Pricing Models

Equity

Heston

HestonModel

ql.HestonModel(HestonProcess)

today = ql.Date().todaysDate()
riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
dividendTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))

initialValue = ql.QuoteHandle(ql.SimpleQuote(100))

v0 = 0.005
theta = 0.010
kappa = 0.600
sigma = 0.400
rho = -0.15

hestonProcess = ql.HestonProcess(riskFreeTS, dividendTS, initialValue, v0, kappa, theta, sigma, rho)
hestonModel = ql.HestonModel(hestonProcess)

PiecewiseTimeDependentHestonModel

ql.PiecewiseTimeDependentHestonModel(riskFreeRate, dividendYield, s0, v0, theta, kappa, sigma, rho, timeGrid)

today = ql.Date().todaysDate()
riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
dividendTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))

initialValue = ql.QuoteHandle(ql.SimpleQuote(100))

times = [1.0, 2.0, 3.0]
grid = ql.TimeGrid(times)

v0 = 0.005
theta = [0.010, 0.015, 0.02]
kappa = [0.600, 0.500, 0.400]
sigma = [0.400, 0.350, 0.300]
rho = [-0.15, -0.10, -0.00]

kappaTS = ql.PiecewiseConstantParameter(times[:-1], ql.PositiveConstraint())
thetaTS = ql.PiecewiseConstantParameter(times[:-1], ql.PositiveConstraint())
rhoTS = ql.PiecewiseConstantParameter(times[:-1], ql.BoundaryConstraint(-1.0, 1.0))
sigmaTS = ql.PiecewiseConstantParameter(times[:-1], ql.PositiveConstraint())

for i, time in enumerate(times):
    kappaTS.setParam(i, kappa[i])
    thetaTS.setParam(i, theta[i])
    rhoTS.setParam(i, rho[i])
    sigmaTS.setParam(i, sigma[i])

hestonModelPTD = ql.PiecewiseTimeDependentHestonModel(riskFreeTS, dividendTS, initialValue, v0, thetaTS, kappaTS, sigmaTS, rhoTS, grid)

Bates

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Short Rate Models

One Factor Models

• Vasicek: (r0=0.05, a=0.1, b=0.05, sigma=0.01, lambda=0.0)

• BlackKarasinski: (YieldTermStructure, a=0.1, sigma=0.1)

• HullWhite: (YieldTermStructure, a=0.1, sigma=0.01)

• Gsr()

Vasicek

ql.Vasicek(r0=0.05, a=0.1, b=0.05, sigma=0.01, lambda=0.0)

BlackKarasinski

ql.BlackKarasinski(termStructure, a=0.1, sigma=0.1)

HullWhite

ql.HullWhite(termStructure, a=0.1, sigma=0.01)

Gsr

One factor gsr model, formulation is in forward measure.

ql.Gsr(termStruncture, volstepdates, volatilities, reversions)

Two Factor Models

G2

ql.G2(termStructure, a=0.1, sigma=0.01, b=0.1, eta=0.01, rho=-0.75)