105–18barrier shifts 60–3, 64, 67–9, 96, 104,161–3Black–Scholes options pricing formula6–7call spread option strategy 35–7cliquet options 83–5concepts 3–8, 12, 16–18definition 3–4, 105forward starting options 71–5, 80–1,83–5, 111forwards 6, 8–9, 12implied volatility 27–34, 35, 36–7, 58,66–8, 71, 72–5, 85, 141–2, 147–8,156lookback options 79–81put spread option strategy 37–9put–call parity 12skew 27–34, 35, 58, 66–8, 71, 72–5,85, 141–2, 147–8, 156variance swaps 139–49, 155,169–74structured productsdouble barrier options 68down-and-in put barrier options 57financially engineered structures157–65hybrids 138supertrackers 164–5swaps 91, 139–49, 169–74see also variance swaps
Index
Taylor expansion 147, 167term structure of the skewsee also skewconcepts 28–30, 73–4forward starting options 73–4thetaarithmetic Asian out options 110concepts 1, 18–20, 23–4, 75, 110,142–5definition 18expected profits 24gamma 23–4variance swaps 142–5time, theta 18–20, 23–4, 75, 110, 142–5time to maturity 6–21, 23–4, 28–30, 62,75, 110, 121, 142–5Black–Scholes options pricing formula6–7, 121down-and-in put barrier options 62skew 28–30theta 18–20, 23–4, 75, 110, 142–5TomTom shares 41–2, 43–4uncertainty contrasts, volatility 27–8,32–3unconditional coupons, autocallablenotes 94, 97–8unconditional double barrier optionssee also double barrier optionsconcepts 69underlying share pricesBlack–Scholes options pricing formula6–8, 45, 121delta 12–14, 21, 23–4, 25–6, 29–32,40, 58–63, 109–12, 122–3,126–8, 132–3, 156gamma 14–16, 23–4, 25–6, 27, 29, 54,60, 75, 79–80, 110, 113–15,142–5variance swaps 139–49, 155, 169–74up-and-in call barrier options, concepts58, 68up-and-in put barrier options, concepts 58up-and-out call barrier optionsbarrier shifts 64, 68–9concepts 16–17, 58, 63–5, 67–9,78–80, 103definition 63implied volatility 16–17, 64–5pricing 64–5rebates 64, 77–8
187
risk 58, 63–5, 67–8skew 67–8vega exposure 16–17, 64–5up-and-out put barrier optionsconcepts 58, 65, 68definition 65skew 68USD composite options 125–8USD quanto options 119–23USD/EUR exchange rate, skew 32–4vannasee also vegaconcepts 19–21definition 19variancesee also volatilitycomposite options 126, 167–8outperformance options 131, 167–8variance notionalconcepts 140–9, 155vega 147–8, 155variance swapsassumptions 147–8concepts 139–49, 169–74definition 139, 146delta 141–5, 147–8, 156dispersion trading 153, 155event risk 146–7gamma 142–5, 146–7the Greeks 140–7mystery of gamma/delta 144–5payoff profiles 139–40, 142pricing 140–2realised-variance/standard-deviationcontrasts 139–40, 145–6replication 140–9, 169–74skew delta 141–2, 147–8, 156standard deviation 141–2, 145–6theta 142–5vega 142–5, 147–9, 153vegasee also implied volatility; vanna;vommaarithmetic Asian out options 110basket options 153–5concepts 1, 16–18, 37, 64–5, 74–5,80–1, 90–1, 110, 142–5, 147–9,153–5convexity principle 148–9definition 16
188
Index
vega (Continued)dispersion 153–5exotic options 16–17forward starting options 74–5, 80–1gamma comparisons 18ratio’s vega dispersion 155up-and-out call barrier options 16–17,64–5variance notional 147–8, 155variance swaps 142–5, 147–9, 153volatilitysee also implied . . . ; varianceAsian options 107, 115barrier shifts 60–2, 64, 67–9, 96, 161–3basket options 151–6Black–Scholes options pricing formula6–8, 45, 107, 121concepts 6–8, 16–18, 151–6dispersion 151–5down-and-in put barrier options 60–2falling markets 27–8FX 120–3, 126–8uncertainty contrasts 27–8, 32–3variance swaps 139–49, 169–74
volatility hedge, reverse convertibles90–1vommasee also vegaconcepts 19–21definition 19VW shares 37–8, 129–33, 135–8worst of optionsconcepts 135, 137–8correlation risk 135, 137–8definition 135hybrids 138payoff profiles 137pricing 135yield curves 91zero coupon bondssee also financially engineeredstructuresconcepts 157–9, 160–5interest rates 159
Index compiled by Terry Halliday
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