Suppose we have a call option on a stock The stocks volatility is 020 the price of the stock is $10 theprice of the call is So25 the hedge ratio for the call is 030 and the holding period is 10 tradin
To calculate the "dollar" VaR for the call option at the 99% confidence level, we need to consider the following steps:
Step 1: Calculate the daily return volatility of the stock. Daily Return Volatility = Stock Volatility / √(252) Daily Return Volatility = 0.20 / √(252) Daily Return Volatility ≈ 0.0126
Step 2: Calculate the daily price change of the stock. Daily Price Change = Stock Price * Daily Return Volatility Daily Price Change = $10 * 0.0126 Daily Price Change ≈ $0.126
Step 3: Calculate the VaR for the call option. VaR = Hedge Ratio * Daily Price Change * Confidence Level VaR = 0.30 * $0.126 * 2.33 (99% confidence level one-sided) VaR ≈ $0.087
Therefore, the "dollar" VaR for the call option is approximately $0.087
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