As the title implies, I’m having trouble figuring out which approach is best suited to solving for mid price IV, given only a bid price and ask price for an option (assume we also have all necessary parameters to solve for IV such as S, K, T, r, etc).
Approach A - avg the bid price and ask price, the solve for iv on this mid price (Im using Barone-Adesi Whaley to solve for IV).
Ex: Bid price = 1.80 Ask price = 1.90. Therefore Mid price = (1.80+1.90)/2 = 1.85. Then plug 1.85 into pricing model and solve for IV at the mid to get hypothetical Mid IV = .35
Approach B - solve for iv at the bid price and also solve for iv at the ask price, then avg those 2 results to get mid IV.
Ex: Bid price = 1.80 Ask price = 1.90. Plug 1.80 into a pricing model to get hypothetical IV of .3 and then do the same for 1.90 to get hypothetical IV of .4. Therefore Mid IV = (.3+.4)/2 = .35
As you can see, both approaches reach the same solution of .35 IV at the mid, however my issue lies in deep otm / itm options, where solving for IV on the bid price can lead to a convergence at 0 for the bid IV. This can cause the mid IV to be wildly different between approaches A and B. My goal is to eventually take these mid IVs and interpolate them using something like SVI, but im stuck on which approach is better, and im struggling to find literature that speaks about this issue specifically. Any advice is appreciated, and if you have alternative approaches that you think are superior, id be interested to learn more.
Approach A - avg the bid price and ask price, the solve for iv on this mid price (Im using Barone-Adesi Whaley to solve for IV).
Ex: Bid price = 1.80 Ask price = 1.90. Therefore Mid price = (1.80+1.90)/2 = 1.85. Then plug 1.85 into pricing model and solve for IV at the mid to get hypothetical Mid IV = .35
Approach B - solve for iv at the bid price and also solve for iv at the ask price, then avg those 2 results to get mid IV.
Ex: Bid price = 1.80 Ask price = 1.90. Plug 1.80 into a pricing model to get hypothetical IV of .3 and then do the same for 1.90 to get hypothetical IV of .4. Therefore Mid IV = (.3+.4)/2 = .35
As you can see, both approaches reach the same solution of .35 IV at the mid, however my issue lies in deep otm / itm options, where solving for IV on the bid price can lead to a convergence at 0 for the bid IV. This can cause the mid IV to be wildly different between approaches A and B. My goal is to eventually take these mid IVs and interpolate them using something like SVI, but im stuck on which approach is better, and im struggling to find literature that speaks about this issue specifically. Any advice is appreciated, and if you have alternative approaches that you think are superior, id be interested to learn more.