# Tag Info

2

Time is expressed in fractions of year in the GBM formula. Therefore, $T=1$ year and $\Delta t = 1/m$. Considered that you have $253$ observations, I would use $m = 253$, so the second option as Drew suggested. In general, using 253 or 365 days in a year depends on how you consider reality: do you think that when markets are closed (i.e. weekends) the price ...

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The second one will be the best estimate. Also, a smaller timestep usually corresponds to a smaller bias. But I agree, the answer is not obvious. You should be careful about increasing $T$ though, because for negative drifts there is a threshold value ($2\mu + \sigma^2 < 0$) beyond which the variance of the price process stops increasing. It's an ...

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I would suggest you to add spreads to the implied hazard rates, spreads that you regress on the macroeconomic factors. Then you stress by calculating the spreads corresponding to the stressed factors.

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It seems that implicitly you have a multi-objective optimization in mind, hence of course it may happen that you are not able to achieve all the objectives simultaneously. Let's say that output of a more general model is $f(x,y)$ so that the output of the first model is $f(x,0) = f_0(x)$. Denoting market prices by $m_k$ which in your case means $m_1 = A$ and ...

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The most used equity volatility models in the industry are the Black-Scholes model (including its time dependent version) and the local volatility model. It always come along with stochastic rates, discrete dividends and quanto effects (a must-have when pricing even simple payoffs) so the calibration/pricing process is much more involved than what you might ...

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Given that you have swap rates and Cap prices (ATM, I assume), you can back out the IVs for the time periods using by bootstrapping. Strictly speaking, you would need Caplet prices for the given strikes. In such a case, You would look at the shortest dated cap and (assume) it is made up of only one caplet. You can then use black's formula and back out ...

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Thanks to my research leader, I found what I missed. $V_{0,1}$ is vol of swaption that matures at $T_0$ which is not 0 (as I thought), rather it is maturity of the first libor. So $V_{0,1}$ is the closest available point on market. And now this is all clear with table on page 323 in section 7.4. $V_{0,2}$ is realy vol of swaption that matures at $T_0$=1y ...

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