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.
The SVI model specifies the implied volatility curve as an expansion around log moneyness
IVSVI(k)=a+b(km)+c(km)2+d2\begin{align*} IV_{SVI}(k) = a + b \,(k-m) + c \sqrt{(k-m)^2 + d^2} \end{align*}
where we enforce the relation
b=cρ where ρ<1.b = c \rho \text{ where } |\rho| < 1.
The parameters
{a,ρ,c,d,m}\{a, \rho, c, d, m\}
are obtained by fitting this model to market-implied volatility quotes. A separate set of parameters is fitted for each expiration.
To get the benchmark price for an option with strike
and expiration
, we first calculate the log moneyness
k=log(K/St)k = \log{(K/S_{t})}
. We then consult the fitted curve associated with expiration
to get the implied volatility
σT,k=IVSVI,T(k).\sigma_{T,k} = IV_{SVI,T}(k).
The SVI benchmark price is then the BSM price of the option given
benchsvi(K,T)=pbsm(K,T,σT,k)\text{bench}_{svi}(K, T) = p_{bsm}(K, T, \sigma_{T,k})
In practice, the curves are refit at some frequency, and data cleaning needs to occur. Arrow's up-to-date fit frequency and data cleaning steps are maintained in a separate section we will post before launch.