eqAmericanOptionPricer
First introduced in version: 3.00.5
Syntax
eqAmericanOptionPricer(instrument, pricingDate, spot, discountCurve,
dividendCurve, volSurf, [setting], [model='BlackScholes'],
[method='Analytic'])
Details
Prices equity American options.
Parameters
instrument is an Instrument scalar/vector representing the equity American-style option contract(s) to be priced. For field requirements, see the Instrument Field Description.
pricingDate is a DATE scalar/vector specifying the pricing date(s).
spot is a numeric scalar/vector specifying the spot price(s).
discountCurve is a MktData scalar/vector of type IrYieldCurve representing the discount curve(s).
dividendCurve is a MktData scalar/vector of type DividendCurve.
volSurf is a MKTDATA scalar/vector of type VolatilitySurface representing the volatility surface.
setting (optional): a dictionary used to configure pricing outputs. It contains the following keys:
-
calcDelta: Boolean value indicating whether to calculate delta.
-
calcGamma: Boolean value indicating whether to calculate gamma.
-
calcVega: Boolean value indicating whether to calculate vega.
-
calcTheta: Boolean value indicating whether to calculate theta.
-
calcRhoIr: Boolean value indicating whether to calculate rhoIr.
-
calcRhoDividend: Boolean value indicating whether to calculate rhoDividend.
model (optional): a STRING scalar specifying the pricing model to use. Optional values:
-
"BlackScholes" (default): Black–Scholes model
-
"BAW": Barone-Adesi-Whaley formula
-
"AmericanBinomialTree": American binomial tree pricing model
method (optional): a STRING scalar specifying the calculation method. Optional values:
-
"Analytic" (default): Analytic method. Supported when model is BlackScholes or BAW.
-
"tree": Tree-based method. Supported when model is AmericanBinomialTree.
Returns
-
If setting is not specified: returns a DOUBLE scalar representing the net present value (NPV) of the option.
-
If setting is specified: returns a dictionary containing the NPV and the Greeks as specified in setting .
Examples
//Tencent Stock Option Pricing
referenceDate = 2026.02.13
// 1. Discount Curve (HKD Proxy - Simplified)
// Note: In actual production, HIBOR or OIS curve should be used
discountCurveDict = {
"mktDataType": "Curve",
"curveType": "IrYieldCurve",
"curveName": "HKD_RF",
"referenceDate": referenceDate,
"currency": "HKD",
"dayCountConvention": "Actual365",
"compounding": "Continuous",
"interpMethod": "Linear",
"extrapMethod": "Flat",
"dates": [
referenceDate + 1, referenceDate + 30, referenceDate + 90,
referenceDate + 180, referenceDate + 365
],
"values":[0.04, 0.04, 0.04, 0.04, 0.04]
}
discountCurve = parseMktData(discountCurveDict)
// 2. Data Preparation
spot = 532.0
termDates = [2026.02.20, 2026.02.26, 2026.03.30, 2026.04.29, 2026.05.28, 2026.06.29, 2026.09.29, 2026.12.30]
// Matrices are ensured to be dense (no zeros) by Python preprocessing
callPrices = matrix(
[102.240, 92.250, 82.270, 72.300, 62.360, 52.480, 42.710, 33.180, 24.170, 15.940, 9.000, 4.600, 2.130, 0.960, 0.370, 0.130, 0.050, 0.020, 0.010, 0.010],
[102.480, 92.530, 82.620, 72.750, 62.980, 53.350, 43.970, 35.430, 26.800, 19.250, 12.390, 8.200, 5.010, 3.030, 1.710, 0.940, 0.490, 0.250, 0.130, 0.070],
