Derivatives

1.A European call and put share a strike and an expiry. The underlying pays no dividend. Put-call parity says the call minus the put equals what?

2.That parity is rearranged into a long call, a short put, and borrowing the discounted strike. The package replicates what?

3.A covered call is a long share and a short call. Through parity, ignoring the financing detail that parity makes precise, that package has the same payoff shape as what?

4.An American call on a stock that pays no dividend, before expiry, should be exercised early or not?

5.An American put on the same non-dividend stock can be exercised early. Why is the put different from the call?

6.A large discrete dividend is due tomorrow, and an American call is in the money. Early exercise becomes rational when what is true?

7.In the Black-Scholes model a call delta lies between 0 and 1. A deep in-the-money call, well above the strike and not close to expiry, has a delta near what?

8.A put delta in that model lies in what range?

9.You are long a call and you delta-hedge it by trading the share. When the share dips and then recovers, the hedge does what?

10.A short call, delta-hedged, has the opposite hedge. Its gamma profit and loss, before theta, does what when the share moves a lot?

11.A delta-hedged long option, in the simple variance accounting that ignores rates, breaks even on gamma versus theta when realized volatility over the hedge equals what?

12.Realized volatility comes in above the implied volatility you hedged at, and you are long the option and delta-hedged. The gamma-versus-theta result is what?

13.The Black-Scholes price does not depend on the share's expected return. The drift that enters the hedge is what?

14.A desk prices a call with a higher expected return for the share and the same volatility, rates, and dividends. In Black-Scholes the call price does what?

15.Equity index implied volatility is typically higher for low strikes than for high strikes. That shape is what?

16.Short-dated out-of-the-money puts are rich relative to a lognormal model with constant volatility. A jump that can gap the share down does what to that richness?

17.The forward price of a share with continuous dividend yield q is what?

18.The stock is hard to borrow, and the borrow fee is a continuous yield the long stock holder does not receive. Relative to a stock that is easy to borrow, the forward is what?

19.A futures contract is marked to market daily, and a forward is not. If the futures price is positively correlated with interest rates, the futures price sits where relative to the forward?

20.A commodity futures curve sits above the spot. The curve is in what state?

21.The same commodity's futures sit below the spot. A convenience yield is one reason. What is that yield?

22.At the futures expiry the futures price and the spot do what, apart from the last settlement conventions?

23.You hedge an option discretely, once a day, in a model that assumed continuous hedging. The hedge leaves what?

24.A short option is near expiry and the share is near the strike. The delta of a short at-the-money option flips as the share crosses the strike. That expiry risk is called what?

25.A cash-or-nothing binary pays a fixed cash amount if the share expires above the strike. Relative to a vanilla call, its delta just below the strike near expiry is what?

26.A variance swap pays the difference between realized variance and a strike. A replication strip of options that matches it, in the log-contract recipe, weights out-of-the-money options by what?

27.The volatility of a spread, asset A minus asset B, falls when the correlation of A and B does what, holding the two volatilities fixed?

28.The volatility of a basket, asset A plus asset B, rises when correlation does what, holding the two volatilities fixed?

29.A knock-out call dies if the share touches a barrier. Relative to a vanilla call with the same strike, its price is what?

30.A knock-out is monitored only at the close, not continuously. Relative to the same barrier monitored continuously, the discrete knock-out is worth what?

31.An equity futures position is entered at the futures price. The cash posted at inception, relative to the notional, is what?

32.Implied volatility is defined as what?

33.For a standard vanilla call, vega is positive. If two otherwise identical calls differ only in price, the more expensive one has what implied volatility?

34.A box spread buys the call and sells the put at one strike, and sells the call and buys the put at a higher strike, all European and same expiry. The payoff is what?

35.The box is offered cheaper than the discounted strike difference, and you can fund at the rate inside that discount. The trade is what?

36.A payer swaption is an option to enter a swap paying fixed. It gains when rates do what?

37.An option on a futures is priced in Black's model. The underlying in that model is what?

38.A European call's sensitivity to the interest rate, rho, is what sign in the usual Black-Scholes setting with no dividends?

39.A continuous dividend yield rises, and rates stay fixed. The European call and the European put do what?

40.Gamma of a vanilla option is largest in which region, all else equal?

41.Theta of a long at-the-money option, the decay of its price as time passes with the spot unchanged, is typically what sign?

42.A 25-delta risk reversal in an equity index is the implied volatility of a 25-delta call minus the implied volatility of a 25-delta put. In a typical equity skew that quote is what?

