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Future of option pricing: use of log logistic distribution instead of log normal distribution in Black Scholes model

Raja, Ammar (2009): Future of option pricing: use of log logistic distribution instead of log normal distribution in Black Scholes model.

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Abstract

Options are historically being priced using Black Scholes option pricing model and one of the prominent features of it is normal distribution. In this research paper I will calculate European call options using log logistic distribution instead of normal distribution. My argument is that a model with logistic distribution reflects better fit of option prices as compared to normal distribution. In this research paper I have used historic data on stocks, value European call options using both logistic and normal distribution and then finally compare the results in order to check the validity of my argument. What I have found is that European call options prices based on log logistic distribution better reflect stock prices on expiry date and Black Scholes Model based on normal distribution tend to overprice European call options. Another interesting fact is that before 1987 stock market crash, Black Scholes model valued options more correctly on average. But with time as the volatility of stocks increased and with more and more crashes normal distribution tend to underestimate the probability of default and thus generally overpriced options. At this point of time log logistic distribution is better serving the purpose but all depends on volatility of the stocks. If volatility levels further increase then fat tails of log logistic distribution have to become even fatter, that’s why keeping an eye on facts and incorporating all relevant variables in your model is very important. In finance there is never a universal truth every thing depends on what’s happening in the market.

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