[105.350, 94.410, 84.930, 75.670, 66.690, 59.800, 50.880, 41.900, 34.080, 29.030, 23.600, 18.700, 14.700, 11.470, 8.880, 7.000, 5.320, 4.000, 2.990, 2.220],
[107.770, 96.450, 87.340, 78.510, 70.000, 61.880, 55.250, 46.990, 41.510, 34.530, 29.120, 24.370, 20.000, 16.900, 13.980, 11.410, 9.320, 7.760, 6.500, 5.320],
[109.270, 97.890, 89.050, 80.500, 72.290, 64.460, 57.080, 50.140, 45.000, 38.800, 33.130, 28.330, 24.220, 20.630, 17.580, 14.840, 12.540, 10.560, 8.850, 7.440],
[110.210, 98.620, 90.010, 81.730, 73.930, 66.430, 59.420, 52.930, 47.380, 42.070, 36.780, 32.290, 28.310, 24.260, 21.250, 18.380, 15.900, 13.610, 11.710, 10.000],
[115.610, 107.450, 96.760, 89.450, 82.610, 75.990, 69.870, 63.990, 58.540, 54.680, 49.600, 45.520, 40.960, 36.480, 33.520, 30.130, 27.110, 24.080, 21.680, 19.310],
[124.400, 116.880, 109.390, 99.560, 92.910, 89.300, 82.750, 77.110, 69.700, 66.470, 61.260, 56.670, 52.370, 48.220, 44.480, 40.740, 37.360, 34.350, 31.340, 28.570]
)
putPrices = matrix(
[0.010, 0.010, 0.030, 0.050, 0.110, 0.210, 0.460, 0.880, 1.750, 3.450, 6.570, 12.100, 19.820, 28.260, 38.190, 48.020, 58.000, 68.000, 78.000, 88.000],
[0.050, 0.090, 0.160, 0.290, 0.510, 0.900, 1.480, 2.390, 3.930, 6.260, 10.000, 15.350, 21.820, 30.000, 39.150, 48.500, 58.190, 68.000, 80.340, 88.000],
[0.560, 0.900, 1.410, 2.140, 3.160, 4.540, 6.360, 8.640, 11.390, 14.720, 18.710, 24.150, 30.180, 37.360, 44.600, 53.900, 61.660, 70.100, 80.340, 88.940],
[1.310, 1.960, 2.840, 4.000, 5.470, 7.000, 9.210, 11.950, 15.110, 18.850, 23.340, 28.440, 34.710, 41.520, 48.300, 57.590, 64.690, 73.180, 81.860, 90.830],
[2.860, 3.870, 5.230, 6.730, 8.460, 10.740, 13.480, 16.630, 20.240, 24.470, 29.080, 34.410, 40.600, 47.430, 54.580, 62.650, 70.440, 78.580, 86.920, 95.580],
[3.790, 5.140, 6.750, 8.680, 10.870, 13.690, 16.300, 19.650, 23.400, 27.920, 32.950, 38.280, 44.180, 50.760, 57.030, 65.510, 73.230, 78.580, 86.920, 97.520],
[8.130, 10.140, 12.540, 15.140, 17.750, 20.910, 24.310, 28.300, 32.340, 37.020, 42.040, 47.690, 53.480, 60.030, 66.160, 73.900, 80.970, 88.120, 95.810, 101.990],
[14.020, 15.890, 18.190, 21.170, 24.270, 27.800, 31.600, 35.490, 40.040, 44.910, 49.510, 54.850, 60.560, 67.000, 72.830, 78.360, 84.930, 94.000, 102.120, 109.690]
)
strikes = matrix(
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00],
[430.00, 440.00, 450.00, 460.00, 470.00, 480.00, 490.00, 500.00, 510.00, 520.00, 530.00, 540.00, 550.00, 560.00, 570.00, 580.00, 590.00, 600.00, 610.00, 620.00]
)
optionPrices = matrix(
[0.010, 0.010, 0.030, 0.050, 0.110, 0.210, 0.460, 0.880, 1.750, 3.450, 6.570, 4.600, 2.130, 0.960, 0.370, 0.130, 0.050, 0.020, 0.010, 0.010],
[0.050, 0.090, 0.160, 0.290, 0.510, 0.900, 1.480, 2.390, 3.930, 6.260, 10.000, 8.200, 5.010, 3.030, 1.710, 0.940, 0.490, 0.250, 0.130, 0.070],
[0.560, 0.900, 1.410, 2.140, 3.160, 4.540, 6.360, 8.640, 11.390, 14.720, 18.710, 18.700, 14.700, 11.470, 8.880, 7.000, 5.320, 4.000, 2.990, 2.220],
[1.310, 1.960, 2.840, 4.000, 5.470, 7.000, 9.210, 11.950, 15.110, 18.850, 23.340, 24.370, 20.000, 16.900, 13.980, 11.410, 9.320, 7.760, 6.500, 5.320],
[2.860, 3.870, 5.230, 6.730, 8.460, 10.740, 13.480, 16.630, 20.240, 24.470, 29.080, 28.330, 24.220, 20.630, 17.580, 14.840, 12.540, 10.560, 8.850, 7.440],
