which a minimum of a multidimensional function is achieved
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…
- A . Simple time-series regression
- B . Multiple time-series regression
- C . Simple cross-section regression
- D . Multiple cross-section regression
The fundamental theorem of analysis establishes a relation between
- A . First and second derivative of a function
- B . The derivative of a function and the slope of its graph
- C . Integration and differentiation of functions
- D . The derivative of a function and the derivative of its inverse function
If the annual volatility of returns is 25% what is the variance of the quarterly returns?
- A . 0.1250
- B . 0.0156
- C . 0.0625
- D . None of the above
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?
- A . 11.82
- B . 12.33
- C . 12.49
- D . 12.78
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