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Workbook 3: Options

Exercises for Options Part 1: The Basics → Options Part 4: Risk & 0DTE — premium math, spreads, Greeks, and 0DTE risk.

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This workbook covers the Academy's options course — Options Part 1: The Basics (The Basics), Options Part 2: Pricing & the Greeks (Pricing & the Greeks), Options Part 3: Strategies (Strategies), and Options Part 4: Risk & 0DTE (Risk & 0DTE). It is a workbook, not a chapter: read less, calculate more.

How to use it:

  • Do each module's exercises right after re-reading that module, with a pencil and a calculator.
  • Show your arithmetic on paper. The habit of writing the math down is the skill being built.
  • Do not peek. Struggle first, then check the ## Answers section at the very end — every answer shows its working.
  • Every number here follows the rules from the modules: one contract = 100 shares, premium × 100 = real dollars, call breakeven = strike + premium, put breakeven = strike − premium.

Module Options Part 1: The Basics: Options Basics

  1. Math. A call has a premium of $3.20. What does one contract cost? What do two contracts cost?
  2. Math. You buy one put with a strike of $120 for a premium of $4.50. At expiration the stock finishes at $104. (a) What is one contract worth at expiration? (b) What is your profit?
  3. Math. A call has a strike of $30 and a premium of $1.75. What is the breakeven price at expiration?
  4. Math. A put has a strike of $88 and a premium of $2.60. What is the breakeven price at expiration?
  5. Math. An option's premium is $5.40 and its intrinsic value is $3.75. How much extrinsic value are you paying — per share, and per contract?
  6. Fill in the blank. A call option gives the buyer the right to __________ 100 shares at the __________ price, at any time before the __________ date.
  7. Fill in the blank. One standard option contract controls __________ shares of stock, so a premium quoted at $2.50 really costs $__________ per contract.
  8. Spot the mistake. A trader says: "This call's premium is only $0.60, so the whole trade costs me six dollars." What is wrong?
  9. Spot the mistake. A trader buys a call with a $50 strike for $3.00. The stock rises from $50 to $52 by expiration, and the trader says: "The stock went up, so I made money." What is wrong?
  10. Math. A stock trades at $64. (a) A call with a $70 strike — is it in the money, at the money, or out of the money? (b) A put with a $70 strike — in, at, or out of the money?
  11. Scenario. You buy one call on a stock trading at $44: strike price $45, premium $2.00, expiring in three weeks. (a) At expiration the stock closes at $49. What is the contract worth, and what is your profit or loss? (b) Now suppose instead the stock closes at exactly $45 on expiration day. What is the contract worth, and what is your result?

Module Options Part 2: Pricing & the Greeks: Pricing & the Greeks

  1. Math. Your call has a delta of 0.40. The stock rises $3. About how much does the option gain — per share, and per contract — before any other effects?
  2. Math. Your put has a delta of −0.35. The stock falls $4. About how much does the option gain, per share and per contract?
  3. Math. An option has theta of −0.06. You hold two contracts through five quiet days in which the stock does not move. About how much value do you lose to time alone?
  4. Math. An option has vega of 0.14. Implied volatility falls 4 points while the stock sits still. What happens to the option's price, per share and per contract?
  5. Math. A call has delta 0.45 and gamma 0.07. The stock rises $2. About what is the new delta?
  6. Fill in the blank. __________ measures how much an option's delta changes when the stock moves $1 — it is delta's acceleration.
  7. Spot the mistake. Earnings are tonight and implied volatility is extremely high. Dana buys an at-the-money call for $4.00. The report is good, the stock pops 3% the next morning — but her call is now worth $2.60. Dana says the broker must have made an error. What actually happened?
  8. Spot the mistake. A trader says: "This call's delta is only 0.10, but that's fine — it gives me basically the same exposure as owning the stock, just much cheaper." What is wrong?
  9. Scenario. You bought a call for $3.00. Its gauges read: delta 0.50, theta −0.08, vega 0.10. Over the next 7 days the stock does not move at all, but implied volatility falls 2 points. Estimate the option's new price, one Greek at a time.
  10. Fill in the blank. When implied volatility rises, options get __________ even if the stock does not move at all, because buyers are paying more for the movement they expect.
  11. Math. Which Greek can a trader holding a two-week option mostly ignore, and what does it measure?

