option helper

Author: tigersk

tigeropen/examples/option_helpers/__init__.py

@@ -0,0 +1,4 @@
+# -*- coding: utf-8 -*-
+# 
+# @Date    : 2022/4/15
+# @Author  : sukai

tigeropen/examples/option_helpers/helpers.py

@@ -0,0 +1,293 @@
+# -*- coding: utf-8 -*-
+# Helpers for calculating the Greeks of options
+# @Date    : 2022/4/15
+# @Author  : sukai
+import argparse
+import sys
+from typing import List
+
+import QuantLib as ql
+
+
+class FDDividendOptionHelper(ql.DividendVanillaOption):
+    def __init__(self,
+                 engine_class,
+                 option_type: ql.Option,
+                 underlying: float,
+                 strike: float,
+                 risk_free_rate: float,
+                 dividend_rate: float,
+                 volatility: float,
+                 reference_date: ql.Date,
+                 exercise: ql.Exercise,
+                 dates: List[ql.Date] = None,
+                 dividends: List[float] = None,
+                 calendar: ql.Calendar = ql.NullCalendar(),
+                 day_counter: ql.DayCounter = ql.Actual365Fixed()
+                 ):
+        self.dates = dates if dates is not None else list()
+        self.dividends = dividends if dividends is not None else list()
+        super(FDDividendOptionHelper, self).__init__(ql.PlainVanillaPayoff(option_type, strike), exercise, self.dates,
+                                                     self.dividends)
+
+        self.option_type = option_type
+        self.underlying = underlying
+        self.strike = strike
+        self.risk_free_rate = risk_free_rate
+        self.dividend_rate = dividend_rate
+        self.volatility = volatility
+        self.reference_date = reference_date
+        self.exercise = exercise
+        self.calendar = calendar
+        self.day_counter = day_counter
+        self.engine_class = engine_class
+        self.bsm_process: ql.GeneralizedBlackScholesProcess
+        self.underlying_quote = ql.SimpleQuote(underlying)
+        self.risk_free_rate_quote = ql.SimpleQuote(risk_free_rate)
+        self.dividend_rate_quote = ql.SimpleQuote(dividend_rate)
+        self.volatility_quote = ql.SimpleQuote(volatility)
+
+        self.setPricingEngine(self.get_engine(reference_date))
+
+    def get_engine(self, date: ql.Date) -> ql.PricingEngine:
+        spot_handle = ql.QuoteHandle(self.underlying_quote)
+        risk_free_rate_handle = ql.QuoteHandle(self.risk_free_rate_quote)
+        volatility_handle = ql.QuoteHandle(self.volatility_quote)
+
+        r_ts = ql.YieldTermStructureHandle(ql.FlatForward(date, risk_free_rate_handle, self.day_counter))
+        vol_ts = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(date, self.calendar, volatility_handle,
+                                                                    self.day_counter))
+
+        if self.dividend_rate is not None:
+            dividend_handle = ql.QuoteHandle(self.dividend_rate_quote)
+            d_ts = ql.YieldTermStructureHandle(ql.FlatForward(date, dividend_handle, self.day_counter))
+            self.bsm_process = ql.BlackScholesMertonProcess(spot_handle,
+                                                            d_ts,
+                                                            r_ts,
+                                                            vol_ts)
+        else:
+            self.bsm_process = ql.BlackScholesProcess(spot_handle,
+                                                      r_ts,
+                                                      vol_ts)
+
+        return self.engine_class(self.bsm_process)
+
+    def theta(self) -> float:
+        yesterday = self.reference_date - ql.Period(1, ql.Days)
+        tomorrow = self.reference_date + ql.Period(1, ql.Days)
+        if self.exercise.lastDate() == tomorrow:
+            dt = self.day_counter.yearFraction(yesterday, self.reference_date)
+        else:
+            dt = self.day_counter.yearFraction(yesterday, tomorrow)
+            self.setPricingEngine(self.get_engine(tomorrow))
+        value_p = self.NPV()
+        self.setPricingEngine(self.get_engine(yesterday))
+        value_m = self.NPV()
+
+        theta = (value_p - value_m) / dt
+        self.setPricingEngine(self.get_engine(self.reference_date))
+        return theta / ql.Daily
+
+    def vega(self) -> float:
+        return self.numeric_first_order(self.volatility_quote)
+
+    def rho(self) -> float:
+        return self.numeric_first_order(self.risk_free_rate_quote)
+
+    def implied_volatility(self, price: float, accuracy: float = 1.0e-4, max_evaluations: int = 100,
+                           min_vol: float = 1.0e-7, max_vol: float = 4.0, try_times: int = 4) -> float:
