Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 577

INDEX

A regular: Accrual barriers, 515 knock-in call options, 390, Accrual forwards, 395, 518–521 443–444 Accrual options, 395, 515–521 knock-out call options, 390, 439–443 accrual forwards, 518–521 577 range accrual, 516–518 pricing, 445 Adapted , 275–285 reverse: delta, 276–279 knock-in, 390, 445, 450 knock-out, 390, 445–450 gamma, 279–281 pricing, 450–452 risk management with, 282–285 selling, 468–471 vega, 221, 281–282 strike-out options, 454–460 Agreeing broker market data, 311–312 transatlantic, 392–394 American barrier options, 388–394, American digitals, 388 424, 439–460 American keep accrual discrete,COPYRIGHTED 394 MATERIALbarrier, 515 double knock-out and knock-in, American keep range accruals, 390, 391, 452–453 517–518 in-the-money, 392 American vanilla options, 394, knock-in/knock-out replication, 501–510 453–454 call and put, 14 knock-out–knock-in, 394 and Greeks, 506–509 Monte Carlo pricer, pricing, 509 492–493 Arithmetic average, 534 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 578

Asian options, 396, 527–538 seasonality, 346 average rate options, 527–535 slope, 354–356 average strike options, 535–537 theta and roll down, 271, 272 double average rate options, weighted changes in, 154 537–538 ATM gamma, 272 Ask, see Offer(s) ATM position: ATM, see At-the-money defined, 138 ATM calendar spreads: trading, 152–155 price making, 132 ATM and correlation trading exposures, 132 framework, 313–321 vanilla, 132 ATM volatility triangles, 313–319 ATM curve, 103–106 cross-currency positions construction of, 171–191 management, 321 adding weights, 199–204 dephased vega, 319–320 core ATM curve, 172–179 ATM volatility triangles, 313–319 events and holidays, 188–189 At-the-money (ATM). See also ATM in Excel, 193–204 curve and FX forward , 171–172 pricing, 182–184 implied volatilities of, 103–105 578 implied volatility patterns over a market conventions, 118–120 week, 182 vega exposures, 209–211 and volatility smile, 205

INDEX intraday variance patterns, 187 New York cut vs. Tokyo cut volatility spreads, 113–114 pricing, 185–187 zero-delta , 122 overnight ATM on a Friday, Average rate options, 396, 527–535 184–185 Average strike options, 535–537 pricing same-day options, Axe, 468 190–191 for short-dates, 180–191 B using a model, 178–179, Bank trading desks, 39–40. See also 197–199 Interbank broker market using interpolation, 172–178, client types, 40–41 193–197 structure, 41–44 variance, 171–172 internal trading, 43–44 weekday variance patterns, sales desks, 42–43 189–190 support functions, 43 in market instrument analysis, Barrier delta gap (touch options), 344–346 429–430 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 579

Barrier options, 388–394 multi-asset options, 541 American, 389–394. See also one-touch options, 434 American barrier options self-quanto vanilla options, 514 continuous, 388, 424 vanilla, 113–116 discrete, 394, 482 Binary options, 388 European, 388–389. See also Black-Scholes delta, 276 European barrier options Black-Scholes formula, 18, 66–67 in-the-money, 392 Black-Scholes framework, 57–68 late-starting, 478 Black-Scholes formula, 66–67 shadow, 466–467 solving Black-Scholes SDE, 62–65 transatlantic, 392–394 stochastic differential equation, window, 395, 473–482 57–62 front-window, 395, 473–478 terminal spot distributions in generic, 481 calculating option values, 65–66 Monte Carlo option pricer, 493 Black-Scholes option pricer (Excel), rear-window, 395 91–101 risk management, 481–482 generate first-order Greeks, 98–100 Basis point, 120, 164 plot exposures, 100–101 Basket digitals, 543 set up simple option pricer, 91–96 Basket options, 396, 541–543 set up VBA pricing function, 96–98 579 Bending barriers, 466 Black-Scholes stochastic differential INDEX Best-of (BO) options, 396, 548–553 equation (SDE), 57–62 switching hedge, 553 drift in, 58–61 trading risks, 549–553 solving, 62–65 Bet spread, 410 uncertainty in, 61–62 Bid(s), 19–22 Bleed, delta, 266, 268–269 in choice markets, 21 BO options, see Best-of options defined, 19 Breakeven calculation, 323–325 in inverted market, 21 Broker fly, 127, 225 language of, 23 Broker market, see Interbank broker leaving orders, 22 market midmarket, 117–118 Broker market data, agreeing, Bid–offer spread, 22–23 311–312 European barrier options, 418 Bucketed vega exposures, 154 European digital options, 405 Butterfly (fly), 126–128, 225–230 exotic FX derivatives, 462–463 25d vs. 10d, 229–230 front-window barrier options, drivers of, 228 476–478 price making, 128 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 580

Butterfly (fly), (Continued) Continuous compounded interest trading, 228–229 rate, 160 trading exposures, 128 Conventions: vega exposures, 213–215 market, 306 and volatility smile, 106, 205 quoting delta, 264 Buying: Copula approach, 224 in faster markets, 21 Core ATM curve construction, methods of, 20 172–179 Buying interest, 50 using a model, 178–179 using interpolation, 172–178 C Corporate clients, 40–41 Call, 14 Correlation, 313. See also ATM Call/put spreads: volatility and correlation price making, 134 framework vanilla, 132–134 realized spot vs. interest rate, Carry trades, 352–354 336–339 Cash balance theta, 272 trading implied correlation, Cash-or-nothing options, 388 341–342 Cash price, in Excel Black-Scholes Correlation swaps, 342, 397 580 option pricer, 94 Cross-currency pairs, 7 Cash settlement: ATM volatility triangles, 313–319

