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Concept

FAM Option Pricing Fundamentals

FAM option pricing is focused: identify put and call payoffs, price simple European derivatives with binomial or Black-Scholes models, calculate delta hedge, and apply put-call parity.

Quick Answer

FAM does not ask for a full investments course. It asks whether a candidate can value simple European-style derivatives using risk-neutral expected present value under binomial and Black-Scholes models.

Treat option pricing as a small but high-friction block. It is only 2.5-7.5% of the syllabus, but it can feel foreign if FM cash-flow habits are rusty.

Payoff Recognition

A call pays when the asset finishes above the strike. A put pays when the asset finishes below the strike. Before using a pricing formula, write the terminal payoff in each state.

European call and put payoffs
CT=(ST−K)+,PT=(K−ST)+C_T=(S_T-K)_{+},\qquad P_T=(K-S_T)_{+}

Binomial Pricing

In a one-period binomial model, the risk-neutral probability is the probability that makes the discounted stock price a fair value under the model. Price the option by discounting the risk-neutral expected payoff.

The most common FAM mistake is using the real-world probability when the question is asking for risk-neutral valuation.

One-period risk-neutral price
V0=v(qVu+(1−q)Vd),q=1+i−du−dV_0=v\left(qV_u+(1-q)V_d\right),\qquad q=\frac{1+i-d}{u-d}

Black-Scholes Boundary

FAM expects candidates to apply the Black-Scholes formula to simple European options on a non-dividend-paying asset and calculate a delta hedge. The main skill is parameter placement: current price, strike, time, volatility, risk-free rate, and standard normal CDF values.

Do not spend FAM time deriving stochastic calculus. Spend it on payoff recognition, sign discipline, and interpreting delta as the number of shares in the hedge per option.

Put-Call Parity

Put-call parity is both a pricing formula and an error detector. If a call, put, stock, and discounted strike violate parity, one price is inconsistent with the others under the model assumptions.

European put-call parity
C−P=S0−KvTC-P=S_0-Kv^T
Practice

Original Source-Backed Practice

4 questions built from syllabus outcomes and released-exam patterns. The prompts and answers are original, so they train the skill without copying official exam text.

FAM Option Pricing Drill

Original checks for European option payoff recognition, one-period binomial pricing, put-call parity, and delta hedge interpretation.

FAM - 18 min
Source pattern: SOA FAM option-pricing outcome and original prompts.
  1. Question 1/Flashcard

    Call and put payoff

    Write the terminal payoff of a European call and European put with strike K.

    CoreoptionspayofffamFAM Option Pricing Fundamentals
    Solution And Grading Points

    The call payoff is max(S_T - K, 0). The put payoff is max(K - S_T, 0).

    • Uses S_T - K for the call.
    • Uses K - S_T for the put.
    • Floors both payoffs at zero.
  2. Question 2/Calculation

    One-period binomial call

    A stock is 100. In one period it moves to 120 or 90. The one-period risk-free rate is 5%. Find the price of a European call with strike 100.

    Exam Readybinomial-option-pricingrisk-neutralcall-optionFAM Option Pricing Fundamentals
    Solution And Grading Points

    The up payoff is 20 and the down payoff is 0. The risk-neutral probability is q = (1.05 - 0.90) / (1.20 - 0.90) = 0.5. Price = (0.5(20) + 0.5(0)) / 1.05 = 9.52.

    1. Compute up and down payoffs.
    2. Compute the risk-neutral probability.
    3. Discount the risk-neutral expected payoff.
    • Computes up payoff 20 and down payoff 0.
    • Computes q = 0.5.
    • Reports a price near 9.52.
  3. Question 3/Calculation

    Put-call parity

    A non-dividend stock is 50, a European call is 7, the present value of the strike is 45, and the matching put has the same strike and expiry. Find the put price using put-call parity.

    Coreput-call-parityoptionsfamFAM Option Pricing Fundamentals
    Solution And Grading Points

    Put-call parity gives C - P = S_0 - PV(K). Thus 7 - P = 50 - 45 = 5, so P = 2.

    1. Write C - P = S_0 - PV(K).
    2. Substitute C = 7, S_0 = 50, and PV(K) = 45.
    3. Solve for P.
    • Uses European put-call parity.
    • Uses present value of strike, not strike at expiry.
    • Reports put price 2.
  4. Question 4/Written Answer

    Delta hedge interpretation

    In one sentence, what does the delta of a call option mean in a simple hedge?

    CoredeltahedgingoptionsFAM Option Pricing Fundamentals
    Solution And Grading Points

    Delta is the number of shares of the underlying asset held per option in the replicating or hedging portfolio, with the position adjusted as the option sensitivity changes.

    • Interprets delta as shares per option.
    • Connects delta to a hedge or replicating portfolio.
    • Mentions sensitivity or adjustment.

References And Official Sources