LTCM's blowup had nothing to do with any flaw in Black-Scholes. They did lose money on equity volatility strategies but it was because they were betting that volatility in the future would be lower than the volatility implied by Black-Scholes. Volatility ended up going up and they lost money. They lost money because their forecast of volatility was wrong, not because Black-Scholes was wrong about the market's view of volatility.