# SVI

The Arrow Markets pricing engine fits SVI curves for implied volatility

For our benchmark prices, we use SVI models (so-called

*stochastic volatility-inspired*models), which provide tractable volatility curve parameterizations. Options market makers and traders commonly use these models. Here are some key references on the SVI approach: URL.The SVI model specifies the implied volatility curve as essentially a second-order expansion around log moneyness

$k$

$\begin{align*} IV_{SVI}(k) = a + b \,(k-m) + c \sqrt{(k-m)^2 + d^2} \end{align*}$

where we enforce the relation

$b = c \rho \text{ where } |\rho| < 1.$

The parameters $\{a, \rho, c, d, m\}$

are obtained by fitting this model to market-implied volatility quotes. In practice, this curve is refit at some frequency, and data cleaning needs to occur. Arrow's up-to-date fit frequency and data cleaning steps are maintained here: URL.A separate set of parameters is fitted for each expiration. To get the midpoint price for an option with strike

$K$

and expiration $T$

, we calculate the log moneyness $k = \log{K/S_{t}}$

and consult the fitted curve associated with expiration $T$

to get the implied volatility $\sigma_{T,k} = IV_{SVI,T}(k).$

The midpoint price is then the BSM price of the option given $\sigma_{T,k}.$

Last modified 1mo ago