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

Download or read book 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 written by Michel Guirguis and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.