+        """
+
+        :param price: expected option NPV
+        :param accuracy:
+        :param max_evaluations:
+        :param min_vol:
+        :param max_vol:
+        :param try_times:
+        :return:
+        """
+        try:
+            return self.impliedVolatility(price, self.bsm_process, accuracy, max_evaluations, min_vol, max_vol)
+        except RuntimeError as e:
+            if try_times == 0:
+                return 0
+            elif 'root not bracketed' in str(e):
+                return self.implied_volatility(price, accuracy, max_evaluations, min_vol, max_vol * 2, try_times-1)
+            else:
+                raise e
+
+    def update_implied_volatility(self, implied_volatility: float):
+        self.volatility_quote.setValue(implied_volatility)
+
+    def numeric_first_order(self, quote: ql.SimpleQuote) -> float:
+        """
+        reference: https://github.com/lballabio/QuantLib/issues/779
+        https://github.com/frgomes/jquantlib/blob/master/jquantlib-helpers/src/main/java/org/jquantlib/helpers/FDDividendOptionHelper.java
+        :param self:
+        :param quote:
+        :return:
+        """
+        sigma0 = quote.value()
+        h = sigma0 * 1E-4
+        quote.setValue(sigma0 - h)
+        p_minus = self.NPV()
+        quote.setValue(sigma0 + h)
+        p_plus = self.NPV()
+        quote.setValue(sigma0)
+        return (p_plus - p_minus) / (2 * h) / 100
+
+
+class FDAmericanDividendOptionHelper(FDDividendOptionHelper):
+    """American option"""
+
+    def __init__(self,
+                 option_type: ql.Option,
+                 underlying: float,
+                 strike: float,
+                 risk_free_rate: float,
+                 dividend_rate: float,
+                 volatility: float,
+                 settlement_date: ql.Date,
+                 expiration_date: ql.Date,
+                 dates: List[ql.Date] = None,
+                 dividends: List[float] = None,
+                 calendar: ql.Calendar = ql.NullCalendar(),
+                 day_counter: ql.DayCounter = ql.Actual365Fixed(),
+                 engine_class: ql.PricingEngine.__class__ = ql.FdBlackScholesVanillaEngine
+                 ):
+        """
+
+        :param option_type: ql.Option.Call or ql.Option.Put
+        :param underlying:
+        :param strike:
+        :param risk_free_rate:
+        :param dividend_rate:
+        :param volatility:
+        :param settlement_date:
+        :param expiration_date:
+        :param dates:
+        :param dividends:
+        :param calendar:
+        :param day_counter:
+        :param engine_class:
+
+        >>> helper = FDAmericanDividendOptionHelper(ql.Option.Call, 985, 990, 0.017, 0, 0.6153, ql.Date(14, 4, 2022), ql.Date(22, 4, 2022))
+        >>> print(f'value:{helper.NPV()}')
+        >>> print(f'delta:{helper.delta()}')
+        >>> print(f'gamma:{helper.gamma()}')
+        >>> print(f'theta:{helper.theta()}')
+        >>> print(f'vega:{helper.vega()}')
+        >>> print(f'rho:{helper.rho()}')
+        """
+        super(FDAmericanDividendOptionHelper, self).__init__(engine_class=engine_class,
+                                                             option_type=option_type, underlying=underlying,
+                                                             strike=strike, risk_free_rate=risk_free_rate,
+                                                             dividend_rate=dividend_rate, volatility=volatility,
+                                                             reference_date=settlement_date,
+                                                             exercise=ql.AmericanExercise(settlement_date,
+                                                                                          expiration_date),
+                                                             dates=dates, dividends=dividends, calendar=calendar,
+                                                             day_counter=day_counter)
+
+
+class FDEuropeanDividendOptionHelper(FDDividendOptionHelper):
+    """European option"""
+
+    def __init__(self,
+                 option_type: ql.Option,
+                 underlying: float,
+                 strike: float,
+                 risk_free_rate: float,
+                 dividend_rate: float,
+                 volatility: float,
+                 settlement_date: ql.Date,
+                 expiration_date: ql.Date,
+                 dates: List[ql.Date] = None,
+                 dividends: List[float] = None,
+                 calendar: ql.Calendar = ql.NullCalendar(),
