FX Derivatives

FX Option

Also known as: Currency option, Vanilla FX option

The right to exchange currencies at a set rate — hedging with the upside left open.

Asset class
FX derivatives
Instrument type
Option (call/put on a pair)
Traded
OTC (deep interbank market)
Typical users
Corporates, macro funds, dealers
A call on the base currency: limited premium at risk, gains beyond the strike.
KLong callUnderlying price at expiryProfit / loss
BeginnerWhat is it, really?

An FX option gives the right — not the obligation — to exchange one currency for another at a fixed rate before or at a set date. Every FX option is two-faced by nature: a call on euros is a put on dollars; buying the right to sell dollars cheap is the same as buying the right to buy euros cheap.

The classic user is a company bidding on a foreign contract: it might win $50M of revenue in three months — or might not. A forward would lock a hedge on money it may never receive; an option hedges the maybe: pay a premium now, exercise only if the bid wins and the rate moved against them.

Macro traders love FX options for a different reason: they're the cleanest way to bet on turbulence or calm in a currency, not just direction.

Key intuition: forwards hedge certainties, options hedge possibilities. The premium is the price of keeping your choices open.
IntermediateHow it works in practice

How the FX options market talks

The interbank market quotes not prices but implied volatilities, and organises them in a peculiar, elegant grid per tenor:

  • ATM vol: the at-the-money volatility level.
  • Risk reversal (RR): vol of 25-delta call minus 25-delta put — the smile's tilt. A EUR/USD RR "for dollar calls" says crashes are feared in one direction.
  • Butterfly (BF): how much the wings sit above ATM — the smile's curvature, i.e. the price of tail events.

Three numbers per tenor reconstruct the whole smile — a convention unique to FX.

Delta conventions

Strikes are referenced by delta (25d, 10d), not currency levels — and whether delta is spot/forward, premium-adjusted or not, differs by pair. Real desks live and die by getting the convention right.

Structures corporates actually buy

  • Collars/risk reversals: buy protection, sell away some upside — cheap or zero-cost.
  • Participating forwards: full protection, keep half the upside.
  • Straddles/strangles: the volatility trades around elections and central-bank meetings.
Worked example: a UK importer must pay $12M in 6 months. GBP/USD at 1.27; it buys a GBP put / USD call struck 1.25 for 1.4% premium. Sterling crashes to 1.15 → option pays ≈ (1.25−1.15)/1.15 ≈ 8.7% of notional, capping the damage. Sterling rallies to 1.35 → let it expire, buy dollars cheaply, premium was the insurance cost.
AdvancedPricing & valuation

Garman–Kohlhagen

Black–Scholes with the foreign interest rate as a "dividend yield" — a call on the base currency:

$$ C = S_0 e^{-r_f T} N(d_1) - K e^{-r_d T} N(d_2), \qquad d_{1,2} = \frac{\ln(S_0/K) + (r_d - r_f \pm \tfrac{1}{2}\sigma^2)T}{\sigma\sqrt{T}} $$

Domestic-foreign symmetry: a EURUSD call priced in USD equals the corresponding USD put priced in EUR, converted — a consistency check that catches convention bugs.

Smile construction and models

From ATM/RR/BF quotes per tenor, desks build the smile (SVI/vanna-volga/parametric), then a full surface. For exotics, calibrated dynamics matter: local vol underprices barrier/one-touch structures, stochastic vol (Heston) overshoots elsewhere — local-stochastic vol (LSV) mixtures tuned to vanillas and one-touch quotes are the FX-desk standard, because the market for touch products is liquid enough to discipline the model.

Vanna and volga

FX desks manage second-order smile Greeks explicitly: vanna (∂delta/∂vol) and volga (∂vega/∂vol) — the vanna-volga method prices simple exotics off the cost of hedging exactly these with RR and BF instruments.

What the surface reveals

Risk reversals are among macro's best sentiment gauges: EM pairs show persistent skew toward devaluation; pegged pairs price regime break as a far-wing hump. Breeden–Litzenberger on the smile yields full risk-neutral densities — event probabilities readable before referendums and elections.

Practitioner note: in FX options the quoting system is the analytics: ATM = level, RR = direction fear, BF = tail fear. Learn to read a vol run and you can read the market's mind on any currency.