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 28 medium 6 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
C 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
B is correct.

Using a two-period binomial model with S0=100S_0 = 100, u=1.10u = 1.10, d=0.90d = 0.90, r=0.02r = 0.02 per period, K=100K = 100.

Risk-neutral probability:
p∗=1.02−0.901.10−0.90=0.120.20=0.60.p^* = \frac{1.02-0.90}{1.10-0.90} = \frac{0.12}{0.20} = 0.60.

Terminal stock prices: Suu=121S_{uu} = 121, Sud=99S_{ud} = 99, Sdd=81S_{dd} = 81.
Terminal payoffs: Cuu=21C_{uu} = 21, Cud=0C_{ud} = 0, Cdd=0C_{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 \times 21}{1.0404} = \frac{7.56}{1.0404} = 7.27
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