60 lines
1.7 KiB
Python
60 lines
1.7 KiB
Python
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default_kappa= 2
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default_exit_tax = .02
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#value function for a given state (R,S)
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def invariant(R,S,kappa=default_kappa):
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return (S**kappa)/R
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#given a value function (parameterized by kappa)
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#and an invariant coeficient V0
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#return Supply S as a function of reserve R
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def reserve(S, V0, kappa=default_kappa):
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return (S**kappa)/V0
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#given a value function (parameterized by kappa)
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#and an invariant coeficient V0
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#return Supply S as a function of reserve R
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def supply(R, V0, kappa=default_kappa):
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return (V0*R)**(1/kappa)
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#given a value function (parameterized by kappa)
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#and an invariant coeficient V0
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#return a spot price P as a function of reserve R
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def spot_price(R, V0, kappa=default_kappa):
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return kappa*R**((kappa-1)/kappa)/V0**(1/kappa)
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#for a given state (R,S)
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#given a value function (parameterized by kappa)
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#and an invariant coeficient V0
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#deposit deltaR to Mint deltaS
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#with realized price deltaR/deltaS
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def mint(deltaR, R,S, V0, kappa=default_kappa):
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deltaS = (V0*(R+deltaR))**(1/kappa)-S
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realized_price = deltaR/deltaS
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return deltaS, realized_price
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#for a given state (R,S)
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#given a value function (parameterized by kappa)
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#and an invariant coeficient V0
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#burn deltaS to Withdraw deltaR
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#with realized price deltaR/deltaS
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def withdraw(deltaS, R,S, V0, kappa=default_kappa):
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deltaR = R-((S-deltaS)**kappa)/V0
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realized_price = deltaR/deltaS
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return deltaR, realized_price
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def withdraw_with_tax(deltaS, R,S, V0, exit_tax = default_exit_tax, kappa=default_kappa):
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deltaR = R-((S-deltaS)**kappa)/V0
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print(deltaR)
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quantity_taxed = exit_tax*deltaR
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quantity_recieved = (1-exit_tax)*deltaR
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realized_price = quantity_recieved/deltaS
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return quantity_recieved, quantity_taxed, realized_price
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