Building Correlated Distributions

Simulations are key #

Whenever you're dealing with economical data, the stuff that is within the
finance and business realm, you will always be looking at how much money you
will make or lose. This I will loosely define as the payoff of a product, say
you buy $100 worth of gummy bears and the next day all the supply of gummy
bears run out, and suddenly your gummy bears are worth $200. So the payoff
would be $100, since you've made $100 essentially. When you're dealing with
prices that will fluctuate over time, you will want to be able to model what
you think the price will be at a certain time.

In the field of electricity wholesale markets, often you will be trading
multiple products in order to hedge the risk of your portfolio. In other to
determine which products you want to buy/sell, you will need to form an
educated opinion on what is going to happen in the future. One of the ways to
do this is to have a payoff distribution model.

Payoff Distribution Model #

I should have began this post by stating that I am by no means an expert on
this matter, and all this technical jargon is pretty much whatever I think is
correct. I've been working within the electricity industry for not a very long
time, and there are still so many intricacies that I don't know or understand.
So to me, a payoff distribution model is a tool that allows you to build
bespoke distributions that you use to evaluate performance and risk of your
portfolio. These distributions are simulated prices for the underlying
product, which can be made to contain all the correlations you desire.

Within the New Zealand Electricity market, the FTR products are offered during
2 auctions per month, which can allow for 2 opportunities to take a bite of
the apple. In order to form an opinion on what price a product might sell for
in an auction, you can create a distribution of possible prices. This is where
a payoff distribution model comes in. We begin with the historical
distribution of payoffs for each product, which gives us a starting point for
the distributions.


Keeping things correlated #

The input into the model will be the historical payoffs for each product in
the auction, and the desired output will be a distribution of prices for each
product. This new payoff distribution will be possible gains or losses from
the result of the auction. This will give a performance measure of the total
portfolio, as a combination of all the payoff distributions. Because of the
nature of electricity, electrons traveling through the grid, there will always
be correlation between all the FTR products.


One method to keep the correlations in tact is to sample from the historical
distributions by grouping the products into clusters first. The clustering of
historical payoffs can then be given labels, depending on if there is an
historical event that can be attributed to those product times in history.
Then for each cluster, we can adjust the probability of the event happening to
each cluster. Using these adjustment values as probability weights, we can
sample from the historical data to get a simulated distribution.

    distribution = sample(historical_payoffs,
                             size = 10000,
                             replace = TRUE,
                             prob = Weights)

This methodology keeps the correlation of the products since within the
historical payoffs, the correlation is there. The flaws in this procedure lie
in the fact that clustering doesn't allow for custom tailored distributions
for each product, but only for each cluster. This results in product payoff
distributions that are not statistically detailed enough. So ideally we want
to able to select each product, view the historical payoff distributions,
build a target distribution, then create the resulting payoff by sampling
using the target and historical distribution.

But then how do we deal with the correlations?

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