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If for an European call and put option, the stock, stock price, excise price, risk free rate and maturities are

the same, to calculate the implied volatility using Black scholes formula, will it be expected to use the put call parity equation as well resulting in the implied volatility of the put and call options being the same or to use black shoes to calculate the implied volatility for each option separately.

If the implied volatility of the put and call options calculated using black schools model are different, what would be the economic rational for this.

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