FX Options Risk Lab
A pre-hedge USD/MXN options exposure analyzed through pricing, Greeks, stress repricing, hedging, VaR/ES, and P&L attribution.
The book is measured before hedging, then revalued under spot moves, volatility shocks, and one-day risk scenarios. The analysis shows how mark-to-market value can appear controlled while delta, vega, and stress-loss limits remain exposed.
GitHub ↗Market base case
- Spot USD/MXN
- 17.0000
- MXN rate (rd)
- 9.50%
- USD rate (rf)
- 4.50%
- ATM volatility
- 12.00%
- Domestic / foreign
- MXN / USD
- Valuation date
- 2026-06-07
USD/MXN is quoted as MXN per 1 USD. Under Garman-Kohlhagen, MXN is the domestic currency and USD is the foreign currency.
Book risk snapshot (pre-hedge, net exposures)
Net delta and vega are large and directional before hedging, and negative gamma drives nonlinear stress losses.
Pricing
Garman-Kohlhagen FX options
Risk
VaR, ES, stress scenarios
Hedging
Delta and vega exposure
Attribution
Where P&L comes from
USD/MXN Options Book
A pre-hedge exposure across strikes, maturities, calls, and puts. The book is intentionally directional before the hedge is applied.
Composition
- Legs
- 6
- Long / short
- 3 / 3
- Calls / puts
- 3 / 3
- Maturities
- 0.10 to 1.00y
- Strikes
- 16.00 to 18.00
Instruments
| ID | Type | Pos | Notional USD | Strike | Maturity | Implied vol |
|---|---|---|---|---|---|---|
| OPT-001 | call | LONG | USD 1,000,000 | 17.0000 | 0.25y | 12.0% |
| OPT-002 | call | SHORT | USD 750,000 | 17.5000 | 0.25y | 12.5% |
| OPT-003 | put | LONG | USD 1,000,000 | 16.5000 | 0.50y | 13.0% |
| OPT-004 | put | SHORT | USD 500,000 | 17.0000 | 0.10y | 11.5% |
| OPT-005 | call | LONG | USD 600,000 | 18.0000 | 1.00y | 14.0% |
| OPT-006 | put | SHORT | USD 800,000 | 16.0000 | 0.75y | 13.5% |
Instrument Valuation and Risk Sensitivities
Garman-Kohlhagen valuation with position-signed Greeks at instrument and book level. The model extends Black-Scholes to FX by treating the foreign rate as a continuous yield.
Vega per 1 vol point; theta per calendar day. Greeks are position-signed.
| ID | Type | Pos | Px / USD | Mkt Val | Signed MV | Δ signed | Γ signed | Vega/pt | Θ/day |
|---|---|---|---|---|---|---|---|---|---|
| OPT-001 | call | LONG | 0.5129 | 512,860 | +512,860 | +587,542 | +375,915 | +32,592 | -3,378 |
| OPT-002 | call | SHORT | 0.2974 | 223,078 | -223,078 | -302,618 | -271,027 | -24,477 | +2,323 |
| OPT-003 | put | LONG | 0.2519 | 251,945 | +251,945 | -254,425 | +203,035 | +38,140 | -700 |
| OPT-004 | put | SHORT | 0.2050 | 102,505 | -102,505 | +218,089 | -317,334 | -10,547 | +1,127 |
| OPT-005 | call | LONG | 0.8530 | 511,818 | +511,818 | +291,117 | +96,131 | +38,895 | -1,291 |
| OPT-006 | put | SHORT | 0.2049 | 163,914 | -163,914 | +142,825 | -103,757 | -30,361 | +373 |
Signed columns sum to the book-level net exposures above.
Spot and Volatility Stress Repricing
Full-book repricing across USD/MXN spot and implied-volatility shocks. The grid captures nonlinear option behavior that linear Greeks can miss.
Immediate revaluation; no time decay.
columns: USD/MXN spot shock · rows: implied-volatility shock
Each cell is the full repriced book P&L minus the base book value.
Delta Hedge Impact
A static spot hedge offsets first-order exposure while leaving residual gamma, vega, theta, and nonlinear repricing risk.
A static spot hedge offsets first-order exposure while leaving residual gamma, vega, theta, and nonlinear repricing risk.
Simulated 1-Day VaR and Expected Shortfall
Monte Carlo shocks USD/MXN spot and implied volatility, then reprices the full book over a one-day horizon. VaR is a loss threshold at a confidence level; Expected Shortfall is the average loss beyond it.
Spot diffusion uses a 252-trading-day year. Time decay uses ACT/365.
VaR and ES are positive loss numbers; ES exceeds VaR at the same confidence. Tail beyond the selected VaR is highlighted.
95% VaR
159,067 / 300,000
Within limit
53%
99% VaR
225,066 / 420,000
Within limit
54%
Worst stress loss
1,078,362 / 750,000
Breach
144%
Absolute net delta
682,529 / 150,000
Breach
455%
Net vega / vol point
44,242 / 40,000
Breach
111%
Illustrative thresholds used to show utilization and breach behavior. Not calibrated to a real institution's framework.
Scenario P&L Attribution
Greek-based contributions are compared with exact full repricing. The residual captures the difference between the approximation and the full revaluation.
Market-shock scenarios use immediate revaluation. The carry scenario isolates one day of time decay.
| Delta | +MXN 580,150 | First-order spot exposure |
| Gamma | -MXN 6,155 | Nonlinear spot curvature |
| Vega | +MXN 132,726 | Implied vol repricing |
| Theta | MXN 0 | Time decay over horizon |
| Residual | -MXN 19,397 | Full reprice minus Greek terms |
| Full reprice | +MXN 687,324 | Exact revaluation |
Model Assumptions and Validation
Model boundaries, validation checks, and limitations behind the analysis.
Model assumptions
Validation
Custom Garman-Kohlhagen prices and Greeks are benchmarked against QuantLib.
Checks cover pricing, Greeks, book aggregation, scenario repricing, hedging, VaR/ES sign and monotonicity, and the attribution identity.
Disclaimer
This work uses illustrative data and simplified modeling assumptions. It is not intended for trading or production risk management.