eqDigitalOptionPricer

eqDigitalOptionPricer(instrument, pricingDate, spot, discountCurve, dividendCurve, volSurf, [setting], [model], [method])

Prices an equity digital option.

Currently, model only supports "BlackScholes" and method only supports "Analytic".

instrument: An INSTRUMENT scalar or vector indicating the equity digital option to be priced. See Instrument Field Description for field requirements.

pricingDate: A DATE scalar or vector specifying the pricing date.

spot: A numeric scalar or vector specifying the spot price.

discountCurve: A MKTDATA scalar or vector of type IrYieldCurve indicating the discount curve. This curve can be constructed with parseMktData.

dividendCurve: A MKTDATA scalar or vector of type DividendCurve indicating the dividend curve. This curve can be constructed with eqDividendCurveBuilder.

volSurf: A MKTDATA scalar or vector of type VolatilitySurface indicating the equity option volatility surface. This surface can be constructed with eqVolatilitySurfaceBuilder.

setting (optional): A Dictionary<STRING, BOOL> used to specify whether to calculate option price sensitivity measures represented by Greeks. The optional keys are:

model (optional): A STRING scalar indicating the model to use. It can take the following value:

• BlackScholes: Uses the Black-Scholes formula.

method (optional): A STRING scalar indicating the method to use. It can take the following value:

• Analytic: Uses the analytic method.

• If setting is not specified, returns a DOUBLE scalar indicating the option's net present value (NPV), i.e., the theoretical option price.
• If setting is specified, returns a dictionary (Dictionary<STRING, DOUBLE>) containing NPV and the Greeks requested by setting.

The following example builds a discount curve, a dividend curve, and an equity option volatility surface, and then prices an equity digital option.

eqDigitalOptionJson =  {
    "productType": "Option",
    "optionType": "DigitalOption",
    "assetType":"EqDigitalOption",
    "instrumentId":"111222334",
    "notionalCurrency":"CNY",
    "notionalAmount":1,
    "maturity":2026.03.25,
    "strike":3.2000,
    "dayCountConvention":"Actual360",
    "underlying":"CCC",
    "payoffType":"Call",
    "direction":"Buy",
    "discountCurve":"discountCurve",
    "dividendCurve":"dividendCurve"
}

ins3 = parseInstrument(eqDigitalOptionJson)

// ================================================================
// Data sources:
//   Spot price    : akshare fund_etf_hist_sina('sh510050')     -> 3.1140
//   Option chain/IV: akshare option_risk_indicator_sse('20260213')
//                    -> reconstructs the option settlement price with Black-Scholes
//   Interest rate curve: China Foreign Exchange Trade System implied foreign currency
//                    interest rate curve (CNY, USD.CNY/Shibor/swap points)
//                    https://www.chinamoney.com.cn/chinese/bkcurvuiruuh/
//                    API: POST /ags/ms/cm-u-bk-fx/IuirCurvHis  2026-02-13
//
// Pricing target: Call option, strike=3.2000, expiry=2026-03-25
// ================================================================

pricingDate   = 2026.02.13
referenceDate = pricingDate

// ------------------------------------------------------------------
// 1. Spot price
// ------------------------------------------------------------------
spot = 3.1140

// ------------------------------------------------------------------
// 2. Define the pricing contract (near-month ATM/slightly OTM call option)
// ------------------------------------------------------------------

// ------------------------------------------------------------------
// 3. Raw option chain data (used to construct the dividend curve and volatility surface)
//    Expiry sequence: 2026.02.25 | 2026.03.25 | 2026.06.24 | 2026.09.23
//    Strike range: [2.85, 3.60]
// ------------------------------------------------------------------
termDates = [2026.02.25, 2026.03.25, 2026.06.24, 2026.09.23]

callPrices = matrix(
    [0.2655, 0.2155, 0.1656, 0.1156, 0.0318, 0.0039, 0.0015, 0.0008, 0.0003, 0.0001],
    [0.2690, 0.2248, 0.1770, 0.1385, 0.0697, 0.0303, 0.0128, 0.0069, 0.0046, 0.0036],
    [0.3030, 0.2655, 0.2278, 0.1970, 0.1431, 0.0991, 0.0677, 0.0479, 0.0346, 0.0254],
    [0.3330, 0.2987, 0.2681, 0.2388, 0.1883, 0.1448, 0.1139, 0.0899, 0.0715, 0.0574]
)
putPrices = matrix(
    [0.0004, 0.0009, 0.0021, 0.0045, 0.0218, 0.0939, 0.1901, 0.2896, 0.3908, 0.4916],
    [0.0125, 0.0165, 0.0229, 0.0316, 0.0616, 0.1250, 0.2029, 0.2967, 0.3962, 0.4948],
    [0.0396, 0.0507, 0.0634, 0.0798, 0.1253, 0.1814, 0.2499, 0.3321, 0.4175, 0.5077],
    [0.0651, 0.0798, 0.0973, 0.1180, 0.1662, 0.2250, 0.2952, 0.3651, 0.4508, 0.5342]
)
strikes = matrix(
    [2.8500, 2.9000, 2.9500, 3.0000, 3.1000, 3.2000, 3.3000, 3.4000, 3.5000, 3.6000],
    [2.8500, 2.9000, 2.9500, 3.0000, 3.1000, 3.2000, 3.3000, 3.4000, 3.5000, 3.6000],
    [2.8500, 2.9000, 2.9500, 3.0000, 3.1000, 3.2000, 3.3000, 3.4000, 3.5000, 3.6000],
    [2.8500, 2.9000, 2.9500, 3.0000, 3.1000, 3.2000, 3.3000, 3.4000, 3.5000, 3.6000]
)

