Recent geopolitical events and the ongoing effects of the Covid19 pandemic have seen large swings in commodity prices in recent years, particularly in oil and gas prices. Unsurprisingly, many of your clients are trying to understand these markets and your first task, should you choose to accept it, is to analyse the current crude oil and natural gas markets and their forward curves. Such forward curves provide important information about market conditions for traders and investors. Prices for NYMEX Henry Hub Natural Gas futures and NYMEX WTI light sweet crude oil futures contracts (both traded on CME) are presented in Table 1 below. In particular, futures contracts expiring up to July 2024 are provided. We also know that on 19 July 2022 the spot price of natural gas was USD7.531 per MMBtu (one million British thermal units) and the spot price of light crude oil was USD103.45 per barrel. Table 1: NYMEX Henry Hub Natural Gas futures prices and NYMEX WTI light sweet crude oil

futures prices observed on 19 July 2022 Expiry Month Natural Gas Light Crude Oil Aug '22 7.439 102.64 Sep '22 7.326 99.11 Oct '22 7.339 96.00 Nov '22 7.382 93.43 Dec '22 7.485 91.15 Jan '23 7.560 89.37 Feb '23 7.270 88.13 Mar '23 6.264 86.23 Apr '23 4.919 86.15 May '23 4.814 85.32 Jun '23 4.844 84.24 Jul '23 4.912 83.91 Aug '23 4.901 83.30 Sep '23 4.908 82.71 Oct '23 4.952 82.16 Nov '23 5.116 81.65 Dec '23 5.354 80.78 Jan '24 5.483 80.62 Feb '24 5.317 80.11 Mar '24 4.946 79.61 Apr '24 4.329 79.13 May '24 4.279 78.71 Jun '24 4.358 78.05 July '24 4.432 77.88

(a) First, a client asks you to plot the forward curves (as of 19 July 2022) for both the NYMEX Henry Hub Natural Gas futures and the NYMEX WTI light sweet crude oil futures contracts. You should plot these on the same set of axis with timetodelivery on the xaxis rather than the delivery date itself. So you can compare, you should also scale the futures prices by the current spot price, so that both forward curves start at 100 at timetodelivery equals zero. For simplicity you should assume that the timetodelivery is rounded off to the nearest month; e.g. 1 month for Aug 22 contracts, 2 months for Sep 22 contracts.