43.A butterfly built from three calls, long the wings and short the middle, profits most when the share expires where?

44.Call prices as a function of strike, for a fixed expiry, must be convex. A market that violates convexity allows what?

45.A European call price must not increase when the strike increases. A quote screen that shows a higher strike with a higher call price allows what?

46.Total implied variance is implied volatility squared times maturity. A no-arbitrage calendar constraint, in the simple form, says this total as a function of maturity does what?

47.A local-volatility model is calibrated to match today's entire smile. Using it to hedge a forward-starting option, or the future smile, can still fail because of what?

48.You sell an at-the-money straddle and delta-hedge. You are short gamma and short vega. A quiet day with implied volatility unchanged does what?

49.The same short straddle is delta-hedged, and implied volatility jumps up with the share unmoved. The mark-to-market does what?

50.Sticky strike means each strike keeps its implied volatility when the spot moves. Sticky delta means implied volatility is attached to a delta, so a fixed strike's volatility changes as the spot moves and that strike's delta changes. The delta you must hedge differs because of what?

51.An American call on a non-dividend stock equals the European call. The American put is worth at least the European put. American call minus American put, compared with the European parity value, is what?

52.A European call's lower bound, with no dividends, is the larger of zero and what?

53.A deep in-the-money European put, no dividends, can trade below its intrinsic value. That is possible because of what?

54.You are short an American call, and the holder exercises just before a dividend. You are assigned. What do you deliver?

55.A collar buys a put and sells a call against a long share, with the call strike above the put strike. The share's payoff between the strikes is what?

56.A calendar spread buys a longer-dated option and sells a shorter-dated option at the same strike. It is primarily a bet on what?

57.Implied volatility for an equity index is often above the volatility the index later realizes. A short variance position that is hedged collects that gap when the gap is positive. The gap is best described as what?

58.A delta-hedged variance position loses in a crash that realizes far more variance than was implied. The loss comes from what?

59.Garman-Kohlhagen prices a currency option. The two interest rates in it are what?

60.The FX forward is spot times e to the (domestic rate minus foreign rate) times T. If the foreign rate rises and the domestic rate does not, the forward does what?

61.A quanto option pays a foreign asset's return converted at a fixed FX rate, so the holder does not take the FX move. Its forward is not the foreign forward converted at today's spot, because of what?

62.A futures option's put-call parity, in Black's setting, says call minus put equals what?

63.You hedge a short dated option once, at the open, and the share trends smoothly all day. A hedge that was rebalanced every few minutes would have what gamma result, relative to the single morning hedge, if you are long gamma?

64.The share gaps through your strike overnight, and your delta hedge was computed at the previous close. The gap does what to the replication?

65.A convertible bond is a bond plus a call on the share. If the credit spread widens and the share is unchanged, the convertible's bond piece does what?

66.The convertible's embedded call is in the money and the bond floor is far below. The convertible's share delta is near what?

67.An option is priced off a borrow curve that assumes the stock is easy to borrow. The stock becomes special, with a high fee, and the desk does not update the forward. Its calls, relative to a desk that includes the fee, are what?

68.Two European options differ only in that one is struck at 100 and the other at 110. The 100-strike call is offered at 5 and the 110-strike call is bid at 6. What is the violation?

69.A volatility surface is stored as a single number for every strike and maturity. A risk system that deltas with that flat volatility, in a market that has a steep skew, misses what?

70.You are long a downside put as a hedge and short an upside call to pay for it, a risk-reversal hedge on a long book. In a crash, with the skew also steepening, the put does what relative to a flat-vol mark?

71.The funding rate used to discount an option premium is raised, and the forward is held fixed by adjusting the dividend consistently. The effect on a European option price through discounting alone is what?

72.A futures hedge of a stock portfolio uses a beta of 1.1 and a futures contract on the index. The dollar hedge, relative to the portfolio's dollar value, is what?

73.Index futures are in contango, so the deferred contract is richer than the front. A short hedge rolls by buying the expiring contract and selling the deferred one. That roll does what?

74.A portfolio is long the shares and short the futures, and the futures curve is in contango. Over a roll, if nothing else changes, the futures hedge contributes what?

75.A basis trade is long the stock and short the fair futures. If the futures are rich to the fair forward that includes dividends and rates, the trade at initiation does what?

76.Delta of a call plus the absolute value of the delta of the matching put, in Black-Scholes with no dividends, is near 1. More exactly, call delta minus put delta equals what?

77.An option expires in a few minutes and is 5 percent out of the money. Its remaining vega, compared with a one-year option at the same moneyness, is what?

