FX Derivatives Quant Interview Questions: Pricing, Smiles, Greeks and Exotics

1. Get forwards, discounting, and NDFs right first

For a currency pair quoted as domestic currency per unit of foreign currency, the no-arbitrage forward follows from domestic and foreign discount factors. The exact notation matters less than stating which currency is domestic, which is foreign, and how the payoff is settled.

NDFs add fixing and cash settlement instead of physical exchange. Interviewers may ask how fixing source, settlement currency, holidays, or capital controls affect valuation and operational risk.

• State the pair convention before using rates.
• Reconcile forward points with the two discount curves.
• Separate trade maturity, fixing date, and settlement date for NDFs.
• Check signs by asking which currency you receive when spot or forward rises.

2. Use Garman-Kohlhagen as a baseline, not the whole answer

Garman-Kohlhagen adapts Black-Scholes to FX by treating the foreign short rate like a continuous yield. Under the domestic pricing measure, the forward embeds the domestic-foreign rate differential and the option is discounted in the domestic currency.

A strong answer gives the formula structure, then explains assumptions: lognormal spot, deterministic rates, constant volatility, frictionless trading, and continuous hedging. Real FX markets require a volatility surface and often richer dynamics for exotics.

3. Treat delta conventions and the smile as model inputs

FX volatility is frequently quoted by delta rather than strike. Depending on market and tenor, delta may be spot or forward, premium-adjusted or unadjusted. Converting a quoted delta to strike is therefore part of the model input process, not a cosmetic transformation.

Smile quotes may be expressed through ATM, risk reversals, and butterflies. Explain how these reconstruct call and put volatilities at chosen deltas, then how the resulting smile is interpolated in a way that preserves sensible shape and avoids arbitrage.

4. Move from vanillas to barriers, quanto, and richer models

Barrier options are sensitive not only to terminal spot but to whether a level is touched. This creates strong dependence on smile dynamics, monitoring convention, gaps, and numerical method. Explain knock-in/knock-out parity where applicable and why discrete monitoring differs from continuous monitoring.

Quanto or cross-currency payoffs introduce dependence between asset moves and FX. For smile-sensitive exotics, local volatility, stochastic volatility, or hybrid models may be considered. Model choice should be tied to the risk being hedged and the instruments available for calibration.

• Identify path dependence before choosing a pricing engine.
• Discuss correlation and quanto drift adjustments when currencies and underlyings interact.
• Explain which vanilla instruments calibrate each model component.
• State model-risk implications when extrapolating beyond liquid smile quotes.

5. Finish with Greeks, calibration, and validation

FX option risk includes spot delta, gamma, vega, theta, rate sensitivities, and smile sensitivities. For exotics, risk can jump around barriers or become highly dependent on the chosen smile-dynamics assumption. Explain both the mathematical Greek and the hedge instrument or market move it represents.

Validate conventions, forwards, smile reconstruction, interpolation, calibration, numerical convergence, and benchmark prices separately. Reconcile vanilla prices first, then test exotics against independent methods or limiting cases.

• Bump market quotes in the same convention in which the desk manages risk.
• Test put-call parity and forward consistency before exotic validation.
• Compare analytical, PDE, tree, and Monte Carlo results where overlapping methods exist.
• Stress skew, rates, correlation, and barrier proximity rather than reporting one base-case price.

Practise aloud

Interview drills with answer direction

Turn reading into practice

A focused study plan

1. Module 1

   Conventions

   Master pair notation, forwards, discounting, settlements, and NDF mechanics.

2. Module 2

   Vanillas

   Derive Garman-Kohlhagen, parity, Greeks, and limiting cases.

3. Module 3

   Smile

   Practise delta conventions, ATM/RR/BF reconstruction, strike conversion, and interpolation.

4. Module 4

   Exotics

   Work barriers, quanto, correlation, smile dynamics, and numerical methods.

5. Module 5

   Validation

   Run convention, calibration, convergence, benchmark, and stress checks.

Self-review

Frequent mistakes to catch early

• Writing a pricing formula before declaring the currency-pair convention.
• Mixing spot delta, forward delta, and premium-adjusted delta.
• Treating the implied-volatility smile as a single constant volatility.
• Discussing an exotic model without explaining calibration instruments and hedge implications.

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