# FT = S (PTi * TS * (DTi – K))

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FT = S (PTi * TS * (DTi – K))
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: r = correlation (DT, ln(PT))
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))

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

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

Weather Quanto Swap  = T1 T2 Blended Correlation LN(Pgas vs HDD) :
1 2 1 * 1gas * 1HDD *  (T1 – t) + 2 * 2gas * 2HDD *  (T2 – t)  = gas * HDD *  (T2 – 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)

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