INDEX of European digital options, 399 dephased vega, 319–320 of vanilla FX derivatives, 18 managing exposures in, 321 CCY, see Currencies Cross , 224–225 Choice (in spread), 304 Currencies (CCY), 3 Choice markets, 21 delta and CCY1 vs. CCY2 premium, Choice price (risk reversals), 265–267 129, 130 European digital option replication: Client types (derivatives market), CCY1, 402–403 40–41 CCY2, 402 Cliquets, 568 G10, 4 Closed-form approach, 98 one-touch options variations CCY1 Closing out risk, 24 vs. CCY2 payout, 434–435 , see Risk reversal (RR) relative strength of, 219 Compound options, 396, 570–572 self-quanto: Confidence intervals, 248 CCY1 call options, 510 Confidence interval spreading, 541 CCY1 put options, 510–513 Continuous barriers, 388, 424 Currency blocks, 42 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 581

Currency pairs, 3, 8 Delta exchange, 463 ATM volatility triangles, 313–319 Delta gap: cross, 7. See also Cross-currency American barriers, 469 pairs touch options, 429–430 in describing vanilla FX options, 14 Delta hedging, 118, 144–145 G10, 8, 9 , 83 major, 7 Delta risk: market conventions, 118–120 best-of and worst-of multiple, payoff in, see Multi-asset options, 550 options target redemption options, 524 names of, 8–9 Dephased vega, 319–320 pegged, 306–307 Deposits (depos), 160 quoting, 8 principal protected, 466 Cut(s): structured, 465–466 in describing vanilla FX options, 15 Depth (market), 20 New York vs. Tokyo, 185–187 Derivatives, 11. See also foreign exchange (FX) derivatives D Digital bets, 388 Daily variance, 173, 175 Digital options: DCDs (dual currency deposits), 41 American, 388 581 Decay, 143 basket, 543 INDEX Delivery dates, 17, 162–163 dual, 397, 543–548 Delta: trading risks, 545–546 adapted, 276–279 vega risk, 546–548 bleed, 266, 268–269 European, 388, 399–411 CCY1 vs. CCY2 premium, 265–267 bid–offer spread, 405 in Excel Black-Scholes option pricer, European digital range, 401–411 98–101 Greeks, 405–409 forward delta vs., 263–264 pricing, 403–405 low delta vanilla options, 310–311 replication, 400–403 quoting conventions, 264 European digital range, 401–411 sticky, 276 European digital spread, 410 touch options, 424–425, 429–430 Direct market, 39 vanilla FX derivatives, 83–87 Discrete barrier options, 394, 482 vanilla price making, 118 DNT (double-no-touch) vanilla trading low delta options, options, 388 310–311 Double average rate options, Delta bleed, 266, 268–269 537–538 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 582

Double knock-out and knock-in Greeks, 405–409 options: gamma and pin risk, 408–409 American, 390, 391 vega risk, 406–408 American barrier, 452–453 pricing, 403–405 Double-no-touch (DNT) options, 388 replication, 400–403 Drift (SDE), 58–61 CCY1, 402–403 Dual currency deposits (DCDs), 41 CCY2, 402 Dual digital options, 397, 543–548 European digital range, 401–411 trading risks, 545–546 European digital spread, 410 vega risk, 546–548 European knock-in (EKI), 389, 413, 418–420 E European knock-out (EKO), 389, 413, Early ending barriers, 473 416–417 Economic time, 200 European range accruals, 516–517 EKI, see European knock-in European vanilla options: EKO, see European knock-out call and put, 14 Emerging market (EM) countries: variations for changing trading risks currency flows mechanisms, 8 on, 497–514 currency pair names, 9 American , 501–510 582 European accrual barrier, 515 late-delivery, 497–503 European barrier options, 388–389, self-quanto payoff, 509–514

INDEX 413–422 Events: bid–offer spread, 418 and ATM curve construction, Greeks, 419–422 188–189 gamma and pin risk, 422 defined, 188 vega risk, 420–422 EWMA (Exponentially Weighted intrinsic value, 417–418 Moving Average) volatility, knock-in, 413, 418–420 331–333 knock-out, 413, 416–417 Excel: Monte Carlo option pricer, 492 Black-Scholes option pricer, 91–101 pricing, 422 generate first-order Greeks, replication: 98–100 European knock-in, 418–420 plot exposures, 100–101 European knock-out, 416–417 set up simple option pricer, European digital options, 388, 91–96 399–411 set up VBA pricing function, bid–offer spread, 405 96–98 European digital range, 401–411 constructing ATM curve, 193–204 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 583

