CdsParSpread

The par spread of a single-name credit default swap from a survival curve and a discount curve on a common time grid — the closed-form reference for the bootstrapped-hazard CDS pricing in nablatensor-cva.

The grid times[i] (ascending, all > 0) carries the survival probability survival[i] = Q(0, times[i]) and the risk-free discount factor discount[i] = P(0, times[i]); time zero has Q = 1, P = 1 implicitly. Over segment i = (times[i-1], times[i]] of length dt_i:

protection leg  = (1 - R) * sum_i  Dmid_i * (Q_{i-1} - Q_i)
premium annuity = sum_i  dt_i * D_i * (Q_{i-1} + Q_i) / 2      (accrual on default, half period)
par spread      = protection leg / premium annuity

where Dmid_i = (D_{i-1} + D_i) / 2 approximates discounting to the mid-point of the segment in which default occurs. A monthly (or finer) grid keeps the piecewise-flat approximation tight.

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Record components

parSpread: double
protectionLeg: double
premiumAnnuity: double

Methods

static CdsParSpread of(double recovery, double[] times, double[] survival, double[] discount)

recovery: recovery rate R in [0, 1); loss given default is 1 - R
times: ascending segment end times in years, all > 0
survival: Q(0, times[i]), non-increasing, first entry <= 1
discount: P(0, times[i]), positive

double protectionBuyerValue(double contractSpread)

Mark-to-market of a bought-protection position paying contractSpread on unit notional.