[3.790, 5.140, 6.750, 8.680, 10.870, 13.690, 16.300, 19.650, 23.400, 27.920, 32.950, 32.290, 28.310, 24.260, 21.250, 18.380, 15.900, 13.610, 11.710, 10.000],
[8.130, 10.140, 12.540, 15.140, 17.750, 20.910, 24.310, 28.300, 32.340, 37.020, 42.040, 45.520, 40.960, 36.480, 33.520, 30.130, 27.110, 24.080, 21.680, 19.310],
[14.020, 15.890, 18.190, 21.170, 24.270, 27.800, 31.600, 35.490, 40.040, 44.910, 49.510, 56.670, 52.370, 48.220, 44.480, 40.740, 37.360, 34.350, 31.340, 28.570]
)
payoffTypes = matrix(
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"],
["Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call", "Call"]
)
// 3. Build Dividend Curve (CallPutParity)
// Imply the dividend curve from option prices using Call-Put Parity
dividendCurve = eqDividendCurveBuilder(
referenceDate, termDates, "CallPutParity", ,
callPrices, putPrices, strikes, spot, discountCurve, "Actual365"
)
// 4. Build Volatility Surface (SVI Model)
// Build the volatility surface
surface = eqVolatilitySurfaceBuilder(
referenceDate,
termDates,
strikes,
optionPrices,
payoffTypes,
spot,
discountCurve,
dividendCurve,
"SVI"
)
// 5. Pricing Test: eqAmericanOptionPricer
optionDict = {
"productType": "Option",
"optionType": "AmericanOption",
"assetType": "EqAmericanOption",
"notionalCurrency": "HKD", // price currency
"notionalAmount": 1, // 份数
"strike": 530.0,
"maturity": 2026.02.24,
"payoffType": "Call",
"dayCountConvention": "Actual365",
"underlying": "00700.HK"
}
instrument = parseInstrument(optionDict)
res = eqAmericanOptionPricer(
instrument,
referenceDate,
spot,
discountCurve,
dividendCurve,
surface,
setting={"calcDelta": true, "calcGamma": true, "calcVega": true, "calcTheta": true, "calcRho": true, "calcRhoIr": true, "calcRhoDividend": true}
)
print(res)Instrument Field Description
| Field Name | Data Type | Description | Required |
|---|---|---|---|
| productType | STRING | Must be "Option". | Yes |
| optionType | STRING | Must be "AmericanOption". | Yes |
| assetType | STRING | Must be "EqAmericanOption". | Yes |
| notionalAmount | DOUBLE | Notional amount. | Yes |
| notionalCurrency | STRING | Notional currency. Default value: "CNY". | No |
| instrumentId | STRING | Instrument identifier. For example,
TCH250328C0040000 is interpreted as
follows: TCH = underlying (Tencent Holdings);
250328 = maturity date (March 28, 2025);
C = Call option; 0040000 =
strike price 400.00 HKD. |
No |
| direction | STRING | Trade direction: "Buy" (default) or "Sell". | No |
| maturity | DATE | Maturity date | Yes |
| strike | DOUBLE | Strike price. | Yes |
| payoffType | STRING | Payoff type: "Call" or "Put". | Yes |
| underlying | STRING | Underlying futures contract code, e.g., "TCH". | Yes |
| dayCountConvention | STRING | Day count convention. Valid values: "ActualActualISDA", "ActualActualISMA", "Actual365", "Actual360" | Yes |
| discountCurve | STRING | Discount curve name for pricing reference. The default value for RMB deposits is "CNY_FR_007". | No |
| dividendCurve | STRING | Dividend curve name used for pricing. | No |
Related Functions: parseInstrument, parseMktData, eqDividendCurveBuilder, eqVolatilitySurfaceBuilder