Documentation
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Index ¶
- func ExpiryToInstrumentName(underlying shared.Underlying, expiry uint64, strike decimal.Decimal, ...) (name string)
- func GetAlternativeMinimum(spot float64, percent float64) float64
- func GetAmountOTM(spot float64, strike float64, isCall bool) (amount float64)
- func GetCallPrice(spot float64, strike float64, sigma float64, tau float64, rate float64) float64
- func GetDelta(isCall bool, spot float64, strike float64, sigma float64, tau float64, ...) float64
- func GetDeribitSigma(name string) (askSigma float64, bidSigma float64, markSigma float64, err error)
- func GetGamma(spot float64, strike float64, sigma float64, tau float64, rate float64) float64
- func GetInitialMargin(isBuy bool, spot float64, strike float64, sigma float64, tau float64, ...) (margin float64)
- func GetMarkPrice(spot float64, strike float64, sigma float64, tau float64, rate float64, ...) float64
- func GetProbabilityFactors(spot float64, strike float64, sigma float64, tau float64, rate float64) (float64, float64)
- func GetPutPrice(spot float64, strike float64, sigma float64, tau float64, rate float64) float64
- func GetRho(isCall bool, spot float64, strike float64, sigma float64, tau float64, ...) float64
- func GetSigmaByBisection(spot float64, strike float64, tau float64, rate float64, price float64, ...) (float64, error)
- func GetTheta(isCall bool, spot float64, strike float64, sigma float64, tau float64, ...) float64
- func GetVega(spot float64, strike float64, sigma float64, tau float64, rate float64) float64
- func InstrumentNameToID(name string) (uint64, error)
- type VolatilityManager
- func (manager *VolatilityManager) Backstop(strike decimal.Decimal) (float64, error)
- func (manager *VolatilityManager) FindClosestMoneyness(query float64) (index int)
- func (manager *VolatilityManager) FindClosestTau(query float64) (index int)
- func (manager *VolatilityManager) FindClosestTwoMoneyness(query float64) (int, int)
- func (manager *VolatilityManager) FindClosestTwoTau(query float64) (int, int)
- func (manager *VolatilityManager) Interpolate(moneyness float64, tau float64) float64
- func (manager *VolatilityManager) IsEqual(other *VolatilityManager) bool
- func (manager *VolatilityManager) Query(spot decimal.Decimal, strike decimal.Decimal, tauAnnualized float64) float64
- func (manager *VolatilityManager) Tau() uint64
- func (manager *VolatilityManager) TauAnnualized() float64
- func (manager *VolatilityManager) Update(spot decimal.Decimal, strike decimal.Decimal, sigma float64, weight float64) error
Constants ¶
This section is empty.
Variables ¶
This section is empty.
Functions ¶
func ExpiryToInstrumentName ¶
func ExpiryToInstrumentName( underlying shared.Underlying, expiry uint64, strike decimal.Decimal, isCall bool, ) (name string)
ExpiryToInstrumentName - Convert an expiry timestamp to instrument name Arguments:
expiry - Timestamp for expiry
Returns:
name - Name of the instrument on Deribit
func GetAlternativeMinimum ¶
GetAlternativeMinimum - Compute alternative minimum for 1 naked calls / puts.