generating probability density use Black-Scholes to get strike functions from option prices, from 253–259 delta, 235 generating tenor dates, 165–168 Exchange rate, 3 Monte Carlo option pricer, Exercise: 485–496 vanilla call options, 12 extensions, 496 vanilla put options, 13 multi-asset simulation, 494–496 Exotic FX derivatives, 355–356 pricing barrier options, 492–493 defined, 11, 355 set up multiple payoffs, 490–492 pricing, 357–373 set up simulation, 485–487 example of, 359–360 set up vanilla option payoff and path dependence, 373 Monte Carlo loop, 487–490 stopping time, 370–371 numerical integration option pricer, volatility smile pricing, 360–367 69–75 VVV (vega/volga/vanna) pricing, set up option payoff and calculate 368–372 option price, 72–75 pricing models, 375–385 set up terminal spot distribution, interest rate models, 375 69–72 models, 383–384 testing, 75 models, 380–382 583 trading simulator, 27–37 mixed volatility models, 382–383 INDEX extensions, 36–37 smile models, 375 introduce price-making stochastic interest rate models, functionality, 35–36 384–385 set up ticking market price, models, 27–31 377–380 set up two-way price and product classification, 387–397 price-taking functionality, 32–35 accrual options, 395 volatility smile construction, American vanilla options, 394 233–240 Asian options, 396 investigate strike placement, barrier options, 388–394 238–240 basket options, 396 plot implied volatility vs. delta, best-of and worst-of options, 396 234–235 compound options, 396 plot implied volatility vs. strike correlation swaps, 397 with VBA functions, 236–238 dual digital options, 397 set up Malz smile model, European digital options, 388 233–234 first-generation exotics, 387–395 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 584

Exotic FX derivatives, (Continued) F forward start options, 396 Fat-tailed distributions, 244–248 forward volatility agreements, Figure (spot moves), 4 397 Fill-or-kill orders, 22 quanto options, 394–395 Finite difference approach, 98 second-generation exotics, First exit time, 370 395–396 First-generation exotics, 387–395 target redemption options, 395 Fix (FX rate), 8 third-generation exotics, Fixing risk (target redemption 396–397 options), 525 touch options, 388 Fly, see Butterfly volatility and variance swaps, 397 Foreign exchange (FX) derivatives, window barrier options, 395 11–18 trading, 461–471 trading volumes, 18 bid–offer spread, 462–463 vanilla call and put options, 11–18 interbank broker market, 463 Foreign exchange (FX) derivatives investment products, 465–466 market. See also Market analysis recycling risk, 467–468 (FX derivatives) risk management, 461–462 ATM curve construction and 584 and selling American barriers, pricing, 182–184 468–471 liquidity, 294–296 shadow barriers, 466–467 INDEX structure of, 39–55 structured FX hedging strategies, client types, 40–41 463–465 interbank broker market, Expected life, 370 47–55 Expiry/expiry date: interbank direct market, 46–47 in describing vanilla FX options, 15 junior trader tips, 44–46 ‘‘good’’ and ‘‘bad’’ dates, 151 trading desk structure, 41–44 New York vs. Tokyo cuts, 185–187 trading internship tips, 44 stick strike analysis, 351 transaction sizes, 294 vanilla call options, 17 transaction speed, 293–294 vanilla FX derivatives, 162–163 Foreign exchange (FX) market, 3–9 vanilla put options, 13, 17 aspects of, 7–8 Exponentially Weighted Moving cross currency pairs, 7 Average (EWMA) volatility, currencies, 3 331–333 currency pairs, 3 Extensions, in Excel trading simulator, derivatives market language, 36–37 156–157 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 585

exchange rate, 3 FX market, see Foreign exchange forwards (forward outrights), 3 market FX contracts, 4 FX swap contracts, 4. See also Swaps long positions, 5 main product areas, 11 G major currency pairs, 7 Gamma, 270–271 names of currency pairs, 8–9 adapted, 279–281 short positions, 6 ATM, 272 size of, 7 European barrier options, 422 spot rate (spot), 3 European digital options, 408–409 swap points (forward points), 3 gamma/strike profile, 151–152 Forwards (forward outrights), 3, long: 11, 288 P&L distributions from, 273–274 Forward delta, spot delta vs., 263–264 trading, 139–143 Forward extra strategy, 464 positive, 79 Forward implied volatility (forward ‘‘renting,’’ 184 vol), 171–172 short: Forward points, 4. See also Swap points P&L distributions from, 273–274 Forward roll, theta, 271, 272 trading, 145–146 smile gamma effect, 272–273 585

Forward start options (cliquets), 396, INDEX touch options, 428–429 568–570 trading, 138–146 Forward volatility, spot volatility vs., delta hedging, 144–145 470–471 long gamma, 139–143 Forward volatility agreements (FVAs), short gamma, 145–146 341, 397, 566–568 in trading short-date position, Front-window barrier options, 395, 150–152 473–478 vanilla FX derivatives, 88–89 payoff risk, 475–476 Gamma adaption effect, 279 risk, 474–475 Gamma risk (target redemption trading risks, 476–478 options), 524 Future cash, interest rate risk and, 288 Garman and Kohlhagen formula, 67 Future valuing (vanilla FX Gartman’s rules of trading, 300 derivatives), 160 ‘‘Given’’ bids, 23 FVAs, see Forward volatility Greeks: agreements and American vanilla options, FX derivatives, see Foreign exchange 506–509 derivatives European barrier options, 420–422 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 586

Greeks: (Continued) Implied volatility: gamma and in risk, 422 at-the-money contracts, 103–105 vega risk, 420–422 forward ATM, 171–172 European digital options, 405–409 implied vs. realized market analysis, gamma and pin risk, 408–409 325–343 vega risk, 406–408 Exponentially Weighted Moving in Excel Black-Scholes option pricer, Average volatility, 331–333 98–100 realized spot volatility vanilla FX derivatives, 83–90 calculation, 328–331 delta, 83–87 realized spot vs. interest rate gamma, 88–89 calculations, 336–339 vega, 89–90 realized spot vs. realized forward variance swaps, 562–564 volatility, 333–336 volatility swaps, 557–561 realized volatility convexity, 342–343 H trading implied correlation, Hedges: 341–342 delta hedged transactions, 87, 118 trading implied volatility, rho hedge, 463 339–341 586 structured strategies for exotics, at longer tenors, 328 463–465 midmarket, 113 switching hedge, 553 INDEX patterns over a week, 182 vega hedge, 463 quoting, 294 Hedge funds, 41 trading, 339–341 Historic spot volatility, see Realized volatility smiles, 108 spot volatility Implied volatility differential, 130 ‘‘Hit’’ bids, 23 Instant one-touch options, 435 Holding period, bid–offer spread and, Instant touch options, 388 22 Institutional clients, 41 Holidays, ATM curve construction Interbank broker market, 39–40, and, 189 47–55 Horizon date (vanilla call and put agreeing broker market data, options), 17 311–312 Horizontal spreads, 132 broker fly contracts, 127 exotic FX derivatives, 463 I main firms, 47 Implied correlation, trading, 341–342 pricing, 49, 50 Implied skew, 220 quoting implied volatility in, 294 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 587

