Testing the Implied Volatility Smile of a Lognormal Distribution on a 6 - Month EUR/USD Call Currency Option Contract Using a Random Standard Normal Variable

Download or read book Testing the Implied Volatility Smile of a Lognormal Distribution on a 6 - Month EUR/USD Call Currency Option Contract Using a Random Standard Normal Variable 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 a random standard normal variable. 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 when using a random standard normal variable. There are no speculation opportunities as the 6 - month EUR/USD call currency option is steep and the volatility is decreased.