Lesson 4 of 7 · All lessons in this module
  1. Forward price versus forward value: inception and expiration
  2. Valuing a forward during its lifeVideo lesson
  3. Forwards on assets with costs and benefits
  4. Pricing and valuing FX forwardsVideo lesson
  5. Term structure: zero rates and discount factors
  6. Implied forward ratesVideo lesson
  7. Forward rate agreements (FRAs)Video lesson

Lesson 4 of 7 · 12 min

Pricing and valuing FX forwards

An FX forward price is the spot rate adjusted by the interest rate differential between the two currencies, and its MTM value compares today's spot rate with the forward rate discounted at the current differential.

In short

  • Quotes are price currency per unit of base currency: Sf/dS_{f/d}. Here f is the price (foreign) currency and d the base (domestic) currency.
  • Forward price: F0,f/d(T)=S0,f/d e(rf−rd)TF_{0,f/d}(T) = S_{0,f/d}\,e^{(r_f - r_d)T}.
  • The currency with the lower interest rate trades at a forward premium; the one with the higher rate at a forward discount.
  • MTM value of a long (buy base currency) forward: Vt(T)=St,f/d−F0,f/d(T) e−(rf−rd)(T−t)V_t(T) = S_{t,f/d} - F_{0,f/d}(T)\,e^{-(r_f - r_d)(T-t)}, per unit of base currency.
  • A wider differential rf−rdr_f - r_d makes the price currency depreciate on a forward basis and raises the value of a long-base position.

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