Options Market Making and Hedging

1.A call is worth $2.36 per share at your current inputs. Your minimum half-spread is $0.07, and executable quotes must be in $0.05 ticks. What is the tightest outward-rounded quote?

2.A market maker sells 12 contracts at $1.52 versus a fair value of $1.47. Each contract represents 100 shares. What is the gross edge versus fair value at execution?

3.A call's theoretical value is $3.20 and delta is +0.55. Spot rises $0.40. Holding all other inputs fixed and using delta only, what is the new theoretical price?

4.A put's delta is −0.32. Spot rises $0.25. What first-order adjustment should the trader make to its fair value, with volatility and other inputs fixed?

5.A call has vega of $0.14 per share per volatility point and a fair price of $2.80. At fixed spot, the relevant implied volatility rises from 22% to 24%. What is the approximate new fair price?

6.Two series both move by one implied volatility point. Their vegas are $0.06 and $0.19 per share per point. Which quote center moves farther in premium terms, all else equal?

7.A trader quotes 21% bid and 23% offer in implied volatility. For this option, vega is $0.11 per share per point near the center. What is the approximate full premium spread before tick rounding?

8.A volatility surface updates, but the underlying input has not refreshed despite a large stock move. What should the trader do before sending new option prices?

9.A listed option has a theoretical value below its tick size. Why can a fixed one-tick spread be misleading when comparing that quote with a high-premium series?

10.Your book is already long vega in one expiry. You want to attract option buyers and deter new sales into your bid there. At unchanged model values, which inventory adjustment fits?

11.You are short vega in a downside wing. Which quoting adjustment helps buy back some of that exposure while reducing the chance of selling more, all else equal?

12.The stock hedge spread widens during a brief liquidity drop. Your option fair values are unchanged. What quoting adjustment addresses the larger expected hedge cost most directly?

13.A near-expiry at-the-money option has high gamma. Underlying depth is thin and quotes may remain live through several ticks. Why might the trader cut size?

14.An earnings release falls between two expiries. The later expiry includes the event, but the earlier one does not. What should the quoting model distinguish?

15.One downside strike trades much richer in volatility after a large put order, while nearby strikes barely move. What should the trader check before lifting the whole surface?

16.A low-strike put's implied volatility rises 3 points while an at-the-money option's implied volatility rises 1 point in the same expiry. What changed beyond the common increase?

17.A call and put have the same strike and expiry. Assume European exercise, zero rates, no dividends, and stock at $51. The strike is $50 and the call is $2.90. What put value is consistent with parity?

18.Two European calls share an expiry. The lower strike is $45 and the higher strike is $50. A fitted model values the lower-strike call below the higher one. What should happen before quoting?

19.A European call spread buys a $90 strike and sells a $95 strike for the same expiry. Rates are zero. What is the upper bound on its model premium per share under no arbitrage?

20.An option's market bid is above your model offer. Why should you validate data before treating this as an execution opportunity?

21.The desk's fair value model uses the wrong dividend date for contracts expiring near the ex-date. Which quote correction matters?

22.A market maker sells a call at $2.10, with a model mark of $2.04, but the immediate stock hedge costs an estimated $0.08 per option-share equivalent of premium edge. What is net modeled edge after this cost?

23.A market maker can quote a tight option spread only by assuming the entire hedge executes at the best stock offer. What evidence supports a more realistic width?

24.A market has several thin strikes whose posted mids imply erratic volatility jumps. What makes a fair-value fit more robust?

25.A client asks for a 40-lot quote on a call spread. Why check the executable market for the package as well as both legs?

26.A put-spread quote is derived from independent marks for both legs. The quoted package offer would exceed the strike width for a European debit spread with zero rates. What is the appropriate check?

27.Two otherwise comparable series have the same theoretical edge per contract. One hedge must be executed in a slower, thinner underlying market. What belongs in the quote decision?

28.A quoted bid assumes the book can buy 20 calls, but only 8 more calls fit the current vega limit at that series' sensitivity. What is the largest size under that single constraint?

29.A desk sees buyers lift its at-the-money offers repeatedly after an underlying update. Its marks still use the pre-update stock price. What should the desk address first?

30.A market maker uses the same dollar half-spread on options with very different vegas. What comparison reveals how that policy differs across contracts?

31.A market maker leaves old quotes live while entering replacement quotes for the same expiry. What should count in the pre-trade risk check if both sets can execute?

32.A volatility jump raises the model price, but the desk is long vega and wants to quote lower relative to fair. What should the trader track?

33.A call's fair value rises $0.20 after a stock move. Quoted width and inventory preference stay the same, and tick rounding is ignored. What quote update follows?

34.The desk receives a 25-lot buy inquiry for a short-dated straddle. Its model shows attractive edge, but the post-fill loss under a spot-gap scenario would breach the desk's stress limit. What response fits the stated limit?

35.A book is comfortable with parallel vega but close to its downside-skew limit. A trader wants to sell another low-strike put. Which check is most relevant?

36.A quote desk updates its option marks with current implied volatilities, but the implied volatility inputs were calculated from stock prices recorded at different times. What is the risk?

