Lecture 6.2: Model Building Approach

Question 1

What is NOT the main drawback of linear approximation of option price change?

A) It ignores the curvature of the relationship between the option value and the underlying asset
B) It assumes that the relationship between the option price and the underlying asset is linear
C) It assumes that the value of an option has a convex/concave relation with the underlying asset

Answer 1

WRONG: C) It assumes that the value of an option has a convex/concave relation with the underlying asset –> this is what it fails to do

Question 2

A positive gamma (when long positions in options) translates into negative skewness in the return distribution
TRUE/ FALSE

Answer 2

FALSE
A positive gamma (when long positions in options) translates into POSITIVE skewness in the return distribution

Question 3

A negative gamma (when short positions in options) translates into negative skewness in the return distribution
TRUE/ FALSE

Answer 3

TRUE

Question 4

To determine the option value relation with the underlying asset, a POSITIVE gamma leads to a positively skewed distribution.
Under the linear approximation approach, the calculated VaR will therefore be (overestimated/ underestimated)

Select the right word.

Answer 4

To determine the option value relation with the underlying asset, a POSITIVE gamma leads to a positively skewed distribution.
Under the linear approximation approach, the calculated VaR will therefore be OVERESTIMATED

Question 5

Negative gamma –> negatively skewed distribution –> VaR will be underestimated if using linear approximation

TRUE/ FALSE

Answer 5

TRUE

Question 6

Which of the following are determinants for the accuracy of linear approximation?
A) The volatility of the underlying asset
B) The horizon for the VaR calculation - the shorter, the better
C) The probability level for VaR - 95% is better than 99%: the more out in the tail, the poorer it works
D) The degree of non-linearity of the option

Answer 6

All options are correct

Question 7

Delta-hedged portfolio gives a zero-delta, which implies that the linear approximation results in a VaR of zero. Thus, It simply does not make sense to use the linear approximation for a delta-hedged portfolio
TRUE/ FALSE

Answer 7

TRUE

Question 8

Which of the following are methods by which one can take into account non-linearity when calculating VaR for options?
A) Cornish-Fisher expansion
B) Monte Carlo simulation
C) Linear approximation

Answer 8

A) Cornish-Fisher expansion
B) Monte Carlo simulation

Question 9

The quadratic approximation method is an extension of linear approximation, and tends to be more accurate since it takes ______ into account
Fill in the blank.

A) convextiy/ curvature of the option value relation with changes in the underlying’s value
B) time varying volatility
C) exponentially decreasing weights of observations

Answer 9

A) convextiy/ curvature of the option value relation with changes in the underlying’s value