15. (Requires Writing Code) Can GARCH models develop an option smile? Simulate option prices (puts and calls) for a maturity of a half year and an initial stock price of $50; let the initial volatility equal 30% per annum. Choose various strike prices and parameter values for the volatility process such that you are able to generate a left skew of implied volatility where the implieds are generated from the Black-Scholes model after prices are generated by the GARCH model.
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