Put simply, an Asian option is an option contract the payoff of which is determined by the averaging of the underlying over a certain period of time.

Wilmott and E. Haug both point out, Asian options are popular in the OTC energy markets and in other commodity markets lacking liquidity.

In fact, averaging implies reduced price volatility, cheaper option prices, and market manipulations are less-likely. Now, Asian options can be classified along several dimensions , that is: Asian options are classified as average rate or average price or average strike.

For detailed discussions, please refer to P. Wilmott , J.

Hull , and C. The following table shows the possible payoffs:. In the continuous case , the continuously sampled average is modelled as an integral.

Asian option - Wikipedia

In the discrete case, one averages a finite number of option values picked up during the life of the option. For example, we may use a weekly fixing.

In practice due to legal and practical issues , Asian options are generally monitored at discrete time. In the arithmetic case , one has to tackle the problem of solving the standard Black-Scholes equation for V S, A, t with but there is no closed-form solution. In the geometric case , the average is the exponential sum of all the logarithms of the constituent prices, that we divide by the of discretely sampled prices we restrict ourselves to equal time-steps.

But, now the jump condition becomes:. There exist closed-form solutions for geometrically averaged Asian options , as geometric averaging of lognormal random variables preserves lognormality.

And, this is what we are going to code using Quantlib. In fact, Quantlib is endowed with a special option engine to analytically compute the price of discretely and geometrically averaged Asian options using that is the AnalyticDiscreteGeometricAveragePriceAsianEngine class.

We could compare our analytical calculation results with ones drawing from a Monte Carlo simulation if we wish. And, one may wish to price a arithmetic average option thanks to MCDiscreteArithmeticAPEngine.

December 10, Risk-free interest rate: Hi, I wrote an Excel spreadsheet to price Asian options using geometric and arithmetic averages. News and Magazines on Trading GO 2 Computer Science and Trading Technologies.

Recibir nuevas entradas por email. Debe estar conectado para enviar un comentario. The following table shows the possible payoffs: Again, we take the normal Black Scholes equation But, now the jump condition becomes: