Pricing Asian Options Using Maple. Solution using PDE. Monte Carlo Simulation.
The calculation of the Asian option value has posed a great challenge to financial mathematicians as well as practitioners for the last two decades. Since there exists no analytical valuation formula to date, one has to resort to other methods to price this commonly used derivative product. One possibility is the usage of simulation approaches, which however are especially inefficient for Asian options, due to their dependence on the entire stock price trajectory.
Back To Product List. An Asian option or average option is a special type of option contract where the payoff depends on the average price of the underlying asset over a certain period of time. The payoff is different from the case of a European option or American option, where the payoff of the option contract depends on the price of the underlying stcok at exercise date.
Asian options differ in payoff calculation from European and American option. The payoff for an Asian option equals the average price realized minus the strike call or the strike minus the average price realized. Due to the odd payoff of an Asian option, it can not be valued through an analytical formula.
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Asian option also known as average price option is an option whose payoff is determined with respect to the arithmetic or geometric average price of the underlying asset over the term of the option. While the payoff of a standard American and European option depends on the price of the underlying asset at a specific point of time i. There are two types of Asian options with respect to the method of averaging: in arithmetic Asian option, the arithmetic average of the price of the underlying is used in payoff calculations; while in geometric Asian options, geometric average is used.
Calculate price and sensitivities for European or American Asian options using Monte Carlo simulations. For American options, the Longstaff-Schwartz least squares method is used to calculate the early exercise premium. To compute the value of a floating-strike Asian option, Strike should be specified as NaN.
This articles explores Asian options, and offers an Excel spreadsheet based on geometric and arithmetic averages. Of the many types of exotic options that are available for investors, Average Rate Options or, as they are better known, Asian Options are some of the most practical. Asian options are priced based on the average price of the underlying instrument. Both the strike value and expiration value can be calculated from the average value over a period of time.
It is considered "exotic" in the sense that the pay-off is a function of the underlying asset at multiple points throughout its lifetime, rather than just the value at expiry. An Asian option actually utilises the mean of the underlying asset price sampled at appropriate intervals as the basis for its pay-off, which is where the "path-dependency" of the asset comes from. The name actually arises because they were first devised in in Tokyo as options on crude oil futures.
All these methods involve some tradeoffs between numerical accuracy and computational efficiency. This example also demonstrates how variations in spot prices, volatility, and strike prices affect option prices on European Vanilla and Asian options. Asian options are securities with payoffs that depend on the average value of an underlying asset over a specific period of time. Underlying assets can be stocks, commodities, or financial indices.