Module Options Part 3: Strategies: Strategies

  1. Math. Bull call spread: you buy the $60 call for $2.60 and sell the $70 call for $0.90. Find (a) the net debit in dollars, (b) the maximum loss, (c) the maximum profit, and (d) the breakeven price.
  2. Math. Bear put spread: you buy the $90 put for $3.10 and sell the $80 put for $1.10. Find (a) the net debit, (b) the maximum loss, (c) the maximum profit, and (d) the breakeven price.
  3. Math. Bull put spread: you sell the $55 put for $1.40 and buy the $50 put for $0.55. Find (a) the net credit, (b) the maximum profit, (c) the maximum loss, and (d) the breakeven price.
  4. Math. Bear call spread: you sell the $120 call for $1.70 and buy the $125 call for $0.70. Find (a) the net credit, (b) the maximum profit, (c) the maximum loss, and (d) the breakeven price.
  5. Math. Iron condor on a stock at $200: you sell the $190 put and buy the $185 put, and sell the $210 call and buy the $215 call, collecting a total credit of $2.10. Find (a) the maximum profit, (b) the maximum loss, and (c) both breakeven prices.
  6. Math. Straddle: you buy the $150 call for $4.20 and the $150 put for $3.90. Find (a) the total cost per straddle, (b) the maximum loss, and (c) both breakeven prices.
  7. Math. Strangle: you buy the $160 call for $1.30 and the $140 put for $1.20. Find (a) the total cost, (b) the maximum loss, and (c) both breakeven prices.
  8. Math. Covered call: you own 100 shares bought at $72. You sell one $78 call for $1.25. At expiration the stock is at $84 and your shares are called away. (a) How much money do you end up receiving in total? (b) What is your profit compared with your original $7,200 cost? (c) How much upside did you give up, compared with simply holding the shares?
  9. Math. Cash-secured put: you sell one $40 put for $1.50 and set aside $4,000 in cash. At expiration the stock is at $34 and you are assigned. (a) What is your effective cost per share, after the premium? (b) What is your paper loss on the shares at $34?
  10. Math. Protective put: you own 100 shares bought at $130. You buy one $125 put for $2.40. The stock crashes to $100. (a) How much did the shares lose? (b) What is the put worth? (c) What is your total result, including the premium you paid?
  11. Spot the mistake. A trader says: "My credit spread paid $120 into my account on day one. That's $120 of profit already locked in." What is wrong?
  12. Spot the mistake. A trader's spread is losing money, so he says: "I'll just sell off the long option I bought — that cuts my cost and makes the trade cheaper to hold." What is wrong, and what has his trade quietly become?
  13. Fill in the blank. An __________ is built from a bull put spread plus a bear call spread on the same stock with the same expiration, and it profits when the stock stays inside a range.
  14. Scenario. Earnings are tonight. A stock trades at $80, and you are sure it will move a lot — but you honestly do not know which way. You buy a straddle: the $80 call and the $80 put, for a combined cost of $6.00. (a) Between which two prices at expiration do you lose money? (b) The report lands, the stock jumps 5% to $84, and it is still there at expiration. Do you make money? Show why or why not.

Module Options Part 4: Risk & 0DTE: Risk & 0DTE

  1. Math. Your account holds $25,000 and you follow a 2% risk guideline per idea. A spread you like has a maximum loss of $300 per contract. How many contracts can you trade without breaking the guideline?
  2. Math. Your account holds $8,000 and you follow a 1% risk guideline. A call costs $1.10 per share — $110 per contract. Can you buy one contract inside the guideline? Show the numbers.
  3. Math. Hedging: you hold 100 shares of an index ETF at $600 per share, a $60,000 position. You buy one put with a $570 strike for $7.50 — $750 of insurance. The market falls 15%, putting the ETF at $510. (a) How much did the shares lose? (b) What is the put worth? (c) What is your total result, including the premium?
  4. Spot the mistake. A trader says: "0DTE contracts are only $0.40 — forty bucks. That's about as low-risk as options get." What is wrong?
  5. Spot the mistake. A trader says: "There's only $15 of profit left in my spread, so I'll hold it into expiration and grab every last dollar. What could possibly go wrong in a few hours?" Name the trap he is walking into.
  6. Fill in the blank. __________ is the danger when a stock closes on expiration day almost exactly at your sold strike price, so you spend the whole weekend not knowing whether you were assigned.
  7. Fill in the blank. Size options trades by __________ at risk: assume the full amount could be lost, because sometimes it will be — and keep it near 1–2% of your account per idea.
  8. Scenario. At 1:00 PM you buy an index call expiring today for $0.85 — $85. The index goes sideways. (a) By 3:00 PM the call is quoted at $0.15. If you sell now, what is your loss? (b) Instead you hold, the index stays flat, and the call expires. What is your loss now? (c) Which two Greeks dominate an option's final hours and explain both results?

