Quant Derivatives Pricing

Contract

• Input: problem description and inputs defined by the skill body.
• Output: Markdown artifact with completed process steps.
• Side effects: none.
• Dependencies: none.
• Stop condition: all process steps executed; artifact saved with required sections.
• Risk: low.
• Boundary: produces reasoning artifact only; no system changes.

Derivatives Pricing & Calibration

Price a derivative — vanilla option, exotic, structured — using a model, compute Greeks, and validate calibration against market data.

When to use

• The user wants to price an option, swap, exotic, or structured product.
• A risk desk needs Greeks for hedging.
• A quant strategy involves derivatives as a building block.

Process

1. Define the instrument

Name the instrument type (European call, American put, barrier, Asian, quanto, swaption, etc.). Specify underlier, notional, maturity, strike, currency, exercise style (European / American / Bermudan), and payoff structure.

Completion criterion: instrument fully specified with all contractual terms.

2. Choose the model

• Black-Scholes — European options on log-normal underliers; closed-form.
• Black-76 — futures / forward options; cap/floor.
• Binomial / Trinomial trees — American options, early exercise premium.
• Monte Carlo — path-dependent exotics, stochastic vol.
• Heston — stochastic vol; semi-closed form (characteristic function) or MC.
• Local vol — calibrated to vol surface.
• Jump-diffusion — Merton, Kou; for gaps and fat tails.

Name the model and state the SDE.

Completion criterion: model named; SDE or pricing equation written.

3. Price

Run the model:

• Analytical (closed-form formula).
• Numerical (tree steps, MC paths, PDE grid).
• Report the price; state the risk-neutral vs physical measure if relevant.

Completion criterion: price computed; method, steps / paths, and seed (if MC) reported.

4. Compute Greeks

Report at minimum: Δ, Γ, ν (vega), ρ (rho), θ. For American options, also report early exercise boundary. Greeks should be computed via bump-and-reprice or finite differences on the model.

Completion criterion: Δ, Γ, ν, ρ, θ all present; method (bump-and-reprice or finite diff) stated.

5. Calibrate to market

If using a model with free parameters (Heston k, θ, ν, ρ; local vol volatility):

• Fit to market-implied vol surface (minimise squared-error weighted by vega).
• Report calibration error (RMSE in vol points).
• Stress the calibration: what happens to price if one vol parameter changes?

Completion criterion: calibration done; RMSE reported; stressed parameters.

6. Deliver

Markdown artifact: instrument, model, SDE, price, Greeks, calibration (if applicable), and a model risk note — what the model ignores and what the gap to market means.

Completion criterion: deliverable complete; model risk addressed.