Implied Volatility (Simulated Data)¶

Background¶

Black Scholes Iv Simulated

Educational script demonstrating black scholes iv simulated concepts.

Code¶

```python """ Black Scholes Iv Simulated

Educational script demonstrating black scholes iv simulated concepts. """

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black_scholes_IMPLIED_VOLATILITY.py¶

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import black_scholes as bs

Create model with synthetic data¶

if name == "main": model = bs.BlackScholesImpliedVol(S0=100, K=100, T=0.25, r=0.05, sigma=0.2, tol=0.3) model.create_synthetic_data()

# Compute implied volatilities
bs.compute_implied_volatilities_and_summarize(model, sigma_0=2.0)

# Run advanced analysis
bs.run_advanced_analysis_on_implied_vol(model)

```

Exercises¶

Exercise 1. Synthetic option data is generated using known \(\sigma = 0.2\). After computing IV, all recovered values should be 0.2. What errors might cause deviations?

Exercise 2. Explain the flat volatility smile that results from GBM-generated option prices. What model feature would create a non-flat smile?

Exercise 3. For the synthetic data with \(S_0 = 100\), \(\sigma = 0.2\), \(T = 0.25\), compute the ATM straddle price (call + put) and its sensitivity to \(\sigma\).

Exercise 4. The advanced analysis includes term structure and skew metrics. For flat IV, what should the term structure slope and skew be?