Energy Futures Spread/Pairs Trading

- 1 toe (tonne of oil equivalent) = 41.88 GJ (Giga Joules)

- 1 Watt = 1 Joule per second

- 1 kWh = power consumption of 1 kW for one hour

- a 10 W lightbulb left on for two hours will consume 20 Wh

- 1 kWh = (1000 W) * (1 h) = (1000 J/s)*(3600 s) = 3.6 MJ

- Germany consumes around 600 TWh per year, written 600 TWh/a

- 1MBtu = 1 MMBtu = 0.293 MWh

More efficient system consume lower electricity hence it allows firm to pay higher price per electricity using the same budget of 600 euro per tonne

LNG

Exporter: USA, middle east (qatar), russia, australia

Importer: asia (china, japan, korea), europe

Bear calendar spread (also known as a bear time spread)

- works well during contango

- options strategy that involves the simultaneous purchase and sale of two options of the same type (both calls or both puts) on the same underlying asset (natural gas), but with different expiration dates

- 2 legs

- (leg 1) Short Near-Term Option: Selling (writing) a near-term option (call or put) with a closer expiration date.

- (leg 2) Long Far-Term Option: Buying a far-term option (call or put) with a later expiration date.

 

 

A Profit Model for Spread Trading with an Application to Energy Futures

https://www.researchgate.net/publication/254460104_A_Profit_Model_for_Spread_Trading_with_an_Application_to_Energy_Futures

- Natural gas futures trading is more profitable than WTI crude oil and heating oil due to high volatility and long-term mean reversion

- Futures spread trading can produce relatively stable profits for

- To be profitable, (1) incorporate seasonality, (2) require long term mean reversion, (3)  require high volatility

- Assume that price spreads follow a stochastic process. Initial value X at time 0 reaches Y at time τ for the first time. τ is refereed to as the “first hitting time.” τ is presented using a PDF

Case 1: pair converge to 0 within trading period, strategy profits

- fτx→0(t) = first hitting time density

- rp,c = profit if converge  = product of price spread x at time 0 and the probability for price spread convergence until the end of the trading period, because x is given and fixed as an initial value

Case 2: pair doesn't converge to 0 within trading period, strategy losses

- g(y;x,T) = process converge to 0 at time T

- k(y;x,T) = process converge to 0 at time t where t < T. T is the trading period

- x−y = payoff

- rp,nc = profit if no convergence

- g(y;0,T-t) = process start at value x at time t, and end at value y at time T 

- rp = total profit for case 1 and case 2

Curve swtich between backwardation and contango, and curve is sometimes flat during the transition. Strategy: spread trade between different maturity of natural gas futures

Price spreads (Pi−Pj) for i and j month natural gas futures (i<j) --> use a autoregressive 1 lag (AR(1)) model, where εt∼N(0,σ2i,j)

- All coefficients are not effectively 0

- Cij are all negative, meaning theta is negative (theta is long term mean spread), which means long term further-future > nearer-future, hence long term curve is contango

Test statistics < critical level, hence no unit root/ process is stochastic/ process is non-stationary

Order 0 is non-stationary, but first diff is stationary

Linetsky (2004) provides a formula for first hitting time (probability) density for a mean-reverting process from x to 0

large-n asymptotics provide approximations for the terms𝜆𝑛λn​and𝑐𝑛cn​when𝑛n is large

Summary of the 3 Finals Formulas to be used

Total profit

Profitable trades

Losing trades

Applying the 3 equations

- Let κ=0.027,θ=0,and σ=0.013 (estimated using the WTI one- and six- month spread), maturity (or trading period) is 120 days and x=2σ. Then rp = 0.0140

- higher mean reversion or volatility produce a higher expected return

- mean reversion of NG futures price spreads(0.4500) is stronger than for WTI (0.0192) and HO (0.0141). In addition, the volatility of NG(0.0324) is higher than for WTI (0.0081) and HO (0.0101). On the other hand, the expected returnof NG trades (0.0496) is higher than for WTI (0.0050) and HO (0.0029)

Analyzing the strategy and formulas

- keppa (mean reversion strength of spread) and sigma (volatility of spread) affects profitability of strategy 

- The prices are first normalized with the first day’s price as in the figure, which representthe cumulative returnsa

- two assets are chosen such that the standard deviation of the price spreads is the smallest in all combinations of pairs

- (Weather seasonality effect) while the WTI trades produce both gains and losses in the winter, the HO and NG trades always make profits in the winter (Dec -Jan)

- (Weather seasonality effect) NG trade profits in winter (tend to be backwardation) and fall (tend to be contango)