Free SOA Exam FAM (Fundamentals of Actuarial Mathematics) Option Pricing Fundamentals Practice Questions

Explore option pricing fundamentals as tested on Exam FAM. Questions cover put-call parity, binomial pricing models, Black-Scholes, and the Greeks — connecting financial mathematics to actuarial applications.

53 Questions
25 Easy
18 Medium
10 Hard
2026 Syllabus

Sample Questions

Question 1 Easy
A European put has strike \$70 and stock at expiration is \$63. What is the payoff?
Solution
Payoff =max⁡(70−63,0)=7= \max(70-63,0) = 7.

(A) would apply if ST>KS_T > K. (B) wrong. (D) stock price. (E) strike price.

The answer is $7\$7.
Question 2 Medium
Using put-call parity, a synthetic long stock position can be created by:
Solution
From parity S=C−P+PV(K)S = C - P + PV(K). A synthetic long stock = long call + short put + lend PV(K).

(B) creates synthetic short stock. (C) not a standard synthetic. (D) not a standard synthetic. (E) creates a straddle.

The answer is (A).
Question 3 Hard
Two-period binomial model: S0=100S_0 = 100, u=1.10u = 1.10, d=0.90d = 0.90, r=2%r = 2\% per period. European call with strike \$100. Calculate the call price.
Solution
p∗=(1.02−0.90)/(1.10−0.90)=0.12/0.20=0.60p^* = (1.02-0.90)/(1.10-0.90) = 0.12/0.20 = 0.60.

Terminal values: Suu=121S_{uu} = 121, Sud=99S_{ud} = 99, Sdd=81S_{dd} = 81. Payoffs: Cuu=21C_{uu} = 21, Cud=0C_{ud} = 0, Cdd=0C_{dd} = 0.

C=(0.60)2(21)+2(0.60)(0.40)(0)+(0.40)2(0)(1.02)2=0.36×211.0404=7.561.0404=7.27C = \frac{(0.60)^2(21) + 2(0.60)(0.40)(0) + (0.40)^2(0)}{(1.02)^2} = \frac{0.36 \times 21}{1.0404} = \frac{7.56}{1.0404} = 7.27

(A) uses wrong risk-neutral probability. (C) uses r=3%r = 3\%. (B) uses r=3%r = 3\% with rounding. (E) too high.

The answer is $7.27\$7.27.
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More Exam FAM Topics

Short-Term Insurance and Reinsurance Coverages Severity, Frequency, and Aggregate Models Parametric Estimation Introduction to Credibility Pricing and Reserving for Short-Term Insurance Coverages Long-Term Insurance Coverages and Retirement Financial Security Programs Mortality Models Present Value Random Variables for Long-Term Insurance Coverages Premium and Policy Value Calculation for Long-Term Insurance Coverages

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