def test_BlackKarasinskiExampleTwo(): # Valuation of a European option on a coupon bearing bond # This follows example in Fig 28.11 of John Hull's book but does not # have the exact same dt so there are some differences settlementDate = FinDate(1, 12, 2019) expiryDate = settlementDate.addTenor("18m") maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) bond.calculateFlowDates(settlementDate) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) strikePrice = 105.0 face = 100.0 tmat = (maturityDate - settlementDate) / gDaysInYear texp = (expiryDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) curve = FinDiscountCurve(settlementDate, times, dfs) price = bond.fullPriceFromDiscountCurve(settlementDate, curve) print("Fixed Income Price:", price) sigma = 0.20 a = 0.05 # Test convergence numStepsList = [100] #,101,200,300,400,500,600,700,800,900,1000] isAmerican = True treeVector = [] for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesBlackKarasinski(a, sigma) model.buildTree(tmat, int(numTimeSteps), times, dfs) v = model.bondOption(texp, strikePrice, face, couponTimes, couponFlows, isAmerican) end = time.time() period = end - start treeVector.append(v[0]) print(numTimeSteps, v, period)
def test_HullWhiteBondOption(): # Valuation of a European option on a coupon bearing bond settlementDate = FinDate(1, 12, 2019) expiryDate = settlementDate.addTenor("18m") maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) bond.calculateFlowDates(settlementDate) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates[1:]: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) strikePrice = 105.0 face = 100.0 tmat = (maturityDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) curve = FinDiscountCurve(settlementDate, times, dfs) price = bond.fullPriceFromDiscountCurve(settlementDate, curve) print("Spot Bond Price:", price) price = bond.fullPriceFromDiscountCurve(expiryDate, curve) print("Fwd Bond Price:", price) sigma = 0.01 a = 0.1 # Test convergence numStepsList = [100, 200, 300, 400, 500] texp = (expiryDate - settlementDate) / gDaysInYear print("NUMSTEPS", "FAST TREE", "FULLTREE", "TIME") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHullWhite(a, sigma) model.buildTree(texp, numTimeSteps, times, dfs) americanExercise = False v1 = model.americanBondOption_Tree(texp, strikePrice, face, couponTimes, couponFlows, americanExercise) v2 = model.europeanBondOption_Tree(texp, strikePrice, face, couponTimes, couponFlows) end = time.time() period = end - start print(numTimeSteps, v1, v2, period) # plt.plot(numStepsList, treeVector) if 1 == 0: print("RT") printTree(model._rt, 5) print("BOND") printTree(model._bondValues, 5) print("OPTION") printTree(model._optionValues, 5) v = model.europeanBondOption_Jamshidian(texp, strikePrice, face, couponTimes, couponFlows, times, dfs) print("EUROPEAN BOND JAMSHIDIAN DECOMP", v)
def test_HullWhiteCallableBond(): # Valuation of a European option on a coupon bearing bond settlementDate = FinDate(1, 12, 2019) maturityDate = settlementDate.addTenor("10Y") coupon = 0.05 frequencyType = FinFrequencyTypes.SEMI_ANNUAL accrualType = FinDayCountTypes.ACT_ACT_ICMA bond = FinBond(maturityDate, coupon, frequencyType, accrualType) bond.calculateFlowDates(settlementDate) couponTimes = [] couponFlows = [] cpn = bond._coupon / bond._frequency for flowDate in bond._flowDates[1:]: flowTime = (flowDate - settlementDate) / gDaysInYear couponTimes.append(flowTime) couponFlows.append(cpn) couponTimes = np.array(couponTimes) couponFlows = np.array(couponFlows) ########################################################################### # Set up the call and put times and prices ########################################################################### callDates = [] callPrices = [] callPx = 120.0 callDates.append(settlementDate.addTenor("5Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("6Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("7Y")) callPrices.append(callPx) callDates.append(settlementDate.addTenor("8Y")) callPrices.append(callPx) callTimes = [] for dt in callDates: t = (dt - settlementDate) / gDaysInYear callTimes.append(t) putDates = [] putPrices = [] putPx = 98.0 putDates.append(settlementDate.addTenor("5Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("6Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("7Y")) putPrices.append(putPx) putDates.append(settlementDate.addTenor("8Y")) putPrices.append(putPx) putTimes = [] for dt in putDates: t = (dt - settlementDate) / gDaysInYear putTimes.append(t) ########################################################################### tmat = (maturityDate - settlementDate) / gDaysInYear times = np.linspace(0, tmat, 20) dfs = np.exp(-0.05 * times) curve = FinDiscountCurve(settlementDate, times, dfs) ########################################################################### v1 = bond.fullPriceFromDiscountCurve(settlementDate, curve) sigma = 0.02 # basis point volatility a = 0.1 # Test convergence numStepsList = [100, 200, 300, 400, 500, 600, 700, 800, 900, 1000] tmat = (maturityDate - settlementDate) / gDaysInYear print("NUMSTEPS", "BOND_ONLY", "CALLABLE_BOND", "TIME") for numTimeSteps in numStepsList: start = time.time() model = FinModelRatesHullWhite(a, sigma) model.buildTree(tmat, numTimeSteps, times, dfs) v2 = model.callablePuttableBond_Tree(couponTimes, couponFlows, callTimes, callPrices, putTimes, putPrices) end = time.time() period = end - start print(numTimeSteps, v1, v2, period) if 1 == 0: print("RT") printTree(model._rt, 5) print("BOND") printTree(model._bondValues, 5) print("OPTION") printTree(model._optionValues, 5)