Vol Surface Analysis

The scenario

You're handed this morning's option chain for a single name — a grid of strikes and maturities with market prices. The vol desk wants the implied-volatility surface behind it: back out each option's implied vol, assemble the surface, show the smile and term structure, and flag anything that looks like static arbitrage.

Where this shows up

Task brief

# Implied Vol Surface Construction

**Role relevance:** A classic vol-desk research take-home.
**Estimated time:** 60-90 minutes
**Difficulty:** Advanced
**Format:** Jupyter notebook (.ipynb) + option-chain CSV; requires numpy, pandas, scipy, matplotlib

## What you are given
- `option_chain.csv` - strikes x maturities with market call prices
- `vol_surface_analysis_starter.ipynb` - `bs_call` provided; the implied-vol inversion is left to you

## What you must deliver
1. Implied vol for every option (robust root-finder)
2. The implied-vol surface across strike and maturity
3. Smile/skew plots per maturity and the ATM term structure
4. A static-arbitrage (calendar) check

## Constraints
- Use a bracketed root-finder; handle inversion failures gracefully.

## Submission note
Complete `implied_vol` in the notebook, run all cells, then check the mark scheme.

Your tasks

1. 01Invert Black-Scholes to recover the implied volatility for every option in the chain (use a robust root-finder).
2. 02Assemble the implied-vol surface across strike (or moneyness) and maturity.
3. 03Plot the smile/skew per maturity and the at-the-money term structure.
4. 04Check for obvious static-arbitrage violations (e.g. non-increasing ATM total variance across maturities).

How you're assessed

The full points-based mark scheme is included with the pack.

What you'll learn

• ▸Why implied vol differs from a single Black-Scholes number — the smile and skew.
• ▸How to invert a pricing model robustly with a bracketed root-finder.
• ▸The basic no-arbitrage constraints a real vol surface must respect.

Study alongside