Price Formulation

The calculation steps are as follows:

• Subscribe to as many levels of depth as available using each exchange's streaming APIs.
• Remove any price feeds for which there have been no market data updates for the last 30 seconds
• Remove any price feeds with crossed buy and sell prices or whose top-of-book mid-price is more than 10% away from the median top-of-book mid-price across all price feeds.
• Wait until there are at least 6 valid price feeds. If there are not enough price feeds, the BetFury index price will not be updated.
• Combine all resting limit orders from each price feed into a single composite order book. It is okay and expected that the price of some buy orders will exceed the price of some sell orders from other exchanges. Individual order sizes are capped to $1 million to limit the influence of a single large order.
• Using the composite order book, a function is defined to represent the marginal price to buy or sell a given amount. For example, the marginal buying function is:
  P_buy(s) = max{ґp_i | sum_{i in 1..N}{s_i} <= s}
  where p_i | i in 1..N and s_i | i in 1..N are the buy prices and sizes sorted in increasing distance from the top-of-book. This function gives the maximum price one would pay to buy an amount s.
• The marginal buy and sell price functions are then used to define a marginal mid-price function given a size:
  P_mid(s) = (P_buy(s) + P_sell(s)) / 2
• The final index price is then calculated as the weighted average of the marginal mid-prices at each size. The weights are chosen to be the probability density of the exponential distribution, which is monotonically decreasing, resulting in a higher emphasis on prices closer to the top-of-book. The weights are given by:
  w_i = L * exp(-L * v_i)

Where v_i are the sizes at which the mid-prices are calculated and are defined as the union of the cumulative buy and sell sizes from the composite order book. L is a scaling factor defined as 1 / V, where V is the maximum size at which a mid-price is calculated and is defined as the minimum of the sum of buying and selling sizes in the composite order book.

The output of this calculation is a single index price that is used for both long and short bets in the BetFury trading game. Unlike with most other trading platforms, BetFury does not charge a bid-offer spread. Trading with a single price makes it possible to speculate on short-term price moves for which a bid-offer spread would be prohibitively expensive.