Symbolic

Formulas rather than procedures: sympy expressions for prices and greeks, checked against the engines to round-off where the engine computes the same truncation and to the expected order otherwise.

class rl.symbolic.VasicekTwoStateBond(regime=0)

The two-state Vasicek bond to second order in the holding time. .terms holds the state, averaged, Green–Kubo, second-order and memory terms of log P; .price is the formula; .greek("r0"), .greek("theta1"), .greek("lam") differentiate it; .delta(), .gamma(), .theta() are QuantLib’s names; .evaluate(expr, **values) evaluates.

from regimelib.symbolic import VasicekTwoStateBond
f = VasicekTwoStateBond(regime=0)
f.greek("r0")
f.evaluate(f.delta(), r0=0.03, kappa=0.5, theta1=0.06, theta2=0.02, sigma1=0.015, sigma2=0.008, lam=8.0, T=5.0)

class rl.symbolic.VasicekBondFirstOrder

class rl.symbolic.CIRBondFirstOrder

class rl.symbolic.VasicekJumpsBondFirstOrder

The bond under any finite chain at first order in the holding time. The chain enters only through numbers — the stationary averages, the Green–Kubo integrals and the memory coefficients of the starting regime — which coefficients(chain, ...) computes from the generator. The CIR integrals are closed by the Riccati identity, the jump integrals by the substitution u = exp(-kappa t).

from regimelib.symbolic import VasicekBondFirstOrder
f = VasicekBondFirstOrder()
numbers = f.coefficients(chain, kappa_=0.5, thetas=[0.08, 0.05, 0.01], sigmas=[0.015, 0.01, 0.006], regime=0)
f.evaluate(f.price, r0=0.03, kappa=0.5, T=4.0, **numbers)

parameterGreek(chain, wrt, regime=0, **params)

Greeks in the model’s own parameters: wrt = ("theta", i), ("sigma", i), ("intensity", i) for a per-regime parameter or ("q", a, b) for the switching rate out of regime a into b. The chain rule runs through the coefficients, whose derivatives are exact — the Green–Kubo matrix is bilinear in the forcing, and the group inverse and the stationary distribution vary with the generator as dQ# = -Q# dQ Q# + 1 pi dQ (Q#)^2 + (Q#)^2 dQ 1 pi and dpi = -pi dQ Q#. Checked against finite differences of the engine at order 1.

params = dict(r0=0.03, kappa=0.5, T=4.0, thetas=[0.08, 0.05, 0.01], sigmas=[0.015, 0.01, 0.006])
f.parameterGreek(chain, ("theta", 2), regime=1, **params)      # dP / d theta_2
f.parameterGreek(chain, ("q", 0, 1), regime=1, **params)       # dP / d Q_01

class rl.symbolic.TwoStateConstantForcing

The exact, all-orders solution of the two-regime reduced system with constant forcing — a 2 × 2 matrix exponential written with its eigenvalues — which is the closed-form characteristic function of every two-regime Black–Scholes, Merton or variance-gamma model. .a(regime) in q12, q21, g1, g2, T; .blackScholes(regime) in u, sigma1, sigma2.