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Vega Given Delta

The mapping $\Delta\mapsto v_{\sigma}=x e^{-r_f\tau}\sqrt{\tau}n({\cal N}^{-1} (e^{r_f\tau}\Delta))$ is important for trading vanilla options. Observe that this function does not depend on $r_d$ or $\sigma$, just on $r_f$. Quoting vega in % foreign will additionally remove the spot dependence. This means that for a moderately stable foreign termstructure curve, traders will be able to use a moderately stable vega matrix. I.e. for $r_f=3\%$ the vega matrix looks like this.

Mat/$\Delta$ 50% 45% 40% 35% 30% 25% 20% 15% 10% 5%
1D 2 2 2 2 2 2 1 1 1 1
1W 6 5 5 5 5 4 4 3 2 1
1W 8 8 8 7 7 6 5 5 3 2
1M 11 11 11 11 10 9 8 7 5 3
2M 16 16 16 15 14 13 11 9 7 4
3M 20 20 19 18 17 16 14 12 9 5
6M 28 28 27 26 24 22 20 16 12 7
9M 34 34 33 32 30 27 24 20 15 9
1Y 39 39 38 36 34 31 28 23 17 10
2Y 53 53 52 50 48 44 39 32 24 14
3Y 63 63 62 60 57 53 47 39 30 18


next up previous
Next: copyright notice Up: Retrieving the Arguments Previous: Volatility Given Delta

2000-06-11
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