Valuation models

TARFs and accumulators

Leveraged strips of forwards that end on a profit target or a knock-out barrier, by Monte Carlo under Garman-Kohlhagen, local vol or stochastic local vol, with the fair strike, knock-out probability and expected fixings.

Inputs

Results

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Methodology

Conventions

  • Each fixing the holder deals notional at the strike, leverage times notional when the fixing is against them.
  • A TARF ends once gains reach the target; an accumulator once a fixing touches the knock-out barrier.
  • Monte Carlo under Garman-Kohlhagen, Dupire local vol or Heston stochastic local vol, with antithetic paths.

References

  • Wystup, FX Options and Structured Products
  • Guyon and Henry-Labordère, Nonlinear Option Pricing

Formulas

Fixing
c = N [(φ(S − K))⁺ − ℓ (φ(K − S))⁺]
Value
V = E[Σ c_j D(t_j) 1_alive]