question archive Consider the case where the left tail of the implied distribution is fatter than that of the log-normal distribution and the right tail of the implied distribution is thinner than that of the log-normal distribution with the same mean and standard deviation
Consider the case where the left tail of the implied distribution is fatter than that of the log-normal distribution and the right tail of the implied distribution is thinner than that of the log-normal distribution with the same mean and standard deviation
Subject:FinancePrice:2.86 Bought7
Consider the case where the left tail of the implied distribution is fatter than that of the log-normal distribution and the right tail of the implied distribution is thinner than that of the log-normal distribution with the same mean and standard deviation. Which of the following statements is correct?
A. The implied volatility increases as the strike price increases.
B. The implied volatility of a deep out-of-the money call is greater than the price obtained from the Black-Scholes model.
C. The market price of a deep out-of-the money call is smaller than the price obtained from the Black-Scholes model.
D. The implied volatility of a deep out-of-the money put is smaller than the price obtained from the Black-Scholes model.
Please explain and justify your choice using your own words. In your answer, discuss the shape of the relation of implied volatility with the strike price and explain how this is obtained using your own words.
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In this case, it can be seen that the left tail of the implied distribution is fatter than that of the lognormal distribution and the right tail is thinner than that of log normal distribution, and hence it is a reflection of the implied volatility of deep out of the money put is smaller than the price from the black-scholes model as it will be leading into fatter implied distribution and it will be reflecting that the put option is having a lower valuation as it is an out of money option and it will be not equating that of the valuation of the black sholes as per the European Model
All the other options are false.
Correct answer is option (D).
