Valuation models

Average price and strike strips

One Asian option per month or quarter, on the average of the period's fixings against a strike (average price) or against the price at the period's end (average strike), by moment matching, with each period's value, delta, gamma, vega and rho.

Inputs

Results

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Methodology

Conventions

  • One Asian option per month or quarter, on the average of the period's daily or weekly fixings, paid at the period's end.
  • Average price: the average against the strike. Average strike: the price at the period's end against the average.
  • The average is matched to a lognormal by its first two moments (Levy); spot grows at the rate less the convenience yield.

References

  • Hull, Options, Futures, and Other Derivatives
  • Levy (1992), Pricing European average rate currency options

Formulas

Moments
E[A] = (1/n) Σ F(tⱼ), E[A²] = (1/n²) Σ F(tⱼ)F(tₗ) e^(σ² min(tⱼ, tₗ))
Period
c = P(T) [E[A] N(d₁) − K N(d₂)]
Strip
V = q Σₚ cₚ