relative power of brokers, 50 J structure, 47–49 Jargon, 156–157 trader/broker relationship, 49–50 Jump diffusion pricing models, transaction process in, 50–54 383–384 Interbank direct market, 46–47 Junior trader tips, 44–46 Interest rate(s), 4 continuous compounded, 160 K correlation between spot and, 434 KIKO, see Knock-out–knock-in barrier and risk reversals, 219–220 options zero, 160 Knock-in options: Interest rate carry, 456 American barrier options: Interest rate correlation, realized spot regular barrier, 443–444 correlation vs., 336–339 reverse barrier, 445, 450 Interest rates markets, 306 European, 389, 413, 418–420 Interest rate pricing models, 375, European barrier options, 413, 384–385 418–420 Interest rate risk (rho), 287–292 Knock-out–knock-in (KIKO) barrier future cash and forwards, 288 options, 394 long ATM , 291–292 American: double, 452–453 587

long vanilla call options, 288–290 INDEX replication, 453–454 long vanilla put options, 290–291 European, 413, 416–417 Interest rate volatility, 433 Knock-out options: Internal trading, among trading desks, American barrier options: 43–44 front-window, 473–474 In-the-money (ITM): rear-window, 479–480 barrier options, 392 regular barrier, 439–443 vanilla call and put options, 17 reverse barrier, 445–450 Intraday variance patterns, ATM curve European, 389, 413, 416–417 construction and, 187 Intrinsic value, 79 L defined, 417 Late cash vanilla options, 497–498 European barrier options, 417–418 Late delivery, 161, 501 front-window barrier options, 474 Late-delivery vanilla options, 497–503 Inventory management, 26 late cash, 497–498 Inverted market, 21 option on forwards, 498–500 Investment products, exotic, 465–466 Late-starting barriers, 478 ITM, see In-the-money Leaving orders, 22 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 588

Legs, 4, 304 implied vs. realized analysis, Leptokurtotic distributions, 242 325–343 Leverage, 447 Exponentially Weighted Moving Leveraged forward, 131, 311 Average volatility, 331–333 ‘‘Lifted’’ offers, 23 realized spot volatility Limit orders, 21 calculation, 328–331 Linear variance, 174–177 realized spot vs. interest rate Liquidity, 22 correlations, 336–339 in FX derivatives market, 294–296 realized spot vs. realized , 306 volatility, 333–336 Live trading (vanilla price requests), realized volatility convexity, 118 342–343 Local volatility pricing models, trading implied correlation, 380–382 341–342 Log contract, 556 trading implied volatility, Long-dated FX derivatives, 305–306 339–341 Long positions: market instrument analysis, defined, 5 344–352 interest rate risk: ATM curve, 344–346 588 long ATM straddle, 291–292 historical, 350–351 vanilla call options, 288–290 market positioning, 351–352 vanilla put options, 290–291

INDEX value analysis, 346–350 Long strike position, 143 volatility smile, 346, 351 Low delta options, 310–311 Market conventions, 306 at-the-money, 118–120 M vanilla price making, 118–120 Major currency pairs, 7 Market instruments: Malz smile model, 232–234 defining volatility smile, Malz volatility smile formula, 232 205–208 Markets: vega exposures, 209–216 choice, 21 Market instrument analysis, interest rates, 306 344–352 inverted, 21 ATM curve, 344–346 Market analysis (FX derivatives), historical, 350–351 323–354 market positioning, 351–352 breakeven calculation, value analysis, 346–350 323–325 volatility smile, 346, 351 carry trades, 352–354 Market liquidity, 306 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 589

Market making, 23–26 dual digital options, 543–548 Market positioning, 306, 351–352 trading risks, 545–546 Market sentiment, 117 vega risk, 546–548 Market tenor: quanto options, 553–554 ATM contracts, 103–104 trading risks, 539–540 generating dates in Excel, 165–168 N vanilla FX derivatives, 161–163 Non-Deliverable Forward (NDF) expiry dates and delivery dates contracts, 8 calculation, 162–163 Non-optimal exercise, 501 spot dates calculation, 161–162 Notional, 4 Mark-to-market P&L, 155 butterfly, 128 Maturity, 3, 15. See also Tenor in describing vanilla FX options, 15 Merton model, 383–384 European digital replication, Middle office, 42 400–401 Midmarket bid, 117–118 vanilla call and put options, 12 Midmarket offers, 117 No-touch (NT) options, 388, ‘‘Mine!,’’ 23 424, 438 Mixed volatility pricing models, Numerical integration option pricer 382–383 (Excel), 69–75 589 Monte Carlo option pricer (Excel), set up option payoff and calculate INDEX 485–496 option price, 72–75 extensions, 496 set up terminal spot distribution, multi-asset simulation, 494–496 69–72 pricing barrier options, 492–493 testing, 75 set up multiple payoffs, 490–492 set up simulation, 485–487 O set up vanilla option payoff and Offer(s), 19–22 Monte Carlo loop, 487–490 bid–offer spread, 22–23 Moving Average, Exponentially in choice markets, 21 Weighted, 331–333 defined, 19 Multi-asset options, 539–554 in inverted market, 21 basket options, 541–543 language of, 23 best-of and worst-of options, leaving orders, 22 548–553 midmarket, 118 switching hedge, 553 One-touch (OT) options, 388, 424 trading risks, 549–553 bid–offer spread, 434 bid–offer spread, 541 pricing, 430–434 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 590

