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Published byHeath Newnam Modified over 2 years ago

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Payout is on MMBtu currency –F T – payout of quanto swap (US$) –P T – gas prices at maturity (US$/MMBtu) –TS – ticket size - volume (MMBtus/HDD) –D T – HDD at maturity –K – fixed temperature (HDD) –T – end of season –Ti – individual day in the season Weather Quanto Swap F T = (P Ti * TS * (D Ti – K))

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Weather Quanto Swap Model Assumptions: –Gas prices are lognormally distributed at maturity (Ti) with volatility p and expected value P t –HDDs are normally distributed with standard deviation d and expected value D t –The Log of Gas prices and HDD expected values are correlated at maturity = correlation (D T, ln(P T ))

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Weather Quanto Swap Pricing the contract: F t = F ti F ti = e -r(T – t) * TS * E[P Ti (D Ti – K)] t Ti T

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Weather Quanto Swap Pricing: Deltas: Cross Gamma: F ti = e -r(T– t) TS [ P ti (D ti –K) + P ti p d * (T i -t)] pi = e -r(T– t) TS [ D ti + p d * (T i -t)] di = e -r(T– t) TS [ P ti ] dpi = pdi = e -r(T– t) TS

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Blended Correlation LN(P gas vs HDD) : t Gas 1ga s 2ga s T1 T2 t HDD 1HDD 2HDD T1 T2 1 2 gas * HDD * (T2 – t) 1 * 1gas * 1HDD * (T1 – t) + 2 * 2gas * 2HDD * (T2 – t) = Weather Quanto Swap

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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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