Comparing implied vols from two quotes

Two market-makers quote the same European call - identical spot, strike, expiry, and interest rate - but dealer A's price is higher than dealer B's. Realized (historical) volatility of the underlying is the same for both. What can you conclude about the implied volatilities the two dealers are quoting?

Show hints (2)+
  1. Implied vol is backed out of the price; with all else equal, the price differs only through σ.
  2. Vega is positive - a pricier call means a higher implied vol.

Answer

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Dealer A is quoting the higher implied volatility, since option price rises monotonically with vol

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Asked at: Timed Mental-Math & Sequences, Game-Based Aptitude

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