One-touch (OT) options, (Continued) set up multiple payoffs, 490–492 variations, 434–436 set up simulation, 485–487 CCY1 vs. CCY2 payout, set up vanilla option payoff and 434–435 Monte Carlo loop, 487–490 pay-at-maturity vs. pay-at- numerical integration option pricer, touch, 435–436 69–75 O/N options, see Overnight options set up option payoff and calculate Optionality of contracts, 79 option price, 72–75 Option on forward, 498–500 set up terminal spot distribution, Option on strategy, 572 69–72 Option orders, 303–304 testing, 75 Option payoff, in Excel numerical Option values: integration option pricer, 72–75 terminal spot distributions in Option premium: calculating, 65–66 conversions for vanilla FX vanilla FX derivatives, 77–82 derivatives, 163–164 Order book, 20 and delta, 265 OTC (over-the-counter) market, 39, vanilla calls, 12 294 and variance, 180–181 OT options, see One-touch options 590 Option price: Out-of-the-money (OTM), 17 generating probability density Overnight (O/N) options: ATM on a Friday, 184–185

INDEX functions from, 253–259 in numerical integration option expiry and delivery dates, 162 pricer, 72–75 vanilla trading, 296–299 Option pricers (Excel): Over-the-counter (OTC) market, 39, Black-Scholes option pricer, 91–101 294 generate first-order Greeks, 98–100 P plot exposures, 100–101 ‘‘Paid’’ offers, 23 set up simple option pricer, Parallel ATM shift, 106 91–96 Partially exercised options, 151 set up VBA pricing function, Path dependence, in pricing exotic FX 96–98 derivatives, 373 Monte Carlo option pricer, Path-dependent options, in SDE, 485–496 59–60 extensions, 496 Pay-at-maturity one-touch options, 436 multi-asset simulation, 494–496 Pay-at-touch one-touch pricing barrier options, 492–493 options, 436 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 591

Payoff risk (front-window barrier Price takers, 19–20 options), 475–476 Price-taking functionality, in Excel Payout direction risk (best-of and trading simulator, 32–35 worst-of options), 550–553 Pricing. See also Option pricers (Excel) pdfs, see Probability density functions American regular barrier options, Pearson’s coefficient, 336 445 Pegged currency pairs, 306–307 American reverse barrier options, Physical delivery, of vanilla FX 450–452 derivatives, 18 American vanilla options, 509 Pin risk: and ATM curve construction, European barrier options, 422 182–184 European digital options, 408–409 European barrier options, 422 touch options, 428–429 European digital options, 403–405 vanilla trading, 310 exotic FX derivatives, 357–373 Pips (points), 4 example of, 359–360 P&L, see Profit and loss path dependence, 373 Positions, quoting, 5 stopping time, 370–371 Positive spreads, 307–308 volatility smile pricing, 360–367 Premium firm orders, 303–304 VVV (vega/volga/vanna) pricing, Present valuing (vanilla FX derivatives), 368–372 591 159, 160 one-touch options, 430–434 INDEX Price makers, 19–20 same-day options, 190–191 Price making: target redemption options, 525 ATM calendar spreads, 132 vanilla FX derivatives, 103–120 butterfly, 128 maintaining volatility surfaces, call/put spreads, 134 103–116 risk reversal, 129–130 price making, 116–120 seagull, 135 variance swaps, 565–566 straddles, 122 volatility swaps, 564–565 strangles, 125–126 Pricing models, 375–385 success in, 26 interest rate, 375 vanilla FX derivatives, 116–120 jump diffusion, 383–384 market conventions, 118–120 local volatility, 380–382 overview, 116–118 mixed volatility, 382–383 transacting delta hedged or live, smile, 375 118 stochastic interest rate, 384–385 Price-making functionality, in Excel stochastic volatility, 377–380 trading simulator, 35–36 Principal protected deposits, 466 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 592

Probability density functions (pdfs), Realized skew, 220 241–252 Realized (historic) spot volatility: confidence intervals, 248 calculating, 326, 328–331 in Excel numerical integration in market analysis, 325–343 option pricer, 70–72 Exponentially Weighted Moving fat-tailed distributions, 244–248 Average volatility, 331–333 generated from option prices in realized spot vs. interest rate Excel, 253–259 correlations, 336–339 and volatility smile parameterization realized spot vs. realized forward limitations, 249–252 volatility, 333–336 Profit and loss (P&L), 6, 7 realized volatility convexity, distributions from long or short 342–343 gamma, 273–273 trading implied correlation, quoting, 5 341–342 trading, 155–156 trading implied volatility, in trading short-date position, 339–341 148–149 and sample frequency/sample time, vanilla call and put options, 15–16 327–328 Public holidays, 189 Realized volatility convexity, 342–343 592 Put–call parity, 86–87 Real money, 41 Rear-window barrier options, 395, Q

