Valuation models

Autocallables, reverse convertibles and cliquets

Autocallables with memory coupons and protection barriers, barrier reverse convertibles and cliquets, by Monte Carlo under Dupire local volatility, with autocall and coupon probabilities, expected life, chance of loss, delta and vega.

Inputs

CurrencyNotionalSpot (initial = spot)Dividend yield%MaturityyObservationsCoupon% a yearAutocall barrier%Coupon barrier%Protection barrier%VolatilityPathsDiscount curveDiscount curve: flat rate% cc

Memory coupons

Results

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Methodology

Conventions

Paths under Dupire local vol from the surface (or a flat vol), weekly steps plus every observation date, half antithetic.
Levels are relative to the initial fixing; the issuer's credit is not priced.

References

Gatheral, The Volatility Surface
Bouzoubaa and Osseiran, Exotic Options and Hybrids

Formulas

Dynamics: d ln S = (r − q − ½σ²) dt + σ_loc(t, S) dW
Autocall: S(tᵢ) ≥ B·S₀ ⇒ N (1 + c τᵢ) at tᵢ