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1

You can compute the implied volatility in terms of the Bachelier model. That is, compute the volatility parameter in the Bachelier that corresponds to the BS price.


0

Not sure if I am allowed to post them (or if you expect them to - because it may affect your own research) but; there have been some research done already on the Bachelier vs. BSM vs. other models. With regards to the negative price range, my opinion is that you simply should leave it out from the comparison. In addition to the RMS of the difference between ...


2

Buy MXN spot and then swap MXN spot with forward is equivalent to an outright forward in MXN. Outright forwards are one well established way of implementing the Carry Trade. Why they prefer to do it in 2 steps rather than one, I don't know.


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"Would you be able to explain the rationale behind this [buy spot...enter a FX swap where you sell spot and buy it back forward]?" Very few accounts want to take delivery of a spot position therefore they roll via the swap.


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At time $T_0$, the strike price becomes known and the option turns into a ``normal'' put option, i.e. \begin{align*} V(T_0,S_{T_0}) &= S_{T_0}e^{-r(T-T_0)}\Phi(-d_2)-S_{T_0}e^{-q(T-T_0)}\Phi(-d_1) \\ &= S_{T_0}\underbrace{\left(e^{-r(T-T_0)}\Phi(-d_2)-e^{-q(T-T_0)}\Phi(-d_1)\right),}_{=:p} \end{align*} where $p$ is indeed independent of the stock ...


1

The OpenGamma guide (https://quant.opengamma.io/Interest-Rate-Instruments-and-Market-Conventions.pdf) has info on both TONAR and TIBOR. It was published in 2013 so some info might now be out-of-date, but it's a useful starting point.


1

Just expand the term: \begin{align} \mathrm{E}(S_T) &= pS_o u + (1 - p)S_0 d \\ &= pS_o u - pS_0 d + S_0 d \\ &= pS_o (u - d) + S_0 d \end{align}


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