Options are securities that are difficult to price. In particular American options, which can be exercised at any time posed a serious challenge that could only be solved in approximation with some Nobel Prize winning work. European options are simpler because they can only be exercised at maturity. Today, I learned there are also Asian options. Asia seem really to catch up in all aspects of economic life. Asian options are American options with the difference that the exercise price is some form of average of the underlying price.
Paolo Foschi, Stefano Pagliarini and Andrea Pascucci provide a way to price Asian options in a first approximation under local volatility, that is the price volatility depend on the current price level, and provide an algorithm for higher order approximations. As you may guess, it is not straightforward. Along the way, I also learned about the Greeks in option pricing. They measure various aspects of the sensitivity of option prices to underlying parameters, and they are usually represented by Greek letters. Now that I have learned that, I'll leave the actual pricing of Asian options to others.