Comparing European and American Implied Volatility from a CEV Model

Summary

The document proposes simulating equity prices under a constant elasticity of variance model, then pricing European and American options across strikes and maturities. It asks whether implied volatilities inferred from those prices would form the same surface for both exercise styles. The implied volatility is defined by fitting a constant volatility geometric Brownian model to each option price.

This setup highlights that implied volatility depends on the pricing model and option exercise feature, not only on strike and maturity. The document offers a research question rather than a result: it gives no simulation output, comparison, or explanation of how early exercise affects the inferred values. Any conclusion would also depend on the model parameters, rates, dividends, and numerical pricing methods, none of which are specified beyond the proposed dynamics.

Key ideas

• The proposed experiment simulates equity paths using a CEV process and prices options across strikes and maturities.
• It compares implied volatilities fitted from European and American option prices.
• The fitted volatility comes from a geometric Brownian pricing model, distinct from the CEV process used to generate prices.
• The document asks whether the resulting surfaces match but supplies no findings.

Tags

# Implied Vol under CEV model


# Implied Vol under CEV model












Consider the following steps:

- Suppose the underlying equity follows a CEV model $dS_t = rS_t dt + \sigma S^{0.5} dW_t$.

- Use the above CEV model to simulate Monte Carlo paths and price a large set (across different maturities and strikes) of European and American prices.

- Backout the implied volatilities, for each $(K,T)$ pair using the options prices. By implied volatility, I mean the $\sigma$ in $dS_t = rS_tdt + \sigma S_t dW_t$ to match the option prices (either American or European).

My question is: Is the implied volatility surface using the European options the same as the one using the American options?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.