func GetAmountOTM ¶
GetAmountOTM - Compute the amount out the money Cannot be a negative amount, if ITM, returns 0
func GetCallPrice ¶
func GetCallPrice( spot float64, strike float64, sigma float64, tau float64, rate float64, ) float64
GetCallPrice - Compute Black Scholes price of call Formula:
C = SN(d1)-Ke^{-rt}N(d2)
func GetDelta ¶
func GetDelta( isCall bool, spot float64, strike float64, sigma float64, tau float64, rate float64, ) float64
GetDelta - Compute delta of an option Formula:
delta = N(d1) if call delta = N(d1) - 1 if put
Notes:
https://en.wikipedia.org/wiki/Greeks_(finance)#Vega http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf
Arguments:
isCall - whether this is a call or a put spot - Spot price strike - Strike price sigma - Annualized implied volatility tau - Time to expiry (annualized) rate - The risk-free rate
Returns:
delta - The delta for an option
func GetDeribitSigma ¶
func GetDeribitSigma(name string) ( askSigma float64, bidSigma float64, markSigma float64, err error, )
GetDeribitSigma Get IV From Instrument ID Arguments:
ID - Instrument ID. See `InstrumentNameToID`
Returns:
askSigma - Implied volatility of the best ask price bidSigma - Implied volatility of the best bid price markSigma - Implied volatility of the best mark price err - Error. Nil if no error
func GetGamma ¶
GetGamma - Compute gamma of an option Formula:
gamma = N'(d1) / (sigma * spot * sqrt{tau})
Notes:
https://en.wikipedia.org/wiki/Greeks_(finance)#Vega http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf Call and put gamma are equal
Arguments:
spot - Spot price strike - Strike price sigma - Annualized implied volatility tau - Time to expiry (annualized) rate - The risk-free rate
Returns:
gamma - The gamma for an option
func GetInitialMargin ¶
func GetInitialMargin( isBuy bool, spot float64, strike float64, sigma float64, tau float64, rate float64, isCall bool, minMarginPerc float64, ) (margin float64)
GetInitialMargin - Compute the initial margin requirements Arguments:
isBuy - If the margin is for buyer or seller spot - Spot price strike - Strike price (not level) sigma - Annualized implied volatility tau - Time to expiry (annualiezd) rate - Risk-free interest rate isCall - If the option is a call or put minMarginPerc - Alternative minimum percentage
func GetMarkPrice ¶
func GetMarkPrice( spot float64, strike float64, sigma float64, tau float64, rate float64, isCall bool, ) float64
GetMarkPrice - Helper function to return call or put prices Arguments:
See `GetCallPrice` and `GetPutPrice` isCall - Boolean that is true if call else put
func GetProbabilityFactors ¶
func GetProbabilityFactors( spot float64, strike float64, sigma float64, tau float64, rate float64, ) (float64, float64)
GetProbabilityFactors - Compute d1 and d2 in Black Scholes Formula:
d1 = (log(S/K) + (r + sigma^2/2*tau)) / (sigma*sqrt(tau)) tau = T - t = time to maturity r = rate of return S = spot price K = strike price sigma = implied volatility
Arguments:
spot - Spot price strike - Strike price sigma - Annualized implied volatility tau - Time to expiry (annualized) rate - The risk-free rate
Returns:
d1 Probability factor one d2 Probability factor one
func GetPutPrice ¶
GetPutPrice - Compute Black Scholes price of put Formula:
P = Ke^{-rt}N(-d2)-SN(-d1)
func GetRho ¶
func GetRho( isCall bool, spot float64, strike float64, sigma float64, tau float64, rate float64, ) float64
GetRho - Compute rho of an option Notes:
https://en.wikipedia.org/wiki/Greeks_(finance)#Vega http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf
Arguments:
isCall - whether this is a call or a put spot - Spot price strike - Strike price sigma - Annualized implied volatility tau - Time to expiry (annualized) rate - The risk-free rate
Returns:
rho - The rho for an option
func GetSigmaByBisection ¶
func GetSigmaByBisection( spot float64, strike float64, tau float64, rate float64, price float64, isCall bool, maxIter int, tolerance float64, ) (float64, error)
GetSigmaByBisection - Solve for volatility from call price iteratively using Bisection method Resources:
https://en.wikipedia.org/wiki/Bisection_method
Notes:
We found this to be more stable and efficient than Newton Raphson which struggles with Vega -> 0 for strikes from the spot
Arguments:
isCall - boolean that is true if option is a call maxIter - Maximum number of iterations for convergence tolerance - Maximum discrepancy to define convergence
func GetTheta ¶
func GetTheta( isCall bool, spot float64, strike float64, sigma float64, tau float64, rate float64, ) float64
GetTheta - Compute rho of an option Notes:
https://en.wikipedia.org/wiki/Greeks_(finance)#Theta http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf
Arguments:
isCall - whether this is a call or a put spot - Spot price strike - Strike price sigma - Annualized implied volatility tau - Time to expiry (annualized) rate - The risk-free rate
Returns:
theta - The theta for an option
func GetVega ¶
GetVega - Compute vega of an option Formula:
vega = S * sqrt{tau} * N'(d1)
Notes:
