# Loss probability and VaR

I would like to estimate Value-at-Risk analytically and through delta-gamma aproximation. I don't know if my idea is ok, but i would like to build a portfolio of European option. Suppose that in this moment ($t=0$) investor buying a option with strike price $K=55$, current price of derivative is $S_0=50\$$, T=1 (year), r=5\% and \sigma=30%. I use Black-Scholes formulas so I can compute$$S_T=S_0 \exp \left( \left(r-\frac{1}{2}\sigma^2 \right)t+ \sigma\sqrt{T}Z \right),$$where Z \sim \mathcal{N}(0,1). Any ideas what next? In my opinion, I should use Black-Scholes formula to calculate the price of European call option, so the loss is$$L=-\Delta V=-(e^{-rT}C_T -C_0 ).$$But there is$d_1$and$d_2\$ and I don't know which price and time I should use.

Maybe someone explain it to me?

• Perhaps better asked at quant.stackexchange – Henry Jun 3 '16 at 14:50