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

Financial derivatives on SOA Exam FAM cover put-call parity, the binomial option pricing model, the Black-Scholes formula, and the Greeks (delta, gamma, theta, vega), connecting financial mathematics to actuarial applications.

62 Questions
28 Easy
24 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
B is correct.

Payoff =max⁡(70−63,0)=7= \max(70-63,0) = 7. The answer is $7\$7.
Question 2 Medium
Using put-call parity, a synthetic long stock position can be created by:
Solution
B is correct.

From put-call parity: S = C - P + PV(K). A synthetic long stock position is created by buying a call and selling a put with the same strike and expiry, plus lending PV(K).
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
C is correct.

Using a two-period binomial model with S_0 = 100, u = 1.10, d = 0.90, r = 0.02 per period, K = 100.

Risk-neutral probability:
p^* = (1.02-0.90)/(1.10-0.90) = 0.12/0.20 = 0.60.

Terminal stock prices: S_{uu} = 121, S_{ud} = 99, S_{dd} = 81.
Terminal payoffs: C_{uu} = 21, C_{ud} = 0, C_{dd} = 0.

Call price:
C=(p∗)2Cuu+2p∗(1−p∗)Cud+(1−p∗)2Cdd(1+r)2=(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{(p^*)^2 C_{uu} + 2p^*(1-p^*) C_{ud} + (1-p^*)^2 C_{dd}}{(1+r)^2} = \frac{(0.60)^2(21) + 2(0.60)(0.40)(0) + (0.40)^2(0)}{(1.02)^2} = \frac{0.36 × 21}{1.0404} = \frac{7.56}{1.0404} = 7.27
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