LP Hedge - @CK_2049

Bachelier Option Put

Replace "bk" with "asian" below to see liquidity fingerprint of an asian option whose vol is v/sqrt(3) of bk option. Counterintuitively, the asian option's delta & gamma are more sensitive than bk, but the asian option is a better payoff match at the moment of initiation.

Expression 74: "f" left parenthesis, "x" , right parenthesis equals "f" Subscript, "b" "k" , Baseline left parenthesis, "x" , right parenthesis

Uniswap Replication Greeks - Sum of all LP Greeks

Expression 86: "y" equals "K" left brace, "x" greater than 0 , right brace

Expression 87: "y" equals "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "K" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "K" , right parenthesis left brace, "x" greater than 0 , right brace

Payoff: left parenthesis, 0 , "K" , right parenthesis

Label:

equals

left parenthesis, 0 , 10 , right parenthesis

Hidden `\Pi`: `${\Pi}` left parenthesis, 0 , "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "K" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "K" , right parenthesis , right parenthesis

Label:

equals

left parenthesis, 0 , 9.9 9 0 5 1 9 4 5 , right parenthesis

Expression 90: left parenthesis, "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "K" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "K" , right parenthesis , right parenthesis less than "y" less than left parenthesis, "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "x" , right parenthesis , right parenthesis

Expression 91: left parenthesis, "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "K" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "K" , right parenthesis , right parenthesis greater than "y" greater than left parenthesis, "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "x" , right parenthesis , right parenthesis

Payoff Structure of European Option + Uniswap LP Replication

Expression 93: "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis plus "P" Subscript, "u" "t" , Baseline left parenthesis, "x" , right parenthesis

Payoff Structure of Asian Option + Uniswap LP Replication

Expression 95: "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis plus "P" Subscript, "a" , Baseline left parenthesis, "x" , right parenthesis

Payoff Structure of Bachelier Option + Uniswap LP Replication

Expression 97: "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis plus "P" Subscript, "B" , Baseline left parenthesis, "x" , right parenthesis

Expression 98: "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis equals total left parenthesis, "w" Subscript, "e" "i" "g" "h" "t" , Baseline left parenthesis, left brace, 0 less than "x" less than or equal to "p" Subscript, "a" "r" , Baseline : left parenthesis, StartFraction, 1 Over StartRoot, "p" Subscript, "a" "r" , Baseline , EndRoot , EndFraction minus StartFraction, 1 Over StartRoot, "p" Subscript, "b" "r" , Baseline , EndRoot , EndFraction , right parenthesis "L" , "p" Subscript, "a" "r" , Baseline less than "x" less than or equal to "p" Subscript, "b" "r" , Baseline : StartFraction, "L" Over StartRoot, "x" , EndRoot , EndFraction minus StartFraction, "L" Over StartRoot, "p" Subscript, "b" "r" , Baseline , EndRoot , EndFraction , "p" Subscript, "b" "r" , Baseline less than "x" : 0 , right brace times "x" plus left brace, 0 less than "x" less than or equal to "p" Subscript, "a" "r" , Baseline : 0 , "p" Subscript, "a" "r" , Baseline less than "x" less than or equal to "p" Subscript, "b" "r" , Baseline : "L" StartRoot, "x" , EndRoot minus "L" StartRoot, "p" Subscript, "a" "r" , Baseline , EndRoot , "p" Subscript, "b" "r" , Baseline less than "x" : left parenthesis, StartRoot, "p" Subscript, "b" "r" , Baseline , EndRoot minus StartRoot, "p" Subscript, "a" "r" , Baseline , EndRoot , right parenthesis "L" , right brace , right parenthesis , right parenthesis

Expression 99: negative "v" Subscript, "l" "p" "s" , Baseline left parenthesis, "x" , right parenthesis plus "K"

Expression 100: "v" Subscript, "l" "p" , Baseline left parenthesis, "x" , right parenthesis equals "w" Subscript, "e" "i" "g" "h" "t" , Baseline left parenthesis, left brace, 0 less than "x" less than or equal to "p" Subscript, "a" "r" , Baseline : left parenthesis, StartFraction, 1 Over StartRoot, "p" Subscript, "a" "r" , Baseline , EndRoot , EndFraction minus StartFraction, 1 Over StartRoot, "p" Subscript, "b" "r" , Baseline , EndRoot , EndFraction , right parenthesis "L" , "p" Subscript, "a" "r" , Baseline less than "x" less than or equal to "p" Subscript, "b" "r" , Baseline : StartFraction, "L" Over StartRoot, "x" , EndRoot , EndFraction minus StartFraction, "L" Over StartRoot, "p" Subscript, "b" "r" , Baseline , EndRoot , EndFraction , "p" Subscript, "b" "r" , Baseline less than "x" : 0 , right brace times "x" plus left brace, 0 less than "x" less than or equal to "p" Subscript, "a" "r" , Baseline : 0 , "p" Subscript, "a" "r" , Baseline less than "x" less than or equal to "p" Subscript, "b" "r" , Baseline : "L" StartRoot, "x" , EndRoot minus "L" StartRoot, "p" Subscript, "a" "r" , Baseline , EndRoot , "p" Subscript, "b" "r" , Baseline less than "x" : left parenthesis, StartRoot, "p" Subscript, "b" "r" , Baseline , EndRoot minus StartRoot, "p" Subscript, "a" "r" , Baseline , EndRoot , right parenthesis "L" , right brace , right parenthesis

100

Expression 101: "L" equals left brace, "p" Subscript, 0 , Baseline less than "p" Subscript, "a" , Baseline : StartFraction, "v" Subscript, "d" "e" "p" "o" "s" "i" "t" , Baseline Over "p" Subscript, 0 , Baseline left parenthesis, StartNestedFraction, 1 NestedOver StartRoot, "p" Subscript, "a" , Baseline , EndRoot , EndNestedFraction minus StartNestedFraction, 1 NestedOver StartRoot, "p" Subscript, "b" , Baseline , EndRoot , EndNestedFraction , right parenthesis , EndFraction , "p" Subscript, 0 , Baseline greater than "p" Subscript, "b" , Baseline : StartFraction, "v" Subscript, "d" "e" "p" "o" "s" "i" "t" , Baseline Over left parenthesis, StartRoot, "p" Subscript, "b" , Baseline , EndRoot minus StartRoot, "p" Subscript, "a" , Baseline , EndRoot , right parenthesis , EndFraction , StartFraction, "v" Subscript, "d" "e" "p" "o" "s" "i" "t" , Baseline Over "p" Subscript, 0 , Baseline left parenthesis, StartNestedFraction, 1 NestedOver StartRoot, "p" Subscript, 0 , Baseline , EndRoot , EndNestedFraction minus StartNestedFraction, 1 NestedOver StartRoot, "p" Subscript, "b" , Baseline , EndRoot , EndNestedFraction , right parenthesis plus StartRoot, "p" Subscript, 0 , Baseline , EndRoot minus StartRoot, "p" Subscript, "a" , Baseline , EndRoot , EndFraction , right brace

equals

22.6 4 5 1 4 2 4 0 7

101

Expression 102: "p" Subscript, 0 , Baseline equals "K"

equals

102

Riemann Integral

103

To-do derive Barrier (vertical spread synthetic)

133

134

Delta Subscript, "l" "p" , Baseline

4.8 3

Gamma Subscript, "l" "p" , Baseline

negative 3.5 8

"E" [ Theta Subscript, "l" "p" , Baseline

0.1 3

Payoff

sigma Subscript, "i" "v" , Baseline

: 27