Options Market Making Using ML
Options Market Making Using ML Circulum Vite LLC [email protected]
Financial Products -
Interest Rate -
-
Stocks -
-
No risk ( ? ) Valuation Relative Value
Derivatives ( Exchange Traded !!) -
-
Futures - Relative Value - Leverage Options - Relative Value - High Leverage - Hedging
Efficient Market Theory Cash(t) = Cash(T) / ( 1 + r ) Fut(t) = E(t)[ S(T) ] Opt(t) = E(t) [ { Max ( 0, S(T) - K ) } ] / ( 1 + r ) E(t) [ { Max ( 0, K - S(T) ) } ] / ( 1 + r )
Option Pricing C(t) = F ( T-t, K, r, Sig, St ) E [ dSt / St ] = r * dt Var [ dSt / St ] = Sigt * Sigt dSt/St = F ( E, V ) dC(t) = dCt/dSt * dSt + dCt/dSigt * dSigt Var ( dCt/dSigt * dSigt ) / Var ( dCt/dSt * dSt ) ?
REAL DATA Security FutStdev: 6.597439 MktIVStdevPerSec
Delta
Vega
Second/First
C0_O4
0.174
6.133
0.368
C0_O3
0.270
7.896
0.276
C0_O2
0.380
9.092
0.225
C0_O1
0.497
9.508
0.174
C0_A
0.608
9.131
0.138
C0_I1
0.707
8.142
0.223
C0_I2
0.788
6.814
0.192
C0_I3
0.854
5.333
0.152
C0_I4
0.907
3.783
0.128
P0_I2
-0.615
9.087
0.149
P0_I1
-0.497
9.508
0.160
P0_A
-0.388
9.145
0.164
P0_O1
-0.294
8.230
0.186
P0_O2
-0.217
7.025
0.233
P0_O3
-0.157
5.760
0.266
P0_O4
-0.113
4.574
0.359
Market Implied Vol Curves
Data Driven - ML Models 1) Current IV 2) MovingAvg IV 3) ATM IV + SpreadFunctions 4) Current Fut Stdev + ATM IV + SpreadFunctions 5) ExternalSourcesIV + CurrentFutStdev + ATM IV + Spread 6) PCA 7) Regression 8) LongTerm (SABR/GARCH/HESTON) + ShortTerm 9) Interpolation using cubic spline 10) Kalman Features a) StrikeDiff b) VolRatio c) StdevRatio d) PutCallParityRelationship
Premium and Risk Management FairPrice +/- (Premium / 2) : -
Premium Features: BidAskSpread, FuturesStdev, OptionsStdev, TurnOverRate, Delta ? Premium Optimization Function: Func ( Volume, Pnl, ? )
Delta Hedging: Trade is made up of two legs, second leg can be executed in Futures market, allows us to keep quoting in the market.
Financial Products -
Interest Rate -
-
Stocks -
-
No risk ( ? ) Valuation Relative Value
Derivatives ( Exchange Traded !!) -
-
Futures - Relative Value - Leverage Options - Relative Value - High Leverage - Hedging
Efficient Market Theory Cash(t) = Cash(T) / ( 1 + r ) Fut(t) = E(t)[ S(T) ] Opt(t) = E(t) [ { Max ( 0, S(T) - K ) } ] / ( 1 + r ) E(t) [ { Max ( 0, K - S(T) ) } ] / ( 1 + r )
Option Pricing C(t) = F ( T-t, K, r, Sig, St ) E [ dSt / St ] = r * dt Var [ dSt / St ] = Sigt * Sigt dSt/St = F ( E, V ) dC(t) = dCt/dSt * dSt + dCt/dSigt * dSigt Var ( dCt/dSigt * dSigt ) / Var ( dCt/dSt * dSt ) ?
REAL DATA Security FutStdev: 6.597439 MktIVStdevPerSec
Delta
Vega
Second/First
C0_O4
0.174
6.133
0.368
C0_O3
0.270
7.896
0.276
C0_O2
0.380
9.092
0.225
C0_O1
0.497
9.508
0.174
C0_A
0.608
9.131
0.138
C0_I1
0.707
8.142
0.223
C0_I2
0.788
6.814
0.192
C0_I3
0.854
5.333
0.152
C0_I4
0.907
3.783
0.128
P0_I2
-0.615
9.087
0.149
P0_I1
-0.497
9.508
0.160
P0_A
-0.388
9.145
0.164
P0_O1
-0.294
8.230
0.186
P0_O2
-0.217
7.025
0.233
P0_O3
-0.157
5.760
0.266
P0_O4
-0.113
4.574
0.359
Market Implied Vol Curves
Data Driven - ML Models 1) Current IV 2) MovingAvg IV 3) ATM IV + SpreadFunctions 4) Current Fut Stdev + ATM IV + SpreadFunctions 5) ExternalSourcesIV + CurrentFutStdev + ATM IV + Spread 6) PCA 7) Regression 8) LongTerm (SABR/GARCH/HESTON) + ShortTerm 9) Interpolation using cubic spline 10) Kalman Features a) StrikeDiff b) VolRatio c) StdevRatio d) PutCallParityRelationship
Premium and Risk Management FairPrice +/- (Premium / 2) : -
Premium Features: BidAskSpread, FuturesStdev, OptionsStdev, TurnOverRate, Delta ? Premium Optimization Function: Func ( Volume, Pnl, ? )
Delta Hedging: Trade is made up of two legs, second leg can be executed in Futures market, allows us to keep quoting in the market.
