As the maturity of the option increases, the percentage impact of non-constant volatility on prices becomes more pronounced, but its percentage impact on implied volatility usually becomes less pronounced. The percentage impact of jumps on both prices and the implied volatility becomes less pronounced as the maturity of the option is increased. The result of all this is that the volatility smile becomes less pronounced as option maturity increases.

Further Explanation

A volatility smile is a pattern in which the implied volatility of options on a particular security or market index increases as the options get further in-the-money or out-of-the-money. This is often seen in markets, including foreign exchange markets, where the underlying price dynamics are not perfectly captured by the lognormal distribution assumption. This can be due to the presence of jumps or changes in volatility, among other factors. When the maturity of an option increases, the impact of short-term jumps or changes in volatility becomes less pronounced, as these short-term effects are averaged out over a longer time period. This can lead to a less pronounced volatility smile for longer maturity options.

Things to Remember

• Volatility smile: A pattern where the implied volatility of options on a security or index increases as the options move further in-the-money or out-of-the-money.
• Implied volatility: The market's expectation of future volatility implied by option prices.
• Lognormal distribution: A probability distribution often used to model asset prices, but may not accurately capture all market dynamics.
• Jumps: Sudden and significant changes in asset prices that can impact option pricing and volatility.
• Option maturity: The time remaining until an option contract expires, affecting the pricing and behavior of options.