78.That same short-dated option is moved to the strike, still with minutes left. Its gamma, compared with the one-year at-the-money option, is what?

79.You sell the near-expiry at-the-money option and hedge the delta. Into the close the share oscillates around the strike. Your hedge does what?

80.A portfolio of options is vega-flat and gamma-flat at the spot, and it is long a wing and short the body, a butterfly. A large move that also lifts the wing's implied volatility does what?

81.The rebate on a knock-out is zero, and the barrier is just above the spot for an up-and-out call that is struck below the barrier. If the barrier is hit immediately, the option's value becomes what?

82.A down-and-in put comes alive only if the barrier is hit. If the barrier is never hit, its payoff is what?

83.A down-and-out put plus a down-and-in put, same strike and barrier, replicate what?

84.You hedge a barrier option with a vanilla delta taken from a model that ignores the barrier. As the spot approaches a knock-out barrier, that vanilla delta does what relative to the true barrier delta?

85.A swaption is exercised into a swap. The swap's value at exercise is positive for the holder. Exercising is compared with selling the swaption. Early exercise of a European swaption is what?

86.A physically settled swaption that finishes in the money delivers the swap. A cash-settled swaption delivers what?

87.A caplet is a call on a future interest rate. A floorlet is the corresponding put. Caplet minus floorlet, by put-call parity on the rate, relates to what?

88.You mark a book of options at mid volatility, and the book is short the wings. The bid-ask in the wings is wide. Marking at mid does what to the liquidation value?

89.A long wing, marked at mid, with the same wide spread, has a liquidation value that is what relative to the mid mark?

90.An option's theoretical value uses a borrow fee of zero. The desk's funding of the hedge stock actually pays a fee. Ignoring the fee in the theoretical value, and hedging as if the forward were the easy-borrow forward, leaves the book with what?

91.A delta hedge is rebalanced to the model delta at each close, and the model delta uses yesterday's implied volatility. Today's volatility has jumped. Until the model is updated, the hedge is what?

92.The share splits 2-for-1. Listed options are adjusted by the exchange. An unadjusted model that still shows the old strike and the old share price, the morning of the split, shows a moneyness that is what?

93.After the adjustment the multiplier doubles and the strike halves. The position's dollar delta, compared with the day before, should be what if the split is the only event?

94.A trader hedges an option with the underlying future and uses the future's delta as if it were the spot delta, one for one. When the future has a delta to the spot of e to the (r − q) T, which is not 1, that shortcut does what?

95.You compute the Black-Scholes delta with volatility 20 percent and the market's implied volatility is 40 percent. For an at-the-money option, which delta is the one consistent with the market price?

96.A book is long 100 calls and the delta is 0.4 each. The share hedge that flattens delta is a short of how many shares, if the multiplier is 1?

97.The multiplier is 100 shares per contract, and you are long one call with delta 0.4. The share hedge is what?

98.Vega is quoted per 1 percentage point of volatility. An option has vega of 0.20 in price units per volatility point, and implied volatility rises by 2 points. The price change from vega alone is what?

99.That vega move assumed the spot fixed. The spot also fell, and the option is a call. The total mark is vega times the volatility change plus what else, to first order?

100.A risk report shows a large positive vanna, the sensitivity of delta to volatility. Implied volatility rises and the spot is unchanged. The delta hedge that was correct a moment ago does what?

101.Theta is collected overnight, including over a weekend, and the model theta is a one-day decay. A desk that books one day of theta on Friday night and nothing for Saturday and Sunday is missing what, if the model clock includes the weekend?

102.The premium is paid up front for a listed equity option. A futures-style option, margined like a future, pays no premium up front and pays variation margin. Its forward price, compared with the prepaid premium option, differs because of what?

103.A dividend forecast used in the forward is cut in half after the company guides lower. Calls marked on the old dividend are, relative to the new forward, what?

104.The same dividend cut, with puts marked on the old dividend. Those put marks are what?

105.Put-call parity is checked after the dividend update, using the new forward. The call mark was updated and the put mark was not. Parity now fails by about the put's stale amount. The clean trade, if you can do it without more spread, is what?

106.A trader refuses the parity trade because the stock is hard to borrow and the parity check used an easy-borrow forward. The refusal is justified when?

107.All of the parity inputs are updated: rates, dividend, and borrow. Call minus put still exceeds the forward value by more than the spread. That remainder is what?

108.A junior hedges a short put by selling shares, copying the call hedge. The put's delta is −0.4 and one contract is 100 shares. The correct share trade is what?