Core of v3.0 Daily Premium The Daily Premium shall be paid between short and long options as followings:
TO Earn with Short Option
For example, if there are 10 options short overall and someone is long only 3 of them. In that case, 7 are Balanced by LP on Uniswap.
P r e m i u m / S h o r t O p t i o n = ( 7 ∗ F e e U n i s w a p + 3 ∗ P r e m i u m l o n g ) 10 Premium / Short Option = \frac{(7*Fee_{Uniswap} + 3 * Premium_{long})}{10} P re mi u m / S h or tOpt i o n = 10 ( 7 ∗ F e e U ni s w a p + 3 ∗ P re mi u m l o n g ) Long Option with Paying Premium
It is calculated from the followings:
(Note:The following may require mathematical verification.)
I n t e r e s t i n g R a t e Interesting Rate I n t eres t in g R a t e Aave
P r e m i u m T h e o r e t i c a l Premium_{Theoretical} P re mi u m T h eore t i c a l F e e U n i s w a p Fee_{Uniswap} F e e U ni s w a p
P r e m i u m l o n g = T i m e E l a p s e d ∗ I n t e r e s t i n g R a t e ∗ V a l u e L P T + P r e m i u m T h e o r e t i c a l t w h e r e , V a l u e L P T = 2 L x − L p a − L x p b ・・・ ( 1 ) L = x y , P a = 1.000 1 l o w e r T i c k , P b = 1.000 1 u p p e r T i c k , \begin{align*}
Premium_{long} &=Time_{Elapsed} * \frac{InterestingRate*Value_{LPT}+Premium_{Theoretical}}{t}&\\
&where,Value_{LPT}= 2L\sqrt{x}-L\sqrt{p_a}-L\frac{x}{\sqrt{p_b}}・・・(1)&\\
&L = \sqrt{xy}, P_a =1.0001^{lowerTick} , P_b=1.0001^{upperTick}, &\\
\end{align*} P re mi u m l o n g = T im e El a p se d ∗ t I n t eres t in g R a t e ∗ Va l u e L PT + P re mi u m T h eore t i c a l w h ere , Va l u e L PT = 2 L x − L p a − L p b x ・・・ ( 1 ) L = x y , P a = 1.000 1 l o w er T i c k , P b = 1.000 1 u pp er T i c k , I n t e r e s t i n g R a t e InterestingRate I n t eres t in g R a t e The determination of interest rates refers to the Aave Protocol approach. It is basically proportional to the Utilization Ratio, but the slope becomes steeper above a certain Utilization Ratio.
I n t e r e s t i n g R a t e = I n t e r e s t i n g R a t e b a s e + U U o p t i m a l S l o p e 1 ( U < U o p t i m a l ) = I n t e r e s t i n g R a t e b a s e + S l o p e 1 + U − U o p t i m a l 1 − U o p t i m a l S l o p e 2 ( U ≥ U o p t i m a l ) w h e r e , U = U t i l i z a t i o n R a t i o \begin{align*}
InterestingRate&=InterestingRate_{base}+\frac{U}{U_{optimal}}Slope_1\ (U<U_{optimal})&\\
&=InterestingRate_{base}+Slope_1+\frac{U-U_{optimal}}{1-U_{optimal}}Slope_2\ (U≥U_{optimal})&\\
&where, U= UtilizationRatio&\\
\end{align*} I n t eres t in g R a t e = I n t eres t in g R a t e ba se + U o pt ima l U Sl o p e 1 ( U < U o pt ima l ) = I n t eres t in g R a t e ba se + Sl o p e 1 + 1 − U o pt ima l U − U o pt ima l Sl o p e 2 ( U ≥ U o pt ima l ) w h ere , U = U t i l i z a t i o n R a t i o P r e m i u m T h e o r e t i c a l Premium_{Theoretical} P re mi u m T h eore t i c a l ( 1 ) (1) ( 1 ) x ∗ ( 1 − e − σ 2 8 ) ≓ x σ 2 8 \sqrt{x}*(1-e^{-\frac{\sigma^2}{8}})\risingdotseq \frac{\sqrt{x}\sigma^2}{8} x ∗ ( 1 − e − 8 σ 2 ) ≓ 8 x σ 2 discussion , V a l u e L P T / L Value_{LPT}/L Va l u e L PT / L
v L = 2 x − P a − x P b P r e m i u m T h e o r e t i c a l / L = 2 ∗ x σ 2 8 = x σ 2 4 w h e r e , L = x y , P a = 1.000 1 l o w e r T i c k , P b = 1.000 1 u p p e r T i c k \begin{align*}
&\frac{v}{L}=2\sqrt{x}-\sqrt{P_a}-\frac{x}{\sqrt{P_b}}&\\
&Premium_{Theoretical} / L =2 * \frac{\sqrt{x} \sigma^2}{8}=\frac{\sqrt{x}\sigma^2}{4}&\\
&where, L = \sqrt{xy}, P_a =1.0001^{lowerTick} , P_b=1.0001^{upperTick}&\\
\end{align*}
L v = 2 x − P a − P b x P re mi u m T h eore t i c a l / L = 2 ∗ 8 x σ 2 = 4 x σ 2 w h ere , L = x y , P a = 1.000 1 l o w er T i c k , P b = 1.000 1 u pp er T i c k σ 2 = V a r i a n c e L \sigma^2=Variance_{L} σ 2 = Va r ian c e L F e e U n i s a w p W h o l e Fee_{UnisawpWhole} F e e U ni s a wp Wh o l e F e e L P T Fee_{LPT} F e e L PT
V a r i a n c e L = V a r i a n c e A a v e P r o t o t o c o l A p p r o a c h ∗ F e e L P T F e e U n i s a w p W h o l e V a r i a n c e A a v e P r o t o t o c o l A p p r o a c h = B a s e V a r i a n c e + U U o p t i m a l S l o p e 1 ( U < U o p t i m a l ) V a r i a n c e A a v e P r o t o t o c o l A p p r o a c h = B a s e V a r i a n c e + S l o p e 1 + U − U o p t i m a l 1 − U o p t i m a l S l o p e 2 ( U ≥ U o p t i m a l ) w h e r e , U = U t i l i z a t i o n R a t i o
\begin{align*}
&Variance_{L}=Variance_{AavePrototocolApproach}*\frac{Fee_{LPT}}{Fee_{UnisawpWhole}}&\\
&Variance_{AavePrototocolApproach} = BaseVariance+\frac{U}{U_{optimal}}Slope_1\ (U<U_{optimal}) &\\
& Variance_{AavePrototocolApproach}= BaseVariance +Slope_1+\frac{U-U_{optimal}}{1-U_{optimal}}Slope_2\ (U≥U_{optimal}) &\\
&where, U= UtilizationRatio&\\
\end{align*} Va r ian c e L = Va r ian c e A a v e P ro t o t oco l A pp ro a c h ∗ F e e U ni s a wp Wh o l e F e e L PT Va r ian c e A a v e P ro t o t oco l A pp ro a c h = B a se Va r ian ce + U o pt ima l U Sl o p e 1 ( U < U o pt ima l ) Va r ian c e A a v e P ro t o t oco l A pp ro a c h = B a se Va r ian ce + Sl o p e 1 + 1 − U o pt ima l U − U o pt ima l Sl o p e 2 ( U ≥ U o pt ima l ) w h ere , U = U t i l i z a t i o n R a t i o 