Baran

 

37、If a 1-day 95 percent VAR is $5 million, the 250-day 99 percent VAR level would be closest to:

A) $55.89 million.

B) $83.84 million.

C) $111.79 million.

D) $21.00 million.

Baran

 

The correct answer is C

 

First it is necessary to adjust for confidence levels (2.326/1.645), then by days (√250). In this case, ($5 million)(2.326/1.645)(√250) = $111.79 million.

Baran

 

38、The relationship between a three month call option and its underlying stock are presented in the following table.

Volatility: σ            = 15.0% Risk-free rate        = 6.0% Exercise price (X) = 24 Time to maturity    = 3 months S                          = $25.00 C                          = $1.60
Stock Price, S	$21.00	$22.00	$23.00	$24.00	$24.75	$25.00
Value of Call, C	$0.04	$0.15	$0.42	$0.91	$1.41	$1.60
Percentage Decrease in S	–16.00%	–12.00%	–8.00%	–4.00%	–1.00%
Percentage Decrease in C	–97.46%	–90.39%	–73.55%	–43.37%	–11.92%
Delta (ΔC%/ΔS%)	6.09	7.53	9.19	10.84	11.92

Using the linear derivative VAR method and the information in the above table, what is a five percent VAR for the call option’s weekly return?

A) 10.8%.

B) 40.9%.

C) 15.8%.

D) 21.3%.

Baran

 

The correct answer is B

The weekly volatility is approximately equal to 2.08 percent a week (). The 5 percent VAR for the stock price is equivalent to a one standard deviation move, or 1.65 for the normal curve. The 5 percent VAR of the underlying stock is 0 – 2.08%(1.65)= –3.432%. A one percent change in the stock price results in a 11.92 percent change in the call option value, therefore, the delta = 0.1192/0.01 = 11.92. For small moves, delta can be used to estimate the change in the derivative given the VAR for the underlying asset as follows: VARCall = ΔVARStock =11.92(3.432%) = 0.409 or 40.9%. In words, the 5 percent VAR implies there is a 5 percent probability that the call option value will decline by 40.9% or more.

Baran

 

Using the linear derivative VAR method and the information in the table, and assuming 255 trading days in a year, what is a 1-percent VAR for the call option’s daily return?

A) 11.9%.

B) 15.8%.

C) 43.4%.

D) 26.1%.

Baran

 

The correct answer is D

The daily volatility is approximately equal to 0.94 percent a dayThe 1 percent VAR for the stock price is equivalent to a two standard deviation move, or 2.33 for the normal curve. The 1 percent VAR of the underlying stock is 0 – 0.94%(2.33) = 2.19%. A one percent change in the stock price results in a 11.92 percent change in the call option value, therefore, the delta = 0.1192/0.01 = 11.92. For small moves, delta can be used to estimate the change in the derivative given the VAR for the underlying asset as follows: VAR_Call = ΔVAR_Stock = 11.92(2.19%) = 0.261 or 26.1%. In words, the 1 percent VAR implies there is a 1 percent probability that the call option value will decline by 26.1% or more.

Baran

 

39、The most important way in which the Monte Carlo approach to estimating operational VAR differs from the historical method and variance-covariance method is:

A) its heavy dependence on historical data.

B) it involves repeatedly shocking a model of risk data to produce a range of potential losses.

C) its computational simplicity. 

D) its inability to account for non-linear risk structures. 

Baran

 

The correct answer is B

 

The Monte Carlo approach uses simulation techniques, repeatedly shocking a model of loss data in order to produce a range of potential losses. It is more computationally intensive than either the historical or variance-covariance approaches. The model used can account for nonlinear risk structures and need not be limited by historical data.

Baran

 

40、The VaR measure obtained from simulating data based on assumptions concerning the return distributions is called:

A) Prospective VaR.

B) Stochastic VaR. 

C) Monte Carlo VaR.

D) Kurtotic VaR. 

Baran

 

The correct answer is C

Monte Carlo VaR uses data generated from a simulation procedure.