INDEX 478–481 Quants (quantitative analysts), 42 Rebates, 388 Quanto options, 394–395, 553–554 Recycling risk, 467–468 self-quanto, 394, 509–514 Rega, 230, 231 bid–offer spread, 514 Regional banks, 41 CCY1 call options, 510 Regular barrier options (American): CCY1 put options, 510–513 knock-in call options, 443–444 third currency, 395, 553–554 knock-out and knock-in, 390 knock-out call options, 439–443 R pricing, 445 Rainbow options, 548 Replication: Ranges: American barrier DNT options as, 388 knock-in/knock-outs, European digital, 401–411 453–454 Range accrual options, 516–518 European digital options, 400–403 American keep range, 517–518 CCY1, 402–403 European, 516–517 CCY2, 402 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 593

European options: touch options, 428–429 barrier, 416–420 vanilla trading, 310 digital, 402–403 recycling risk, exotic FX derivatives, Replication spreading, 541 467–468 Retail clients, 41 trading risks: Reverse barrier options (American), best-of and worst-of options, 439 549–553 knock-in, 445, 450 dual digital options, 545–546 knock-out, 445–450 European vanilla options, 497 knock-out and knock-in, 390 front-window barrier options, pricing, 450–452 476–478 Rho, see Interest rate risk multi-asset options, 539–540 Rho hedge, 463 vega risk: Risk: best-of and worst-of options, closing out, 24 549–550 cross risk reversal, 224–225 dual digital options, 546–548 delta risk: European barrier options, best-of and worst-of options, 550 420–422 target redemption options, 524 European digital options, fixing risk, target redemption 406–408 593 options, 525 target redemption options, INDEX front-window barrier options, 522–524 474–475 touch options, 425–428 gamma risk, target redemption warehousing, 24 options, 524 writing off risk, 308–310 interest rate risk, 287–292 Risk management: future cash and forwards, 288 with adapted Greeks, 282–285 long ATM straddle, 291–292 exotic FX derivatives, 461–462 long vanilla call options, 288–290 success in, 26 long vanilla put options, 290–291 vanilla FX derivatives, 137–157 payoff risk, front-window barrier FX derivatives market language, options, 475–476 156–157 payout direction risk, best-of and trading ATM position, 152–155 worst-of options, 550–553 trading gamma, 138–146 pin risk: trading P&L, 155–156 European barrier options, 422 trading short-date position, European digital options, 146–152 408–409 volatility smile, 230–231 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 594

Risk management: (Continued) Shadow barriers, 466–467 window barrier options, 481–482 Short-date positions: writing off, 308–310 ATM curve construction, 180–191 Risk reversal (RR), 128–131, 217–225 events and holidays, 188–189 25d vs. 10d, 222–224 FX derivatives market pricing, cross, 224–225 182–184 drivers of, 219–220 implied volatility patterns over price making, 129–130 a week, 182 trading, 220–222 intraday variance patterns, 187 trading exposures, 130–131 New York cut vs. Tokyo cut vega exposures, 211–213 pricing, 184–187 and volatility smile, 106, 205 overnight ATM on a Friday, Risk reversal multipliers, 222 184–185 Risk/reward preference, bid–offer pricing same-day options, spread and, 22–23 190–191 RR, see Risk reversal weekday variance patterns, Run (of prices), 103 189–190 defined, 138 S long ATM vs. short wings, 302–303 594 SABR model, 232 spot ladder, 138 Sales desks, interaction of trading desks trading, 146–152

INDEX and, 42–43 gamma, 150 Same-day options, pricing, 190–191 gamma/strike profile, 151–152 SDE, see Black-Scholes stochastic P&L balance, 148–149 differential equation strikes, 150–151 Seagull, 134–135 theta, 149–150 Second-generation exotics, 395–396 vanilla trading, 302–303 Sega, 230, 231 Short positions, 6 Self-quanto options, 394 ‘‘Short ten dollar-cad,’’ 5 Self-quanto vanilla options, 509–514 Skew: bid–offer spread, 514 in analyzing value, 346–348 CCY1 call options, 510 implied, 220 CCY1 put options, 510–513 and pdf tilt, 242–243 Selling: pricing the, 361–364 American barriers, 468–471 realized, 220 in faster markets, 21 volatility smile, 106, 112, 217, 346. methods of, 20 See also Risk reversal Selling interest, 50 Slang, 156–157 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 595

Smile gamma effect, 272–273 one-touch options, 434 Smile position, 272 self-quanto vanilla options, 514 Smile pricing models, 375 vanilla, 113–116 jump diffusion, 383–384 call/put: local volatility, 380–382 price making, 134 mixed volatility, 382–383 vanilla, 132–134 stochastic volatility, 377–380 confidence interval spreading, 541 Smile volatility roll, theta, 271 defined, 304 Smoothing barriers, 466 horizontal, 132 Sovereigns, 41 positive, 307–308 Speed of transactions, in FX derivatives replication spreading, 541 market, 293–294 vanilla trading: Spot (spot rate), 3–6, 11 positive, 307–308 Spot dates, 3, 161–162 quoting, 304–305 Spot delta, see Delta vertical, 134 Spot dynamic, 469 Spread contracts, see Risk reversal (RR) Spot firm orders, 303 Spread price: Spot jumps, 245, 246 call/put, 134 Spot ladder, 138 risk reversals, 130 Spot market: Standardized language, 8–9 595 limited open hours, 469–470 Stick strike analysis, 351 INDEX speed of transactions, 3 Sticky delta, 276 Spot rate (spot), 3–6, 11 Sticky strike, 276 Spot volatility, forward volatility vs., Stochastic interest rate pricing models, 470–471 384–385 Spread(s): Stochastic local volatility models, 382 ATM calendar: Stochastic Volatility Inspired (SVI), 232 price making, 132 Stochastic volatility pricing models, trading exposures, 132 377–380 vanilla, 132 Stop-loss orders, 22, 429 bet, 410 Stopping time, in pricing exotic FX bid–offer, 22–23 derivatives, 370–371 European barrier options, 418 Straddles: European digital options, 405 long ATM, interest rate risk, exotic FX derivatives, 462–463 291–292 front-window barrier options, price making, 122 477–478 trading exposures, 124 multi-asset options, 541 vanilla, 121–124 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 596