// ------------------------------------------------------------------
// 4. Discount curve -- CNY rates from China Foreign Exchange Trade System
//    implied foreign currency interest rate curve (2026-02-13)
//    Data source: https://www.chinamoney.com.cn/chinese/bkcurvuiruuh/
//    USD.CNY / Shibor / average spot inquiry quote / swap points -> rmbRateStr field
// ------------------------------------------------------------------
discountCurveDict = {
    "mktDataType"       : "Curve",
    "curveType"         : "IrYieldCurve",
    "curveName"         : "CNY_FR_007",
    "referenceDate"     : referenceDate,
    "currency"          : "CNY",
    "dayCountConvention": "Actual365",
    "compounding"       : "Continuous",
    "interpMethod"      : "Linear",
    "extrapMethod"      : "Flat",
    "dates"             : [referenceDate + 1, referenceDate + 7, referenceDate + 14, referenceDate + 21, referenceDate + 30, referenceDate + 61, referenceDate + 91, referenceDate + 182, referenceDate + 273, referenceDate + 365, referenceDate + 547, referenceDate + 730, referenceDate + 1095],
    "values"            : [0.016134, 0.016107, 0.016102, 0.016102, 0.016102, 0.016103, 0.016029, 0.015832, 0.015889, 0.015898, 0.015561, 0.015583, 0.015892]
}
discountCurve = parseMktData(discountCurveDict)

// ------------------------------------------------------------------
// 5. Dividend curve -- implied with Call-Put parity (CallPutParity)
// ------------------------------------------------------------------
dividendCurve = eqDividendCurveBuilder(
    referenceDate, termDates, "CallPutParity", ,
    callPrices, putPrices, strikes, spot, discountCurve,
    "Actual365", "510050"
)

// ------------------------------------------------------------------
// 6. Volatility surface -- SABR model, using OTM options
//    Strike < Spot -> OTM Put; Strike >= Spot -> OTM Call
// ------------------------------------------------------------------
optionExpiries = termDates

optionPrices = matrix(
    [0.0004, 0.0009, 0.0021, 0.0045, 0.0218, 0.0039, 0.0015, 0.0008, 0.0003, 0.0001],
    [0.0125, 0.0165, 0.0229, 0.0316, 0.0616, 0.0303, 0.0128, 0.0069, 0.0046, 0.0036],
    [0.0396, 0.0507, 0.0634, 0.0798, 0.1253, 0.0991, 0.0677, 0.0479, 0.0346, 0.0254],
    [0.0651, 0.0798, 0.0973, 0.1180, 0.1662, 0.1448, 0.1139, 0.0899, 0.0715, 0.0574]
)
payoffTypes = matrix(
    ["Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call"],
    ["Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call"],
    ["Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call"],
    ["Put", "Put", "Put", "Put", "Put", "Call", "Call", "Call", "Call", "Call"]
)
volSurface = eqVolatilitySurfaceBuilder(
    referenceDate,
    optionExpiries,
    strikes,
    optionPrices,
    payoffTypes,
    spot,
    discountCurve,
    dividendCurve,
    "SABR",
    "50ETF_SABR_20260213"
)

// ------------------------------------------------------------------
// 7. Pricing -- single-contract NPV
// ------------------------------------------------------------------
npv = eqDigitalOptionPricer(ins3, pricingDate, spot, discountCurve, dividendCurve, volSurface)
print("NPV = " + string(npv))

// ------------------------------------------------------------------
// 8. Pricing -- with Greeks
// ------------------------------------------------------------------
setting = {
    "calcDelta"      : true,
    "calcGamma"      : true,
    "calcVega"       : true,
    "calcTheta"      : true,
    "calcRho"      : true
}
result = eqDigitalOptionPricer(ins3, pricingDate, spot, discountCurve, dividendCurve, volSurface, setting)
print(result)
// output:
// npv->0.279855211680205
// delta->2.043402240346535
// gamma->6.568738172923309
// vega->1.121915880314628
// theta->-0.675386277908325
// rho->0.675922151639878

Related Functions: parseInstrument, parseMktData, eqDividendCurveBuilder, eqVolatilitySurfaceBuilder