Explanation:
The implied volatility of a European call option is the same as that of a European put option when they have the same strike price and time to maturity. The volatility smile provides their pictorial representation.
Things to Remember
The 'volatility smile' is a graphical representation of an option's implied volatility. It is called a 'smile' because the graph typically slopes upwards at both ends, resembling a smile.
The implied volatility of a European call option is the same as that of a European put option when they have the same strike price and time to maturity. Therefore, their volatility smiles would also be the same.
The volatility smile is dependent on the strike price and time to maturity of the option. Therefore, options with different maturities would have different volatility smiles, even if their strike prices are the same.
Traders often use the volatility smile as a pricing tool for their financial securities.
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Q.1707 The term “volatility smile” is a pictorial representation of an option’s implied volatility and it is being used by the traders as a pricing tool for their financial securities. Which of the following statement is correct about volatility smiles?
A
The volatility smile for European call-options with a certain maturity and strike price is the same as that for European put-options with the same maturity and strike price.
B
The volatility smile for European call-options with a certain maturity and strike price is different from that for European put-options with the same maturity and strike price.
C
The volatility smile for European call-options with a shorter maturity and same strike price is the same as that for European put-options with a longer maturity and the same strike price.
D
None of the above.
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