Weather Quanto Swap Payout is on MMBtu currency

Weather Quanto Swap • Payout is on MMBtu “currency” – – – – FT – payout of quanto swap (US$) PT – gas prices at maturity (US$/MMBtu) TS – ticket size - volume (MMBtus/HDD) DT – HDD at maturity K – fixed temperature (HDD) T – end of season Ti – individual day in the season FT = S (PTi * TS * (DTi – K))

Weather Quanto Swap • Model Assumptions: – Gas prices are lognormally distributed at maturity (Ti) with volatility sp and expected value Pt – HDDs are normally distributed with standard deviation sd and expected value Dt – The Log of Gas prices and HDD expected values are correlated at maturity r = correlation (DT, ln(PT))

Weather Quanto Swap • Pricing the contract: Ft = S Fti = e-r(T – t) * TS * E[PTi (DTi – K)] t Ti T

Weather Quanto Swap • Pricing: Fti = e-r(T– t) TS [ Pti (Dti –K) + Pti p dr* (Ti-t)] • Deltas: Dpi = e-r(T– t) TS [ Dti + p dr* (Ti-t)] Ddi = e-r(T– t) TS [ Pti ] • Cross Gamma: Gdpi = Gpdi = e-r(T– t) TS

Weather Quanto Swap • Blended Correlation LN(Pgas vs HDD) : Gas 1 gas t HDD t = 1 1 HDD 2 gas T 1 2 2 HDD T 2 1 * 1 gas * 1 HDD * (T 1 – t) + 2 * 2 gas * 2 HDD * (T 2 – t) gas * HDD * (T 2 – t)

Weather Quanto Swap • Relevant points: – Bending the LN(gas)-HDD correlation – Blending the gas volatilities – Delta hedging the gas position close to daily maturity (Ti)