Answers

Options Part 1: The Basics — Options Basics

  1. One contract: $3.20 × 100 = $320. Two contracts: $320 × 2 = $640.
  2. (a) A put pays the distance the stock finished below the strike: ($120 − $104) × 100 = $16 × 100 = $1,600. (b) You paid $4.50 × 100 = $450. Profit = $1,600 − $450 = $1,150.
  3. Call breakeven = strike + premium = $30 + $1.75 = $31.75.
  4. Put breakeven = strike − premium = $88 − $2.60 = $85.40.
  5. Extrinsic value = premium − intrinsic value = $5.40 − $3.75 = $1.65 per share, which is $1.65 × 100 = $165 per contract. That $165 is the part that melts to zero by expiration.
  6. buy — strike — expiration. A call is the right to buy 100 shares at the strike price before the expiration date.
  7. 100 shares — so $2.50 × 100 = $250 per contract.
  8. Premiums are quoted per share, and one contract covers 100 shares. $0.60 × 100 = $60 per contract — ten times what he said. Forgetting the × 100 is the classic beginner sizing error.
  9. At expiration the call is worth $52 − $50 = $2.00 per share. He paid $3.00, so he loses $1.00 per share — $100 per contract. His breakeven was $50 + $3.00 = $53. The stock rose, but not past the breakeven: right direction, not enough move.
  10. (a) The $70 call is out of the money — for a call, a strike above the stock price ($70 > $64) means the right has no built-in value yet. (b) The $70 put is in the money — for a put, a strike above the stock price means selling at $70 is already worth something when the market pays $64.
  11. (a) Contract value = ($49 − $45) × 100 = $400. You paid $2.00 × 100 = $200, so your profit = $400 − $200 = +$200. (b) At exactly $45 the right to buy at $45 is worth $0 — the stock finished at the strike, not past it. You lose the full $200 premium. An option only pays on the distance finished past the strike.

Options Part 2: Pricing & the Greeks — Pricing & the Greeks

  1. Delta estimate: 0.40 × $3 = $1.20 per share, which is $1.20 × 100 = about $120 per contract.
  2. A put gains when the stock falls: 0.35 × $4 = $1.40 per share, or about $140 per contract. (Use the size of delta, 0.35 — the negative sign only tells you the direction: puts rise when the stock drops.)
  3. Per contract per day: $0.06 × 100 = $6. Five days: $6 × 5 = $30 per contract. Two contracts: $30 × 2 = about $60 lost to theta, with the stock doing nothing at all.
  4. Vega loss: 0.14 × 4 = $0.56 per share, which is $56 per contract — lost purely because expectations cooled, with the stock completely still.
  5. New delta ≈ 0.45 + (0.07 × $2) = 0.45 + 0.14 = about 0.59. Each $1 rise added 0.07 of delta.
  6. Gamma.
  7. No error — this is IV crush. Before earnings, her premium carried a large fear surcharge: she paid $4.00 for an option whose value depended on a huge expected move. The moment the news printed, the uncertainty vanished, implied volatility collapsed, and the extrinsic value she had paid for evaporated faster than the stock's 3% rise could replace it. She was right about direction and still lost $1.40 per share — $140 per contract.
  8. Delta of 0.10 means the option moves only about $0.10 for every $1 the stock moves — roughly one-tenth of the stock's exposure, not the same exposure. It is cheap because the market gives it roughly a one-in-ten ballpark chance of expiring in the money. He is holding a lottery ticket and describing it as a stock position.
  9. One Greek at a time: Delta: the stock did not move, so delta contributes $0. Theta: −$0.08 × 7 days = −$0.56. Vega: −0.10 × 2 points = −$0.20. Total change ≈ −$0.56 − $0.20 = −$0.76. New price ≈ $3.00 − $0.76 = about $2.24. The stock did nothing and the position still lost about a quarter of its value.
  10. more expensive (pricier). Higher IV means buyers pay a bigger surcharge for expected movement, so premiums rise even with the stock frozen.
  11. Rho — it measures how much an option's price changes when interest rates move 1 percentage point. Over days or weeks that effect is tiny, so short-term traders can safely spend their attention on delta, theta, gamma, and vega.