37.A trader starts flat and sells 18 calls with delta +0.45 per option share and a 100-share multiplier. What immediate stock trade offsets the new delta?

38.A trader buys 25 puts with delta −0.36 and a 100-share multiplier. How does the fill change book delta?

39.A trader sells 30 puts with delta −0.25 and a 100-share multiplier. The rest of the book is delta neutral. What stock hedge restores neutrality?

40.A desk is +350 shares delta before buying 20 calls with delta +0.40 and multiplier 100. What is the resulting delta before a new hedge?

41.A market maker is short 40 calls and buys back 15. Each has current delta +0.60 and multiplier 100. What delta remains from that option position alone?

42.A put bid for 40 contracts fills 17 at a multiplier of 100 and delta −0.28. What should the book record as the actual delta change?

43.A package fill buys 20 calls at delta +0.65 and sells 20 calls at delta +0.30, all with multiplier 100. What is the package delta?

44.A call spread fill buys a high-delta leg with vega $0.12 and sells a lower-delta leg with vega $0.16 per share per point. The fill is for 10 spreads with multiplier 100. What vega does it add?

45.A 100-share multiplier applies to 12 filled short straddles. Each straddle has combined vega of +$0.20 per share per point when long. What is the fill's vega?

46.A desk buys 10 calls and 10 puts with the same strike and expiry. Both have positive vega and their deltas offset. What exposure remains?

47.A desk sells a straddle, then hedges the small initial delta with stock. What changed after the stock trade?

48.A desk bought options near the offer after expecting a passive bid fill. Which data should a fill review compare to estimate price edge?

49.A desk sells 10 contracts for $1.24 per share. Its midpoint-based fair value at fill is $1.20, then rises to $1.31. With multiplier 100, what is mark-based P&L on the option at the later value, ignoring other trades?

50.A market maker receives two reports for the same fill through separate feeds. Which step keeps the hedge from doubling?

51.A desk sells calls to a customer, buys stock to hedge, and then receives a confirmed bust of the option trade. What should it do?

52.An adjusted option represents 150 shares. You buy 10 contracts whose delta is +0.40 per deliverable share. What spot delta is added under these terms?

53.A trader sells 20 calls at one venue and buys 20 of the identical series elsewhere at a lower price. Assuming both trades settle into the same netted position, what remains from the options themselves?

54.A book receives a long put fill and a short call fill on the same underlying. Each has a 100-share multiplier and the same positive gamma when long. Sizes are equal. Which Greek can cancel while delta moves negative?

55.A market maker buys 15 puts at delta −0.40 and simultaneously sells 10 calls at delta +0.60. Both have multiplier 100. What is the combined delta change?

56.A book's options delta moves from −900 to −1,300 after a fill. It already holds +900 shares. How many extra shares restore neutrality?

57.A book holds +1,000 shares against −1,000 option delta. A buyback of short calls raises option delta to −750. What should the trader do to return to neutral?

58.A book has +$2,200 of vega per point. A fill sells $500 per point of vega in one expiry. What is the new aggregate vega if nothing else changes?

59.A trader buys 40 options from a seller and quickly sees downside vol drop at neighboring strikes. What should the post-fill review separate?

60.A desk fills only the long leg of a planned option spread. The other leg is still live. What should the live risk view show?

61.A trader trades stock to hedge a call fill, but only 60% of the stock order fills before the market moves. What measure should guide the next hedge?

62.A desk bought a series and is now close to its long gamma limit. Which live option orders should it check first for additional gamma exposure?

63.A buyer lifts offers in several strikes while your book is already short the expiry's vega. Which action controls further exposure while preserving a path to reduce it?

64.A desk has $400 per point of headroom for additional long vega. Two live bids can each add $250 per point if fully filled. What risk action is justified?

65.An options book is neutral in aggregate vega after two fills, but short $800 per point in front-month and long $800 per point in the next month. What should the trader highlight?

66.A multi-strike fill contains put and call legs, and its net price is reported as a credit. What must be verified before updating Greeks?

67.A trader sold 30 calls marked at $1.80, earning 4 cents of edge per option share. The multiplier is 100, and total fees and immediate hedge slippage are $75. What is net initial edge?

68.A long 10-lot put order fills just before the surface changes. Should its delta be frozen at the order-entry model when sizing a new stock hedge?

69.A desk holds options on two stocks with deltas of +500 and −500 shares respectively. What is the problem with calling the portfolio delta neutral from that sum alone?

70.A desk is short 35 options after a wave of sales. Its policy caps short positions in the series at 50 contracts, including live offers. There are 12 live offers still executable. What additional offer size fits?

71.A firm receives a series of fills and the observed vega swings between +$500 and −$500 per point. The strategy limits apply to strike buckets as well as aggregate vega. What display helps detect the relevant breach?

72.A package trade leaves near-zero delta and vega but doubles short gamma near an event. What should the trader decide before replacing the quotes?

73.A delta-neutral book has +250 shares of gamma per $1 of spot movement. Spot rises $2. What stock trade restores neutrality under a constant-gamma approximation?

