Testing the Implied Volatility Smile of a Lognormal Distribution on a 6 – Month EUR/USD Call Currency Option Contract Using the Ratio of Strike and Share Price

We analyze the implied volatility smile of a lognormal distribution on a on a 6 – month EUR/USD call currency option contract using the ratio of strike and share price. 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 6 – month EUR/USD call currency option contract is overpriced relative to other call market prices. The 6 – month call contract with long maturity show low market standard deviation relative to the other call prices. Arbitrageurs check regularly the bid – ask spread to benefit from the mispricing. They check the steepness of the volatility smile to benefit from in the money call option