Options Part 3: Strategies — Strategies

  1. (a) Net debit = $2.60 − $0.90 = $1.70, which is $170. (b) Maximum loss = the debit = $170. (c) Maximum profit = width − debit = ($70 − $60) − $1.70 = $8.30, which is $830. (d) Breakeven = lower strike + debit = $60 + $1.70 = $61.70.
  2. (a) Net debit = $3.10 − $1.10 = $2.00, which is $200. (b) Maximum loss = $200. (c) Maximum profit = ($90 − $80) − $2.00 = $8.00, which is $800. (d) Breakeven = higher strike − debit = $90 − $2.00 = $88.
  3. (a) Net credit = $1.40 − $0.55 = $0.85, which is $85. (b) Maximum profit = the credit = $85. (c) Maximum loss = width − credit = ($55 − $50) − $0.85 = $4.15, which is $415. (d) Breakeven = $55 − $0.85 = $54.15.
  4. (a) Net credit = $1.70 − $0.70 = $1.00, which is $100. (b) Maximum profit = $100. (c) Maximum loss = ($125 − $120) − $1.00 = $4.00, which is $400. (d) Breakeven = $120 + $1.00 = $121.
  5. (a) Maximum profit = the total credit = $2.10, which is $210, kept if the stock finishes between $190 and $210. (b) Maximum loss = one side's width − credit = $5.00 − $2.10 = $2.90, which is $290. (The stock can only finish on one side, so only one spread can lose in full.) (c) Breakevens: $190 − $2.10 = $187.90 below, and $210 + $2.10 = $212.10 above.
  6. (a) Total cost = $4.20 + $3.90 = $8.10, which is $810. (b) Maximum loss = $810, if the stock finishes at $150. (c) Breakevens: $150 + $8.10 = $158.10 above, and $150 − $8.10 = $141.90 below.
  7. (a) Total cost = $1.30 + $1.20 = $2.50, which is $250. (b) Maximum loss = $250. (c) Breakevens: $160 + $2.50 = $162.50 above, and $140 − $2.50 = $137.50 below. The strangle costs less than a straddle but demands a bigger move.
  8. (a) Shares called away at $78: 100 × $78 = $7,800, plus the $125 premium collected = $7,925 received in total. (b) Profit = $7,925 − $7,200 = $725. (c) The shares were worth 100 × $84 = $8,400. You gave up $8,400 − $7,925 = $475 of the rise — the ceiling you agreed to when you sold the call.
  9. (a) Effective cost = strike − premium = $40.00 − $1.50 = $38.50 per share. (b) At $34, you are down $38.50 − $34.00 = $4.50 per share, which is $450 on 100 shares. This is why you only sell a cash-secured put on a stock you genuinely want to own at the strike.
  10. (a) Share loss = ($130 − $100) × 100 = $3,000. (b) Put value = ($125 − $100) × 100 = $2,500. (c) Total = −$3,000 + $2,500 − $240 premium = −$740. Without the put, the loss was $3,000 and still falling; the insurance converted it into a known, survivable number.
  11. The credit is not profit — it is a deposit held against a possible loss, yours to keep only if the spread expires safely. His real numbers are the pair: maximum profit $120, and maximum loss = width − credit, which is larger than $120. Size credit trades by the loss column, never by the income column.
  12. The long option he bought is the protective leg — the piece that caps his loss and makes the trade defined-risk. Selling it leaves a naked sold option: undefined risk with no built-in limit. He did not make the trade cheaper; he removed its brakes.
  13. iron condor.
  14. (a) Breakevens are $80 + $6.00 = $86 and $80 − $6.00 = $74. You lose money on any finish between $74 and $86 (and lose the full $600 at $80). (b) At $84, the call is worth $84 − $80 = $4.00 and the put is worth $0, so the straddle is worth $4.00. You paid $6.00, so you lose $2.00 — $200. A 5% jump was not enough: the move had to beat the $6.00 move already priced in, and IV crush after the report would have made the position look even worse before expiration.

Options Part 4: Risk & 0DTE — Risk & 0DTE

  1. Risk allowed = 2% × $25,000 = $500. $500 ÷ $300 per contract = 1.67, so 1 contract. Two contracts would risk $600, breaking the guideline — round down, always.
  2. Risk allowed = 1% × $8,000 = $80. One contract risks the full premium of $110, which is $110 ÷ $8,000 = 1.375% of the account — over the guideline. Correct moves: use a cheaper structure such as a spread, wait for a smaller premium, or skip the trade. Skipping is a legitimate answer.
  3. (a) Share loss = ($600 − $510) × 100 = $9,000. (b) Put value = ($570 − $510) × 100 = $6,000. (c) Total = −$9,000 + $6,000 − $750 premium = −$3,750, instead of −$9,000 unhedged. The hedge did not make the crash painless; it made it survivable.
  4. Cheap in dollars is not the same as low-risk. A 0DTE contract lives its entire life in the zone of maximum theta and maximum gamma: value drains by the minute, prices swing violently on tiny index moves, and most of those $0.40 contracts expire worth exactly $0. Repeated daily, "only forty bucks" is how accounts quietly bleed out.
  5. Pin risk (with surprise assignment riding along). If the stock closes almost exactly at his sold strike, he cannot know over the weekend whether he was assigned — while the protective leg of his spread may have expired worthless by a few cents. Experienced traders close spreads before expiration for this reason: the last $15 is the most expensive money in options.
  6. Pin risk.
  7. premium.
  8. (a) Loss = ($0.85 − $0.15) × 100 = $70. (b) The full premium: $85 — an option that expires out of the money is worth $0. (c) Theta and gamma. Theta is at full speed in the final hours — the contract's remaining time value melted away minute by minute while the index went nowhere. Gamma is at its maximum near the strike near expiration, which is why 0DTE prices can whipsaw wildly on even a small late move. Flat market, melting clock: that combination is the whole result.