document: Option pricing formulas based on a non-Gaussian stock price model Options are financial instruments that depend on the underlying stock . We explain their non-Gaussian fluctuations using the nonextensive thermodynamics parameter q . A generalized form of the Black-Scholes -LRB- BS -RRB- partial differential equation -LRB- 1973 -RRB- and some closed-form solutions are obtained . The standard BS equation -LRB- q = 1 -RRB- which is used by economists to calculate option prices requires multiple values of the stock volatility -LRB- known as the volatility smile -RRB- . Using q = 1.5 which well models the empirical distribution of returns , we get a good description of option prices using a single volatility
doc_bio_tags: B I I O O O B I I I O O B I O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O
extractive_keyphrases: nongaussian stock price model financial instruments option pricing formulas nonextensive thermodynamics parameter stock volatility volatility smile empirical distribution
abstractive_keyphrases: black-scholes partial differential equation closed-form solutions