HullWhiteAnalytic

The Hull-White one-factor short-rate model made term-structure-consistent: given today's discount curve P^M(0, .) and the two parameters (a, sigma), it reprices that curve exactly and prices European bond options, caplets/floorlets and — by Jamshidian decomposition — European swaptions in closed form.

This is the analytic companion to the HullWhite1F Monte-Carlo step block (whose flat-forward assumption it removes) and the pricing engine HullWhiteCalibration fits (a, sigma) to a swaption grid with.

The bond reconstitution is @@PRE0@@ so today's curve is fitted with no separate theta(t) calibration; theta is exposed for a simulation that needs it. The a -> 0 limit is the Ho-Lee model and is handled without dividing by a.

View source ↗Full module reference on javadoc.io ↗

Methods

static HullWhiteAnalytic of(YieldCurve discountCurve, double a, double sigma)

static HullWhiteAnalytic of(CurveSet curves, double a, double sigma)

double a()

double sigma()

double r0()

Today's initial short rate r(0) = f^M(0, 0).

double bFactor(double t, double bondMaturity)

B(t, T) = (1 - e^{-a(T-t)}) / a, with the a -> 0 limit T - t.

double instantaneousForward(double t)

Instantaneous forward f^M(0, t) = -d ln P^M / dt.

double theta(double t)

The Hull-White drift term theta(t) = d f^M/dt + a f^M(0,t) + (sigma^2 / (2a)) (1 - e^{-2 a t}) — needed only to simulate the short rate; the analytic prices in this class do not use it.

double bondReconstitution(double t, double bondMaturity, double shortRate)

Bond P(t, T) reconstituted from a realised short rate r(t).

double zeroBondCall(double optionExpiry, double bondMaturity, double strike)

European call on P(T, S) struck at K, T < S.

double zeroBondPut(double optionExpiry, double bondMaturity, double strike)

European put on P(T, S) struck at K, T < S.

double caplet(double resetTime, double accrual, double strikeRate)

A caplet on the simply-compounded rate for [resetTime, resetTime + accrual], strike rate strikeRate, unit notional — priced as (1 + K tau) puts on P(T, T+tau) struck at 1/(1 + K tau).

double floorlet(double resetTime, double accrual, double strikeRate)

A floorlet — (1 + K tau) calls on the same bond.

double cap(double firstReset, double accrual, int periods, double strikeRate)

A cap: the sum of its caplets on an equally spaced schedule.

double payerSwaption(double expiry, double accrual, int periods, double strikeRate)

Physically-settled European payer swaption: expiry expiry, then periods fixed payments of accrual accrual at expiry + i*accrual, strike strikeRate, unit notional.

Jamshidian: the payer swaption is a put on the fixed-coupon bond, which decomposes into a portfolio of puts on the individual zero-coupon bonds once the critical short rate r* (where the coupon bond is worth par) is found by a 1-D solve.

double receiverSwaption(double expiry, double accrual, int periods, double strikeRate)