Valuation models

Range accruals

The expected share of observation days with the index in range, from 1bp call-spread digitals on the forward, expected coupons by period, price, PV01 and vega.

Inputs

CurrencyNotionalMaturityyCoupon in range%Lower bound%Upper bound%Index observedCoupon frequencyNormal volbpDiscount and projection curveDiscount and projection curve: flat rate% cc

Lower boundUpper boundPrincipal repaid at maturity

Results

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Methodology

Conventions

Each observation day earns the coupon if the index fixes in range; paid at the period end.
A day is a pair of digitals, each a 1bp call spread on the smile.

References

Hull, Options, Futures, and Other Derivatives, ch. 34

Formulas

In range: p = P(R > L) − P(R > U)
Coupon: V = N c τ D(T) · mean(p)