# Tagged Questions

Black-Scholes is a mathematical model used for pricing options.

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### Analytical solution for a modified Black-Scholes equation

Recently, a modified Black-Scholes equation was proposed (Zheng), namely Please consider the case when $$\sigma \left( S,t \right) =\sigma\,{S}^{k/2}$$ and with the European put option Using ...
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### Option writing optimal sell time

When selling options, e.g. a straddle I read often the optimal time for selling options is 30-40 days until expiration. For me intuitively the optimal time would be around one week until expiration ...
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### Why $N(d_1)$ and $N(d_2)$ are different in Black & Scholes

I'm struggling to understand the meaning of $d_1$ and $d_2$ in Black & Scholes formula and why they're different from each other. As per the formula, $$C = SN(d_1) - e^{-rT}XN(d_2)$$ which ...
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### Connection between implied volatily and implied probability

I am reading some lecture notes about Black-Scholes (BS) option pricing. Since the BS-formula is not supported by observed data because of the dependence of the implied volatility on the strik and ...
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