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strategy: bollmaker: sensitivity factor of BB width ratio

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This commit is contained in:
Raphanus Lo 2022-08-30 22:39:03 +08:00
parent c8f3dae34a
commit 0b6cc6d3cd
2 changed files with 42 additions and 22 deletions
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5
config/bollmaker.yaml
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@ -98,6 +98,11 @@ exchangeStrategies:
# # - To ask spread, the higher neutral band get greater ratio
# # - To bid spread, the lower neutral band get greater ratio
# # The weighted ratio always positive, and may be greater than 1 if neutral band is wider than default band.
#
# # Sensitivity factor of the weighting function: 1 / (1 + exp(-(x - bd_mid) * sensitivity / (bd_upper - bd_lower)))
# # A positive number. The greater factor, the sharper weighting function. Default set to 1.0 .
# sensitivity: 1.0
#
# askSpreadScale:
# byPercentage:
# # exp means we want to use exponential scale, you can replace "exp" with "linear" for linear scale

59
pkg/strategy/bollmaker/dynamic_spread.go
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@ -153,6 +153,10 @@ type DynamicSpreadBollWidthRatioSettings struct {
// BidSpreadScale is used to define the bid spread range with the given percentage.
BidSpreadScale *bbgo.PercentageScale `json:"bidSpreadScale"`
// Sensitivity factor of the weighting function: 1 / (1 + exp(-(x - mid) * sensitivity / width))
// A positive number. The greater factor, the sharper weighting function. Default set to 1.0 .
Sensitivity float64 `json:"sensitivity"`
neutralBoll *indicator.BOLL
defaultBoll *indicator.BOLL
}
@ -160,6 +164,9 @@ type DynamicSpreadBollWidthRatioSettings struct {
func (ds *DynamicSpreadBollWidthRatioSettings) initialize(neutralBoll, defaultBoll *indicator.BOLL) {
ds.neutralBoll = neutralBoll
ds.defaultBoll = defaultBoll
if ds.Sensitivity <= 0. {
ds.Sensitivity = 1.
}
}
func (ds *DynamicSpreadBollWidthRatioSettings) getAskSpread() (askSpread float64, err error) {
@ -187,40 +194,48 @@ func (ds *DynamicSpreadBollWidthRatioSettings) getWeightedBBWidthRatio(positiveS
//
// Given the default band: moving average default_BB_mid, band from default_BB_lower to default_BB_upper.
// And the neutral band: from neutral_BB_lower to neutral_BB_upper.
// And a sensitivity factor alpha, which is a positive constant.
//
// width of default BB w = default_BB_upper - default_BB_lower
//
// 1 x - default_BB_mid
// sigmoid weighting function f(y) = ------------- where y = --------------------
// 1 + exp(-y) default_BB_width
// 1 + exp(-y) w / alpha
// Set the sigmoid weighting function:
// - to ask spread, the weighting density function d_weight(x) is sigmoid((x - default_BB_mid) / (default_BB_upper - default_BB_lower))
// - to bid spread, the weighting density function d_weight(x) is sigmoid((default_BB_mid - x) / (default_BB_upper - default_BB_lower))
// - To ask spread, the weighting density function d_weight(x) is sigmoid((x - default_BB_mid) / (w / alpha))
// - To bid spread, the weighting density function d_weight(x) is sigmoid((default_BB_mid - x) / (w / alpha))
// - The higher sensitivity factor alpha, the sharper weighting function.
//
// Then calculate the weighted band width ratio by taking integral of d_weight(x) from bx_lower to bx_upper:
// infinite integral of ask spread sigmoid weighting density function F(y) = ln(1 + exp(y))
// infinite integral of bid spread sigmoid weighting density function F(y) = y - ln(1 + exp(y))
// Then calculate the weighted band width ratio by taking integral of d_weight(x) from neutral_BB_lower to neutral_BB_upper:
// infinite integral of ask spread sigmoid weighting density function F(x) = (w / alpha) * ln(exp(x / (w / alpha)) + exp(default_BB_mid / (w / alpha)))
// infinite integral of bid spread sigmoid weighting density function F(x) = x - (w / alpha) * ln(exp(x / (w / alpha)) + exp(default_BB_mid / (w / alpha)))
// Note that we've rescaled the sigmoid function to fit default BB,
// the weighted default BB width is always calculated by integral(f of y from -1 to 1) = F(1) - F(-1)
// F(y_upper) - F(y_lower) F(y_upper) - F(y_lower)
// weighted ratio = ------------------------- = -------------------------
// F(1) - F(-1) 1
// where y_upper = (neutral_BB_upper - default_BB_mid) / default_BB_width
// y_lower = (neutral_BB_lower - default_BB_mid) / default_BB_width
// the weighted default BB width is always calculated by integral(f of x from default_BB_lower to default_BB_upper)
// F(neutral_BB_upper) - F(neutral_BB_lower)
// weighted ratio = -------------------------------------------
// F(default_BB_upper) - F(default_BB_lower)
// - The wider neutral band get greater ratio
// - To ask spread, the higher neutral band get greater ratio
// - To bid spread, the lower neutral band get greater ratio
defaultMid := ds.defaultBoll.SMA.Last()
defaultWidth := ds.defaultBoll.UpBand.Last() - ds.defaultBoll.DownBand.Last()
yUpper := (ds.neutralBoll.UpBand.Last() - defaultMid) / defaultWidth
yLower := (ds.neutralBoll.DownBand.Last() - defaultMid) / defaultWidth
var weightedUpper, weightedLower float64
defaultUpper := ds.defaultBoll.UpBand.Last()
defaultLower := ds.defaultBoll.DownBand.Last()
defaultWidth := defaultUpper - defaultLower
neutralUpper := ds.neutralBoll.UpBand.Last()
neutralLower := ds.neutralBoll.DownBand.Last()
factor := defaultWidth / ds.Sensitivity
var weightedUpper, weightedLower, weightedDivUpper, weightedDivLower float64
if positiveSigmoid {
weightedUpper = math.Log(1 + math.Pow(math.E, yUpper))
weightedLower = math.Log(1 + math.Pow(math.E, yLower))
weightedUpper = factor * math.Log(math.Exp(neutralUpper/factor)+math.Exp(defaultMid/factor))
weightedLower = factor * math.Log(math.Exp(neutralLower/factor)+math.Exp(defaultMid/factor))
weightedDivUpper = factor * math.Log(math.Exp(defaultUpper/factor)+math.Exp(defaultMid/factor))
weightedDivLower = factor * math.Log(math.Exp(defaultLower/factor)+math.Exp(defaultMid/factor))
} else {
weightedUpper = yUpper - math.Log(1+math.Pow(math.E, yUpper))
weightedLower = yLower - math.Log(1+math.Pow(math.E, yLower))
weightedUpper = neutralUpper - factor*math.Log(math.Exp(neutralUpper/factor)+math.Exp(defaultMid/factor))
weightedLower = neutralLower - factor*math.Log(math.Exp(neutralLower/factor)+math.Exp(defaultMid/factor))
weightedDivUpper = defaultUpper - factor*math.Log(math.Exp(defaultUpper/factor)+math.Exp(defaultMid/factor))
weightedDivLower = defaultLower - factor*math.Log(math.Exp(defaultLower/factor)+math.Exp(defaultMid/factor))
}
// The weighted ratio always positive, and may be greater than 1 if neutral band is wider than default band.
return (weightedUpper - weightedLower) / 1.
return (weightedUpper - weightedLower) / (weightedDivUpper - weightedDivLower)
}