Asian option code

Asian options are path-dependent options whose payoff depends on the average value of the underlying asset during a specific set of dates across the life of the option. Because the payoff of the Asian options depends on the average value of the underlying asset, volatility in the average value is lower than that of the plain vanilla options. Thus Asian options tend are less expensive than the comparable plain vanilla options. This makes Asian options ideal for use in hedging positions. The averaging in Asian options can either be arithmetic or geometric. In this blog post we will be pricing continuously sampled arithmetic Asian options using moment matching under the Black Scholes framework. We compare this moment matching with a Monte Carlo simulation.

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.

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.

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