Consider a European call option on a non-dividend paying stock, where the option has strike K = 100 and expiry T = 0.25, i.e. the option expires 3 months from now. The option is on a single share. The current price of the stock is 100, the riskfree interest rate is zero, and the option premium (i.e. price) is equal to the price given by the Black-Scholes formula using a volatility of 30% (where this is quoting volatility on an annualized basis). The expected return on the stock is 10% annually.
Let Π denote a portfolio consisting of a long position of 100, 000 of these options. At a confidence level of 95%, what is the 1-day Value-at-Risk of the portfolio Π?
What changes it instead of a long position I take it short?