74.A delta-neutral book has −180 shares of gamma per $1 of spot movement. Spot falls $1.50. What is the approximate delta hedge adjustment?

75.A trader is short gamma and delta hedges after each move. Spot rises and then falls back to its starting point, with constant gamma and no intervening volatility change. What hedge pattern results?

76.A long-gamma book begins delta neutral. Spot falls. What direction is the first stock rebalance if other inputs are fixed?

77.A book is delta neutral with gamma of −$400 per squared dollar of underlying move. Under the quadratic estimate ½ × gamma × move², what is gamma P&L after a $3 spot gap?

78.A book's delta is +900 shares and gamma is −200 shares per $1 increase in spot. Spot rises $2. Ignoring changes in other inputs, what is the new delta before hedging?

79.A delta-neutral options book is short $1,800 of vega per implied volatility point. Vol rises 2.5 points in a parallel shift. What is first-order vega P&L?

80.A book has short vega of $960 per point. An eligible option adds $24 per point per contract when bought. How many contracts offset the local exposure?

81.A vega hedge buys 30 options, each contributing +20 shares of delta. The original book was delta neutral. What follow-up trade restores delta neutrality?

82.A short-gamma book needs +500 shares of gamma per $1. A hedge option adds +25 per contract in the same units, plus $12 of vega per point per contract. If you buy exactly enough to neutralize gamma, what vega is added?

83.A desk wants to neutralize both gamma and vega. Available hedge options have the same gamma-to-vega ratio as each other, which differs from the ratio required by the book. What should the desk do?

84.A desk is short front-week gamma but has ample long vega in a three-month expiry. Which hedge addresses the near-term curvature most directly?

85.A book is short downside-wing vega and long equal at-the-money vega in the same expiry. Spot stays fixed and only the wing volatility rises. What hedge is most directly aligned with the risk?

86.A desk is short $700 per point in one-month vega and long $700 per point in six-month vega. The front expiry rises 4 points and the back rises 1. What is the first-order volatility P&L?

87.A short option is hedged with stock. Why can a large overnight move still cause a sizable loss?

88.A desk holds long gamma and negative theta. Spot stays nearly flat and implied volatility is unchanged for a day. Which P&L driver is most likely to dominate under the stated assumptions?

89.A delta-hedged long-gamma book earns $900 from the spot path and loses $650 of theta and $180 in hedge costs. Implied volatility is unchanged. What is the net contribution under this breakdown?

90.A desk's hedge policy rebalances at every small spot tick, producing high turnover. What should it compare when considering a wider delta band?

91.A book is delta neutral but has vanna of −80 shares per implied volatility point. Vol rises 3 points at unchanged spot. What stock adjustment offsets this first-order delta change?

92.An option book is delta neutral at today's close. Your model expects its delta to become +150 shares by the next morning solely from time passing, with other inputs fixed. What is that risk driver called?

93.A book expects to lose on a large volatility rise even though current vega is close to zero. Which revaluation best tests the concern?

94.A book has net delta +600 shares and vega −$500 per volatility point. Spot falls $1.20 and implied volatility rises 2 points. What is first-order combined P&L, ignoring cross terms?

95.A short downside put book is locally delta hedged. A stress moves spot down sharply and steepens downside skew. Which test best captures the combined risk?

96.A desk wants to replace a hedge on an individual stock with an index future because the stock is halted. What limitation must be carried into its risk plan?

97.A book is short a near-expiry physically settled call. The underlying hovers near the strike. What should the trader plan for before the exercise cutoff?

98.A short American call is deep in the money just before an ex-dividend date and has little remaining time value. What is a practical risk to review?

99.A desk is delta neutral using stock, but the expiring options are cash settled and will drop from the book at settlement. What should the trader manage?

100.A trader wants to hedge a short option package with a future. The book has +2,400 shares of delta and one future offsets the equivalent of 250 shares when short. What hedge is closest using whole contracts?

101.A delta-neutral book holds a stock hedge against options on an underlying with thin borrow. Rebalancing would require a new stock short that is unavailable. What should the trader assess?

102.A market maker can hedge short vega with an expensive option that adds unwanted gamma or wait for a cheaper match later. What should drive the choice?

103.A large vega hedge is quoted as one contract size, but only half the planned hedge fills. A volatility shock then pushes the book beyond its limit. What should the trader report?

104.A trader compares two vega hedges with equal local sensitivity. One matches the same strike and expiry, while the other is cheaper but in a distant expiry. What belongs in the comparison?

105.A book's P&L report shows positive execution edge but a large loss after spot and volatility moved. How should the trader explain the result?

106.A delta-neutral book is long near-term gamma and short longer-dated vega. An event passes with a small realized spot move and a sharp fall in near-term implied volatility, while long-dated volatility barely moves. What must be checked to explain the post-event P&L?

107.A desk is flat delta now, short gamma near spot, and short front-month vega. It buys front-month at-the-money options as a hedge. What should it do next?

108.A desk must explain a response to an overnight spot gap and a front-month volatility jump. Which sequence is best?