Straddles: (Continued) Swap points (forward points), 3, 4, 335 zero-delta: Switching hedge (best-of and worst-of ATM contracts, 122 options), 553 strike placement, 122–124 Synthetic forwards, 86–87 Strangles, 125–126 price making, 125–126 T trading exposures, 126 Take-profit orders, 22, 429 Strike(s): Target month, 153 in describing vanilla FX options, 15 Target redemption forward (TARF), gamma/strike profile, 151–152 395 stick strike analysis, 351 Target redemption options, 395, sticky, 276 521–525 in trading short-date position, delta and gamma risk, 524 150–152 fixing risk, 525 vanilla call and put options, 12 pricing, 525 Strike fly, 225 vega risk, 522–524 Strike-in options, 392 Temporary market sentiment, 117 Strike-out options, 392, 454–460 Tenor, on forwards, 3. See also Market Strike placement: tenor 596 and risk reversal trading, 221 Terminal spot distributions: zero-delta straddles, 122–124 in calculating option values, 65–66

INDEX Strike topography, 146, 147 in Excel numerical integration Structural market sentiment, 117 option pricer, 69–72 Structured deposit, 465–466 Terminology, 156–157 Structured FX hedging strategies, Theoretical Value (TV), 357–358 463–465 Theta, 270–271 Structurers, 42 ATM curve roll, 271, 272 SVI (Stochastic Volatility cash balance, 272 Inspired), 232 defined, 143 Swaps, 4 forward roll, 271–272 correlation, 342, 397 in trading short-date position, defined, 11 149–150 variance, 397, 555–557 volatility smile roll, 271 Greeks, 562–564 Third currency quanto options, 395, pricing, 565–566 553–554 volatility, 340, 397, 555–557 Third-generation exotics, 396–397 Greeks, 557–561 Ticking market price, in Excel trading pricing, 564–565 simulator, 27–31 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 597

Time: risk reversal, 130–131 economic, 200 straddles, 124 stopping, 370–371 strangles, 126 Time decay, 143 vanilla FX derivatives, 263–292 Time value, 79 adapted Greeks, 275–285 Time zones, expiry and delivery dates delta, 263–269 and, 153 gamma and theta, 270–274 Touch options, 388, 423–438 interest rate risk, 287–292 barrier delta gap, 429–430 vega and weighted vega, delta risk, 424–425 274–276 gamma and pin risk, 428–429 zeta, 285–287 no-touch options, 438 Trading internship tips, 44 one-touch options: Trading risks: bid–offer spread, 434 best-of and worst-of options, pricing, 430–434 549–553 one-touch variations, 434–436 dual digital options, 545–546 CCY1 vs. CCY2 payout, European vanilla options, 497 434–435 front-window barrier options, pay-at-maturity vs. pay-at-touch, 476–478 597

435–436 multi-asset options, 539–540 INDEX vega risk, 425–428 Trading short-date position, 150 Tradable rates, 104 Trading simulator (Excel), 27–37 Trade queries, 146, 147 extensions, 36–37 Traders, 41–42 introduce price-making Trading, 19–26 functionality, 35–36 bids and offers, 19–22 set up ticking market price, 27–31 bid and offer language, 23 set up two-way price and bid–offer spread, 22–23 price-taking functionality, 32–35 leaving orders, 22 Trading volumes, 18 FX derivatives market, 18 Transactions: market making, 23–26 quoting, 5 price making, 26 size of, 19, 294 risk management, 26 speed of, 293–294 Trading desk structure, 41–44 Transatlantic barrier options, 392–394 Trading exposures: TV (Theoretical Value), 357–358 ATM calendar spreads, 132 TV adjustment, 358 butterfly, 128 Two-way price, 20, 32–35, 113 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 598

U maintaining volatility surfaces, Uncertainty (in SDE), 61–62 103–116 Updating volatility surfaces, 110–113 price making, 116–120 risk management, 137–157 V FX derivatives market language, Value: 156–157 intrinsic, 79 trading ATM position, 152–155 defined, 417 trading gamma, 138–146 European barrier options, trading P&L, 155–156 417–418 trading short-date position, front-window barrier options, 146–152 474 structures, 121–135 terminal spot distributions in ATM calendar spreads, 132 calculating, 65–66 butterfly, 126–128 Theoretical, 357–358 call/put spreads, 132–134 time, 79 leveraged forward, 131 vanilla FX derivatives, 77–82 risk reversal, 128–131 Value analysis, 346–350 seagull, 134–135 Vanilla FX derivatives: straddle, 121–124 598 call and put options, 11–18 strangles, 125–126 American, 14 trading, 293–312

