FIN435 Final Exam • Options Calculation Section

Hypothetical Apple stock option questions. Multiple choice format with detailed solution explanations. Values are for exam calculation only, not current market quotes.

8questions total

40points total

Openbook / notes

A–Dbalanced answers

Important rule: payoff is the option value at expiration. Profit adjusts payoff for the premium.

Long position profit = payoff − premium paid
Short position profit = premium received − payoff owed later

Formula styles used in this exam

Option position	Payoff at expiration	Profit at expiration
Long Call	max(S_T − X, 0)	max(S_T − X, 0) − premium
Long Put	max(X − S_T, 0)	max(X − S_T, 0) − premium
Short Call	−max(S_T − X, 0)	premium − max(S_T − X, 0)
Short Put	−max(X − S_T, 0)	premium − max(X − S_T, 0)

Final Exam Questions

Apple long call payoff

Call payoffIgnore premium

Apple stock price at expiration is $232. A call option has a strike price of $220. The call premium was $9. What is the long call payoff at expiration?

A) $3 B) $0 C) $12 D) $21

Detailed solution

A long call payoff uses the right style:

Long Call Payoff = max(S_T − X, 0)

Substitute the numbers:

max(232 − 220, 0) = max(12, 0) = 12

The premium is not subtracted because the question asks for payoff, not profit.

Correct answer: C) $12

Apple long call profit

Call profitSubtract premium

Apple stock price at expiration is $248. A call option has a strike price of $230. The call premium was $11.25. What is the long call profit at expiration?

A) $6.75 B) $11.25 C) $18.00 D) $29.25

Detailed solution

First find the call payoff, then subtract the premium.

Call Payoff = max(248 − 230, 0) = 18

Long Call Profit = payoff − premium = 18 − 11.25 = 6.75

Correct answer: A) $6.75

Apple long put payoff

Put payoffIgnore premium

Apple stock price at expiration is $162. A put option has a strike price of $175. The put premium was $7.40. What is the long put payoff at expiration?

A) $0 B) $5.60 C) $7.40 D) $13.00

Detailed solution

A long put benefits when the stock price falls below the strike price.

Long Put Payoff = max(X − S_T, 0)

max(175 − 162, 0) = max(13, 0) = 13

The premium is ignored because the question asks for payoff.

Correct answer: D) $13.00

Apple long put profit

Put profitSubtract premium

Apple stock price at expiration is $168. A put option has a strike price of $185. The put premium was $9.50. What is the long put profit at expiration?

A) $17.00 B) $7.50 C) −$9.50 D) $26.50

Detailed solution

First find the put payoff, then subtract the premium paid.

Put Payoff = max(185 − 168, 0) = 17

Long Put Profit = payoff − premium = 17 − 9.50 = 7.50

Correct answer: B) $7.50

Apple long call payoff graph

Graph stylePayoff only

Which graph correctly shows the long call payoff for an Apple option with strike price X = $200?

A) Flat at zero until X, then slopes upward after X

B) Downward to zero at X, then flat

C) Flat at zero until X, then slopes downward below zero after X

D) Below zero before X, slopes upward to zero at X, then stays flat

Detailed solution

A long call payoff is zero when S_T is below the strike price. Once S_T rises above X, the payoff increases dollar-for-dollar.

Long Call Payoff = max(S_T − X, 0)

The correct graph is flat at zero before the strike and slopes upward after the strike. Do not memorize a literal 45-degree visual angle; the angle changes with graph scale. The key idea is the positive slope after X.

Correct answer: A

Apple long put payoff graph

Graph stylePayoff only

Which graph correctly shows the long put payoff for an Apple option with strike price X = $200?

A) Flat at zero until X, then falls at about a 45° angle below zero

B) Flat at zero until X, then slopes upward after X

C) Starts positive, slopes downward to zero at X, then stays flat

D) Below zero before X, slopes upward to zero at X, then stays flat

Detailed solution

A long put payoff is high when the stock price is far below the strike. It declines as the stock price rises, reaches zero at the strike, and stays zero after that.

Long Put Payoff = max(X − S_T, 0)

Correct answer: C

Apple one-step binomial call value

One-step binomialBasic

Apple stock is currently S₀ = $180. In one period, it can move up to S_u = $198 or down to S_d = $162. A one-period call option has strike price X = $185. The one-period risk-free rate is 4%. What is the call value today using the one-step binomial model?

A) $6.25 B) $8.75 C) $9.10 D) $13.00

Detailed solution

Step 1: find the option payoff in each future state.

C_u = max(198 − 185, 0) = 13
C_d = max(162 − 185, 0) = 0

Step 2: find the risk-neutral probability.

p = [(1 + r)S₀ − S_d] / (S_u − S_d)
p = [(1.04)(180) − 162] / (198 − 162)
p = (187.20 − 162) / 36 = 25.20 / 36 = 0.70

Step 3: discount the expected option payoff.

C₀ = [pC_u + (1 − p)C_d] / (1 + r)
C₀ = [0.70(13) + 0.30(0)] / 1.04 = 9.10 / 1.04 = 8.75

Correct answer: B) $8.75

Apple Black-Scholes plug-in call value

Black-ScholesPlug-in only

Use the Black-Scholes model for a European call option on Apple. Assume S₀ = $190, X = $185, r = 4%, T = 0.50 years, and σ = 30%. Which answer is closest to the call value?

A) $8.66 B) $11.73 C) $16.44 D) $20.39

Detailed solution

Use the standard Black-Scholes call formula.

C = S₀N(d₁) − Xe^−rTN(d₂)

d₁ = [ln(S₀/X) + (r + σ²/2)T] / [σ√T]
d₂ = d₁ − σ√T

Plug in the values:

d₁ ≈ 0.3261
d₂ ≈ 0.1139
N(d₁) ≈ 0.6278
N(d₂) ≈ 0.5453

C ≈ 190(0.6278) − 185e^{−0.04(0.50)}(0.5453)
C ≈ 20.39

Correct answer: D) $20.39

Instructor answer pattern: Q1 C, Q2 A, Q3 D, Q4 B, Q5 A, Q6 C, Q7 B, Q8 D.
Distribution: A = 2, B = 2, C = 2, D = 2. The pattern is balanced but not alphabetical/orderly.