For a given:
Stock price ${\displaystyle S\,}$
Strike price ${\displaystyle K\,}$
Risk-free rate ${\displaystyle r\,}$
Annual dividend yield ${\displaystyle q\,}$
Time to maturity ${\displaystyle \tau =T-t\,}$ (represented as a unit-less fraction of one year),
Volatility ${\displaystyle \sigma \,}$
Vega $\mathcal {V}$
Vanna can (in my understanding) be computed from either of the 2 formula below:
rewritten in latex as
$$-e^{-qt}*\phi(d_1)*d_2/\sigma =\mathcal {V}/S*[1-(d_1/ (\sigma*sqrt(t))]$$
which solves into: $$ABC = ABC/100$$
or with the inputs given below, it solves into: $$ .03421= .0003421$$
which seems like it should be wrong.
Inputs I'm using to test are
Stock price ${\displaystyle S\,}$ = $16.31
Strike price ${\displaystyle K\,}$ = $15.00
Volatility ${\displaystyle \sigma \,}$ = 123.58%
Time to maturity ${\displaystyle \tau =T-t\,}$ = 19.319% of a year or 70.5151 days
Risk-free rate ${\displaystyle r\,}$ = .33%
Annual dividend yield ${\displaystyle q\,}$ = 0%
Vega $\mathcal {V}$ = .026109 (based on my calculations)
Any ideas on what the difference is?
God bless,
NN
