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### Estimate Options Delta By Hand [duplicate]

Underlying = 100 K = 90 1 year Put at K is trading 5. What's the approximate delta of the put?
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### How can the implied volatility be calculated?

We all know if you back out of the B.S. option pricing model you can solve for what the option is "implying" about the underlyings volatility. Is there a simple, closed form, formula deriving Implied ...
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What is the fastest way to numerically compute Black-Scholes-Merton option prices? I'm trying to find fastest and still precise method. Currently I'm using numerical approximation of Normal cdf with ...
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I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it. If you have an European ...
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### At-The-Money-Forward option approximation

Given that the Black-Scholes formula for a European Call is given by: $$C(S,t)=Se^{-D(T-t)}N(d_1)-Ke^{-r(T-t)}N(d_2)$$ $S$ is stock price, $K$ is strike price An At-The-Money-Forward option is ...
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### BS and delta hedging questions

I have two related questions concerning Black Scholes and delta hedging. I thought about this two questions, but I could not come up with an answer, so maybe you guys & girls can help me: If an ...
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### European option Vega with respect to expiry and implied volatility

I was told that the Vega of an European option always increases when its time to expiry increases (all else equal). I found this confusing and potentially wrong, but there doesn't seem to be relevant ...
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### at-the-money short term straddle and the implied vol

Here is a passage from "Advanced Equity Derivatives: Volatility and Correlation" by Sebastien Bossu, Wiley (2014). We see the prox $\beta_0,$ it seems to use the approximation that ...