hard · Principles of Finance

An investor views a volatility smile in the S&P 500 index option market where the implied volatility of out-of-the-money (OTM) puts is significantly higher than at-the-money (ATM) calls.

This 'skew' most directly contradicts which assumption of the Black-Scholes-Merton model?

  1. The assumption that the underlying asset price follows a geometric Brownian motion with constant volatility.
  2. The assumption that the options are European-style and cannot be exercised early.
  3. The assumption that there are no transaction costs or taxes in the secondary market.
  4. The assumption that the risk-free rate is known and constant over the life of the option.

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