+                 day_counter: ql.DayCounter = ql.Actual365Fixed(),
+                 engine_class: ql.PricingEngine.__class__ = ql.FdBlackScholesVanillaEngine
+                 ):
+        super(FDEuropeanDividendOptionHelper, self).__init__(engine_class=engine_class,
+                                                             option_type=option_type, underlying=underlying,
+                                                             strike=strike, risk_free_rate=risk_free_rate,
+                                                             dividend_rate=dividend_rate, volatility=volatility,
+                                                             reference_date=settlement_date,
+                                                             exercise=ql.EuropeanExercise(expiration_date),
+                                                             dates=dates, dividends=dividends, calendar=calendar,
+                                                             day_counter=day_counter)
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(description='Helpers for calculating the Greeks of options')
+
+    parser.add_argument('-t', '--type', type=str,
+                        help='Option type, CALL/PUT (C/P)', choices=('C', 'P', 'CALL', 'PUT'))
+    parser.add_argument('-u', '--underlying', type=float,
+                        help='The price of the underlying asset')
+    parser.add_argument('-p', '--strike', type=float,
+                        help='The strike price at expiration')
+    parser.add_argument('-d', '--dividend', type=float, nargs='?', default=0,
+                        help='The dividend rate')
+    parser.add_argument('-r', '--rfrate', type=float, nargs='?', default=0.01,
+                        help='The risk free rate')
+    parser.add_argument('-v', '--volatility', type=float, nargs='?', default=0,
+                        help='The implied volatility')
+    parser.add_argument('-s', '--settlement', type=str,
+                        help='The settlement date, like "2022-04-22"')
+    parser.add_argument('-e', '--expiration', type=str,
+                        help='The expiration date, like "2022-04-29"')
+    parser.add_argument('-n', '--npv', type=float, nargs='?',
+                        help='The expected NPV of option')
+    parser.add_argument('-a', '--ask', type=float, nargs='?',
+                        help='The ask price of option')
+    parser.add_argument('-b', '--bid', type=float, nargs='?',
+                        help='The bid price of option')
+    parser.add_argument('-o', '--european', action='store_true',
+                        help='Is european option')
+
+    args = parser.parse_args()
+
+    if args.type.upper() in ('C', 'CALL'):
+        ql_option_type = ql.Option.Call
+    elif args.type.upper() in ('P', 'PUT'):
+        ql_option_type = ql.Option.Put
+    else:
+        parser.error('Wrong option type')
+    if args.volatility is None and args.npv is None and args.ask is None and args.bid is None:
+        parser.error('Must specify the volatility or option npv(or option\'s ask, bid)')
+
+    print(args.__dict__)
+    settlement_date = ql.DateParser.parseFormatted(str(args.settlement).replace('/', '-'), '%Y-%m-%d')
+    expiration_date = ql.DateParser.parseFormatted(str(args.expiration).replace('/', '-'), '%Y-%m-%d')
+
+    if args.european:
+        helper_class = FDEuropeanDividendOptionHelper
+    else:
+        helper_class = FDAmericanDividendOptionHelper
+
+    helper = helper_class(option_type=ql_option_type,
+                          underlying=args.underlying,
+                          strike=args.strike,
+                          risk_free_rate=args.rfrate,
+                          dividend_rate=args.dividend,
+                          volatility=args.volatility,
+                          settlement_date=settlement_date,
+                          expiration_date=expiration_date)
+
+    if args.volatility is None or args.volatility == 0:
+        expected_npv = None
+        npv_msg = ''
+        if args.ask and args.bid:
+            expected_npv = (args.ask + args.bid) / 2
+            npv_msg = f'with ask {args.ask}, bid {args.bid}, expected_npv {expected_npv}'
+        else:
+            expected_npv = args.npv
+            npv_msg = f'with expected npv: {expected_npv}'
+
+        volatility = helper.implied_volatility(expected_npv)
+        helper.update_implied_volatility(volatility)
+        print(f'The implied volatility {npv_msg} is: {volatility}')
+
+    print(f'npv: {helper.NPV()}, delta:{helper.delta()}, gamma:{helper.gamma()}, theta:{helper.theta()}, '
+          f'vega:{helper.vega()}, rho:{helper.rho()}')