# Tag Info

4

please go to {drvd} BVOL Equity Implied Volatilities Calculations paper. Disclamer: I was working for Bloomberg, that is as far we disclosed.

3

Note that \begin{align*} E(K) &= E\big(\exp(\ln K) \big)\\ &=\exp\Big(E(\ln K) + \frac{1}{2}\sigma_k^2 \Big),\\ E(L) &= E\big(\exp(\ln L) \big)\\ &=\exp\Big(E(\ln L) + \frac{1}{2}\sigma_l^2 \Big),\\ E\Big(\frac{1}{P}\Big) &= E\big(\exp(-\ln P) \big)\\ &=\exp\Big(-E(\ln P) + \frac{1}{2}\sigma_p^2 \Big), \end{align*} and \begin{align*} ...

3

Options on interest rates futures in the listed markets are always traded 1-yield (100-yield) just like the futures which are traded 1-yield. So negative rates aren't an issue and its always black volatility. In the OTC market, both normal and black volatility are quoted, but the common practice is to use black volatility is what is way more frequently used....

2

If $S_t$ is stochastic process and follow geometric Brownian motion with following SDE: $$dS_t=\mu S_t dt + \sigma S_t dW_t$$ then $S_T$ follows lognormal distribution, such that: $$S_T|S_t \sim logN\left(lnS_t+ (\mu - \frac{\sigma^2}{2})(T-t), \quad \sigma^2(T-t)\right)$$ or $$lnS_T|S_t \sim N\left(lnS_t+ (\mu - \frac{\sigma^2}{2})(T-t), \quad \sigma^2(T-... 2 if they are stocks, this problem is called pricing a Margrabe option and it is generally solved by change of numeraire. Take S_2 to be the numeraire. Then the value of the option is$$ S_2(0) \mathbb{E}_{S_2}( (S_1(T)/S_2(T)-1)_+) where the expectation is taken in the measure that has S_1/S_2 as a martingale. Since it's a martingale and log-normal at ... 1 Since S_T = S_0 + \sigma W_T, \begin{align*} C &:= E\left((S_T-K)^+ \right)\\ &= E\left((S_0+\sigma W_T-K)^+ \right)\\ &=\int_{\frac{K-S_0}{\sigma \sqrt{T}}}^{\infty}(S_0+\sigma\sqrt{T} x-K) \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}dx\\ &=(S_0-K)\Phi\left(\frac{S_0-K}{\sigma \sqrt{T}}\right)+\frac{\sigma\sqrt{T}}{\sqrt{2\pi}}e^{-\frac{(S_0-K)... 1 In that case, the problem becomes a non-trivial stopping time problem. Consider a filtered probability space (\Omega, \mathcal{F}, \mathbb{P}) equipped with the natural filtration of a standard Brownian motion W_t^\mathbb{P}. Assuming a geometric Brownian motion for the underlying asset, one gets S_t = S_0 \exp\left((\mu-\frac{1}{2}\sigma^2)t + \...

1

The formula in your skew function is one of skew normal distribution. That distribution has a limit on skew parameter, while in the real world there is no such limit. From personal experience, few years ago I tried doing exactly what you described in your question. After comparing skew normal distribution on SPX with the real world, I concluded that there ...

1

This is a good question which I got stuck on as well. Suppose $X$ is lognormal defined as $X\sim \log \mathcal{N}(\mu, \sigma^2)$. With this notation we mean that if we write $X = e^Z$, then $Z$ follows a normal distribution with mean $\mu$ and variance $\sigma^2$. The mean and variance of $X$ are then $\mu_X = e^{\mu + \frac{1}{2}\sigma^2}$ and \$\sigma_X^...

1

Generally Bloomberg is very open with their methodologies. Look up the documentation as recommended above, and if you have further questions you can ask HELP HELP to put you in touch with someone on their quant development team for more details. As long as you are a paying subscriber it should be no problem.

Only top voted, non community-wiki answers of a minimum length are eligible