INDEX details required to describe, agreeing broker market data, 14–15 311–312 European, 14 client option orders, 303–304 interest rate risk on, 288–291 Gartman’s rules of trading, 300 future valuing, 160 long-dated FX derivatives, Greeks: 305–306 delta, 83–87 low delta options, 310–311 gamma, 88–89 overnight options, 296–299 vega, 89–90 pegged currency pairs, 306–307 market tenor calculations, 161–163 pin risk, 310 option premium conversions, positive spreads, 307–308 163–164 quoting spreads, 304–305 option value, 77–82 short-date trading, 302–303 physical delivery vs. cash settlement vega positioning, 301–302 of, 18 writing off risk, 308–310 present valuing, 159, 160 trading exposures, 263–292 pricing, 103–120 adapted Greeks, 275–285 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 599

delta, 263–269 market instruments, 209–216 gamma and theta, 270–274 at-the-money, 209–211 interest rate risk, 287–292 butterfly, 213–215 vega and weighted vega, 274–276 risk reversal, 211–213 zeta, 285–287 vanilla FX derivatives, 89–90 Vanilla FX derivatives variations, VVV (vega/volga/vanna) pricing, 497–514 368–372 American, 501–510 weighted, 154, 274–276 and Greeks, 506–509 Vega hedge, 463 pricing, 509 Vega positioning, 301–302 late-delivery, 497–503 Vega risk: late cash, 497–498 best-of and worst-of options, option on forwards, 498–500 549–550 self-quanto, 509–514 dual digital options, 546–548 bid–offer spread, 514 European barrier options, 420–422 CCY1 call options, 510 European digital options, 406–408 CCY1 put options, 510–513 target redemption options, 522–524 Vanna, 210, 211, 213–215, 230 touch options, 425–428 defined, 209 Vega/volga/vanna (VVV) pricing, VVV (vega/volga/vanna) pricing, 368–372 599 368–372 Vertical spreads, 134 INDEX Variance: Volatility. See also ATM volatility and and ATM construction, 171–172, correlation framework; Implied 189–190 volatility defined, 171 and bid–offer spread, 22 linear, 174–177 Exponentially Weighted Moving and option premium, 180–181 Average, 331–333 weekday variance patterns, 189–190 and liquidity, 295 Variance (var) swaps, 397, 555–557 realized spot volatility calculation, Greeks, 562–564 328–331 pricing, 565–566 realized spot vs. realized forward Vega, 274 volatility, 333–336 adapted, 221, 281–282 realized volatility convexity, bucketed vega exposures, 154 342–343 defined, 209 spot vs. forward, 470–471 dephased, 319–320 vanilla call options, 12 in Excel Black-Scholes option pricer, zero, 58 98–101 Volatility cones, 344 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 600

Volatility firm orders, 304 Volatility smile construction (Excel), Volatility of volatility, 245 233–240 Volatility smile: investigate strike placement, at-the-money contracts, 205 238–240 butterfly contracts, 205, 225–230 plot implied volatility vs. delta, 25d vs. 10d, 229–230 234–235 drivers of, 228 plot implied volatility vs. strike with exposures, 213–215 VBA functions, 236–238 trading, 228–229 set up Malz smile model, 233–234 construction methods, 232 use Black-Scholes to get strike from defined, 106 delta, 235 in exotic FX derivatives pricing, Volatility surfaces, 169 360–367 ATM curve, 169. See also ATM in market instrument analysis, 346, curve 351 in pricing vanilla FX derivatives, market instruments defining, 103–116 205–208 ATM curve, 103–106 market instrument vega exposures, bid–offer spreads, 113–116 209–216 updating, 110–113 600 at-the-money, 209–211 volatility smile, 106–110 butterfly, 213–215 volatility smile, 169. See also

INDEX risk reversal, 211–213 Volatility smile parameterization limitations, Volatility (vol) swaps, 340, 397, 249–252 555–557 risk management, 230–231 Greeks, 557–561 risk reversal contracts, 205, pricing, 564–565 217–225 Volatility triangles, ATM, 313–319 25d vs. 10d, 222–224 Volga, 210–213, 215, 216, 230, 231 cross, 224–225 defined, 209 drivers of, 219–220 VVV (vega/volga/vanna) pricing, exposures, 211–213 368–372 trading, 220–222 VVV (vega/volga/vanna) pricing, skew, 106, 112, 346, 361–364. See 368–372 also Risk reversal stick strike analysis, 351 vanilla FX derivatives, 106–110 W wings, 106, 112, 348–349, Warehousing risk, 24 364–367. See also Butterfly (fly) Weekday variance patterns, 189–190 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 601

Weights, added to ATM curve, Worst-case selling rate, 13 199–204 Worst-of (WO) options, 396, Weighted ATM shift, 106, 107 548–553 Weighted vega, 154 switching hedge, 553 Window barrier options, 395, trading risks, 549–553 473–482 Write-off book, 309 front-window, 395, 473–478 Writer, 12 payoff risk, 475–476 Writing off risk, 308–310 risk, 474–475 trading risks, 476–478 Y generic, 481 ‘‘Yours!,’’ 23 Monte Carlo option pricer, 493 rear-window, 395, 478–481 Z risk management, 481–482 Zero-delta straddles: Wings (volatility smile), 106, 112, ATM contracts, 122 348–349. See also strike placement, 122–124 Butterfly (fly) Zero interest rates, 160 in analyzing value, 349–350 Zero-premium collar, 129 and pdfs, 241–244 Zero premium transactions, 464 pricing, 364–367 Zero volatility, 58 601 WO options, see Worst-of options Zeta, 285–287 INDEX Worst-case purchasing rate, 12 Z-score, 350 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 602 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 603 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 604 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 605 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 606 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 607 Jewitt bindex.tex V1 - 05/19/2015 1:43 P.M. Page 608