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Answer:
10-Day 99% VaR = 3.61
Explanation:
Data Given:
For First Option:
Stock Price = 50
Strike Price = 51
Volatility = 28% per annum
Time to maturity = 9 months
For Second Option:
Stock Price = 20
Strike Price = 19
Volatility = 25% per annum
Time to maturity = 12 months or 1 year
Risk Free Rate = 6% per annum
Correlation = 0.4
Find 10-day 99% VaR.
Solution:
First of all we need to refer the DerivaGem Model to dig out the change in price equation for both the options.
So, according to DerivaGem Model, We have following data:
For First Option:
Value = -5.413
Delta Value = -0.589
For Second Option:
Value = -1.014
Delta = -0.284
Change in Price = (Delta value of First Option x Stock Price)Y1 + (Delta value of the second option x Stock Price)Y2
Change in Price = (-0.589 x 50)Y1 + (-0.284 x 20)Y2
So, We will get the Change in Price Linear Equation for both the options.
Change in Price = -29.45Y1 -5.68Y2
Now, we have to calculate the Daily Volatility Percentage.
Formula:
Daily Volatility Percentage = Volatility/ Square root of number of days active in annum
Number of Days Active = 252
Volatility for First Option = 28%
Volatility for Second Option = 25%
Daily Volatility Percentage for First Option = 28%/
Daily Volatility Percentage for First Option = 0.0176
Similarly,
Daily Volatility Percentage for Second Option = 25%/
Daily Volatility Percentage for Second Option = 0.0157
Now, utilizing the above calculated data, we can find the one-day variance of change in price.
1-Day Variance =
Solving the above equation:
We get:
1-Day Variance = 0.2396
Now, we have to find the standard deviation of 1-Day Variance:
SD of 1-Day Variance =
SD of 1-Day Variance = 0.4895
So,
Now, in order to find the value of one day 99% VaR from the table, we have all the prerequisites.
So,
Value of One day 99% VaR from table = 2.33
But we need 10-Day 99% VaR.
So, number of days = 10
Hence,
10-Day 99% VaR =
10-Day 99% VaR = 3.61