https://en.wikipedia.org/wiki/Greeks_(finance)#Vega http://www.columbia.edu/~mh2078/FoundationsFE/BlackScholes.pdf Call and put vega are equal
Arguments:
spot - Spot price strike - Strike price sigma - Annualized implied volatility tau - Time to expiry (annualized) rate - The risk-free rate
Returns:
vega - The vega for an option
func InstrumentNameToID ¶
InstrumentNameToID - Get Instrument ID from Name using deribits API
Types ¶
type VolatilityManager ¶
type VolatilityManager struct {
// A single surface will be for a single underlying
Underlying shared.Underlying
// A single surface will be for a single expiry
Expiry uint64
// A surface is stored as N moneyness points
// And N points for time until expiry (or tau)
Surface [20][20]float64
// Moneyness points (sorted)
MoneynessPoints [20]float64
// Minimum moneyness
MinMoneyness float64
// Maximum moneyness
MaxMoneyness float64
// Time to expiry points (sorted & annualized)
TauPoints [20]float64
// Minimum time to expiry (annualized)
MinTau float64
// Max time to expiry (annualized)
MaxTau float64
}
VolatilityManager - A struct to store volatility surfaces
func CreateVolatilityManager ¶
func CreateVolatilityManager( underlying shared.Underlying, expiry uint64, initSigma float64, minMoneyness float64, maxMoneyness float64, ) (*VolatilityManager, error)
CreateVolatilityManager - Create `VolatilityManager` instance Arguments:
underlying - Address for the underlying asset expiry - Expiry timestamp since epoch; unique identifiser initSigma - Value to initialize the surface to (e.g. 0) minMoneyness - Minimum moneyness in surface maxMoneyness - Maximum moneyness in surface
func (*VolatilityManager) Backstop ¶
func (manager *VolatilityManager) Backstop(strike decimal.Decimal) (float64, error)
Backstop - Get deribits implied volatility so we don't end up serving something bad Arguments:
strike - Current strike price isCall - Whether option is a call or put. This doesn't matter that much
Returns:
sigma - Implied volatility (annualized) as used in Black-Scholes
func (*VolatilityManager) FindClosestMoneyness ¶
func (manager *VolatilityManager) FindClosestMoneyness(query float64) (index int)
FindClosestMoneyness - Find the closest index to a query value for moneyness
func (*VolatilityManager) FindClosestTau ¶
func (manager *VolatilityManager) FindClosestTau(query float64) (index int)
FindClosestTau - Find the closest index to a query value for time-to-expiry
func (*VolatilityManager) FindClosestTwoMoneyness ¶
func (manager *VolatilityManager) FindClosestTwoMoneyness(query float64) (int, int)
FindClosestTwoMoneyness - Find the index of the two closest moneyness Notes:
If query is exactly one of the moneyness points, then return the same index twice Otherwise return two indices of the closest neighbors
func (*VolatilityManager) FindClosestTwoTau ¶
func (manager *VolatilityManager) FindClosestTwoTau(query float64) (int, int)
FindClosestTwoTau - Find the index of the (two) closest times to expiries Notes:
If query is exactly one of the tau points, then return the same index twice Otherwise return two indices of the closest neighbors All tau terms below are annualilzed
func (*VolatilityManager) Interpolate ¶
func (manager *VolatilityManager) Interpolate( moneyness float64, tau float64, ) float64
Interpolate - Find the weighted average between the four nearest points Resources:
https://en.wikipedia.org/wiki/Bilinear_interpolation
func (*VolatilityManager) IsEqual ¶
func (manager *VolatilityManager) IsEqual(other *VolatilityManager) bool
IsEqual - Check if two volatility manager are equal
func (*VolatilityManager) Query ¶
func (manager *VolatilityManager) Query( spot decimal.Decimal, strike decimal.Decimal, tauAnnualized float64, ) float64
Query - Given a moneyness, and time until expiry, query for IV Arguments:
spot - Current spot price strike - Current strike price tauAnnualized - Current time to expiry in years useBackstop - If true, use Deribit's API as a backstop. This will update our own surface
Returns:
sigma - Implied volatility (annualized) as used in Black-Scholes
Notes:
The IV is computed as a weighted average over the four closest points
func (*VolatilityManager) Tau ¶
func (manager *VolatilityManager) Tau() uint64
Tau - Return the time to expiry If < 0, returns 0
func (*VolatilityManager) TauAnnualized ¶
func (manager *VolatilityManager) TauAnnualized() float64
TauAnnualized - Return time to expiry in years If < 0, returns 0
func (*VolatilityManager) Update ¶
func (manager *VolatilityManager) Update( spot decimal.Decimal, strike decimal.Decimal, sigma float64, weight float64, ) error
Update - Given a new order, update the surface Notes:
This will perform a local smoothing operation rather than just update a single point
Arguments:
underlying - Enum for underlying spot - Spot price in decimals strike - Strike price in decimals sigma - Implied volatility (annualized) as used in Black-Scholes weight - Weight to give new value. DEfault choice is 0.8
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