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Option Pricing is part of financial engineering that focuses on pricing vanilla options (European style, American style) and exotic options (knockouts, double knockouts, basket options, Asian options). Option pricing rests on two techniques:

1] perfect or imperfect replication of the option with simpler assets whose prices are known,

2] pricing an option by modeling its underlying asset(s) as a complex stochastic process whose parameters are calibrated to the market.

Option pricing involves relatively little statistics. Typically, we are not fitting the model to historical data. We are not concerned with identifying the most statistically efficient technique making use of every observation in a long historical time window. We are fitting the model to one observation only but that fit must be perfect or nearly perfect. The observation represents the most recent prices of the liquid products in the same market. These prices are taken as an axiom and, for that reason, option pricing employs many more results from probability theory than from applied or theoretical statistics.

Option pricing is one the greatest successes of mathematics in the world of finance. Surprisingly many options can be priced relatively accurately by the methods of stochastic calculus, partial differencial equations, numerical methods and Monte Carlo.


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