Testing the Implied Volatility Smile of a Lognormal Distribution on a 3 – Month Danske Bank Call Option Contract Using the Option Delta

We analyze the implied volatility smile of a lognormal distribution on a 3 – month Danske bank call option contract using the option delta. There is significant time variation in the implied volatility smile and the traditional Black – Scholes model can not explain this deviation. The Black – Scholes model is used to calculate the theoretical call option price. Applying a lognormal implied distribution help us to price the contract at a market price and get better estimates of a risk adjusted measure. Deep in or out of the money contract has higher implied volatility. We have found that the 3– month Danske bank call option contract is not overpriced relative to other call market prices. The 3 – month call contract with short maturity show high market standard deviation relative to the other call prices. Possible explanations of volatility smile are bid – ask spreads, transactions costs and leverage