## 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 Apr 10,2024.

**Exam Code:**8007**Exam Name:**Exam II: Mathematical Foundations of Risk Measurement - 2015 Edition**Certification Provider:**PRMIA**Latest update:**Apr 10,2024

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 ofâ€¦

- 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