Learning Objectives: Describe and calculate VaR for linear derivatives. Describe the limitations of the delta-normal method. Explain the Monte Carlo simulation method for computing VaR and ES and identify its strengths and weaknesses. Describe the implications of correlation breakdown for a VaR or ES analysis. Describe worst-case scenario analysis and compare it to VaR
24.4.1 Following a notable surge in the volatility of SONOS INC shares, Julien Garg, a portfolio manager, opts to enlarge his position by purchasing a single contract (250 options) of at-the-money call options. For every $1 increase in the stock price, the call option's price is expected to increase by $0.50. With SONOS INC shares priced at $371 and the daily VaR of the underlying at 95% confidence recorded as $37.41, what is the daily 95% VAR of the options position utilizing the delta-normal method?
a. $5,676.25
b. $4,676.25
c. $9,352.50
d. $46,375.00
24.4.2 At $7.00, the Δ is 0.70. At $4.00, the vertical distance from the plot to the straight-line tangent is equal to $0.56; note this distance is approximated by 0.5*gamma*ΔS^2, which is the second term in the Taylor series. If the stock price drops from $7.00 to $4.00, what is the approximate (Delta + Gamma) change in the option price?
View attachment 4196
a. -$2.10
b. -$1.54
c. -$2.66
d. $3.80
24.4.3 A risk analyst is using the EWMA model to build a daily update of correlation and covariance rates. The two variables are random and are called X and Y. The most recent covariance weight (aka, lambda in the EWMA model) from day n-1 is 0.7. The correlation between X and Y on day N-1 is estimated to be 0.55. X and Y had estimated standard deviations of 0.015 and 0.017 with percentage changes of 3% and 4%, respectively, on day N-1. The updated covariance between X and Y on day n is nearest to which of the following?
a. 1.48 × 10^(-4)
b. 4.58 × 10^(-4)
c. 1.18437
d. 0.04581
Answers here:
24.4.1 Following a notable surge in the volatility of SONOS INC shares, Julien Garg, a portfolio manager, opts to enlarge his position by purchasing a single contract (250 options) of at-the-money call options. For every $1 increase in the stock price, the call option's price is expected to increase by $0.50. With SONOS INC shares priced at $371 and the daily VaR of the underlying at 95% confidence recorded as $37.41, what is the daily 95% VAR of the options position utilizing the delta-normal method?
a. $5,676.25
b. $4,676.25
c. $9,352.50
d. $46,375.00
24.4.2 At $7.00, the Δ is 0.70. At $4.00, the vertical distance from the plot to the straight-line tangent is equal to $0.56; note this distance is approximated by 0.5*gamma*ΔS^2, which is the second term in the Taylor series. If the stock price drops from $7.00 to $4.00, what is the approximate (Delta + Gamma) change in the option price?
View attachment 4196
a. -$2.10
b. -$1.54
c. -$2.66
d. $3.80
24.4.3 A risk analyst is using the EWMA model to build a daily update of correlation and covariance rates. The two variables are random and are called X and Y. The most recent covariance weight (aka, lambda in the EWMA model) from day n-1 is 0.7. The correlation between X and Y on day N-1 is estimated to be 0.55. X and Y had estimated standard deviations of 0.015 and 0.017 with percentage changes of 3% and 4%, respectively, on day N-1. The updated covariance between X and Y on day n is nearest to which of the following?
a. 1.48 × 10^(-4)
b. 4.58 × 10^(-4)
c. 1.18437
d. 0.04581
Answers here:
