Testing the Implied Volatility Smile of a Lognormal Distribution on a 3 – Month Lundbeck Option Call Option Contract Using the Brownian Motion

We analyze the implied volatility smile of a lognormal distribution on a 3 – month Lundbeck call option contract using the Brownian motion. 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 using the Brownian motion help us to price the contract at a different market prices 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 Lundbeck 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. The Brownian motion displays increased volatility of the 3 – month Lundbeck call contract that is due to the interaction of arbitrageurs and noise traders. In addition, brownian motion is used to show the dynamic behaviour of the real value of the 3 -month Lundbeck call contract using the fisher effect