In this tutorial we will be pricing an Average Price Option (APO) otherwise commonly referred to as an Asian Option. We will be pricing a bespoke OTC electricity average rate option in the Australian Electricity Market.

We will also investigate how to use a combination of monte carlo variance reduction techniques to reduce the standard error in our monte carlo pricing in an efficient way. We use the closed form solution for a geometric asian option as a 'good' static hedge within our monte carlo simulation of the arithmetic asian option and show how to decrease the standard error by a factor of 66x by using a combination of monte carlo variance reduction techniques.

Electricity Average Rate Options in Australia / NZ Energy Markets are settled against the final futures prices. As futures are settled against the arithmetic average of the wholesale energy market price. Therefore final futures prices converge on the arithmetic average of wholesale electricity price. This essentially means listed ASX energy average rate options can be priced using blackscholes until the end of the quarter.

However, to demonstrate pricing of and Average Rate Option, and make things more interesting we will be looking at an OTC Asian Option over Q123 with the underlying as the Q123 NSW futures contract. Let's say the average rate option prices are determined by the average of the (closing) daily futures prices across the Q123 period.

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00:00 Intro
01:15 Monte Carlo Pricing of Asian Options
02:54 Australian Electricity Average Rate Options
06:12 In Reality, you can use Black-Scholes .... Why?
07:30 Bespoke OTC Asian Option
08:32 Slow Solution Steps
11:45 Fast Implementation
13:55 Antithetic Variance Reduction
15:47 Geometric Asian Option Control Variate
19:32 Combining Antithetic and Control Variates
20:54 Comparing Variance Reduction Methods

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