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 kkk
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IVSVI(k)=a+b (k−m)+c(k−m)2+d2\begin{align*}   IV_{SVI}(k) = a + b \,(k-m) + c \sqrt{(k-m)^2 + d^2}  \end{align*}IVSVI​(k)=a+b(k−m)+c(k−m)2+d2​​
where we enforce the relation b=cρ where ∣ρ∣<1.b = c \rho \text{ where }  |\rho| < 1.b=cρ where ∣ρ∣<1.
 The parameters {a,ρ,c,d,m}\{a, \rho, c, d, m\}{a,ρ,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 KKK
 and expiration TTT
, we calculate the log moneyness k=log⁡K/Stk = \log{K/S_{t}}k=logK/St​
and consult the fitted curve associated with expiration TTT
 to get the implied volatility σT,k=IVSVI,T(k).\sigma_{T,k} = IV_{SVI,T}(k).σT,k​=IVSVI,T​(k).
The midpoint price is then the BSM price of the option given σT,k.\sigma_{T,k}.σT,k​.
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