# Option Pricing Fundamentals

Study Option Pricing Fundamentals for SOA Exam FAM. Topic weight 5–10%. Per-objective worked-example approaches, exam traps, vendor chapter map (ASM, ACTEX, Coaching Actuaries, TIA), and a 5–7 day micro study plan.

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[Actuarial](https://exclam.ai/actuarial/index.md)›[Exam FAM](https://exclam.ai/actuarial/exam-fam/index.md)›Option Pricing Fundamentals

Exam FAM topic · 5–10% of exam

Introduction to option pricing including put-call parity, binomial models, and Black-Scholes pricing for European options.

[Back to Exam FAM](https://exclam.ai/actuarial/exam-fam/index.md)

## Per-objective worked-example outlines

For each learning objective on Option Pricing Fundamentals, here is the approach an exam item would test — the setup, the ordering of your reasoning, and the formula or identity you need to bring to the page. Approaches, not full solutions, by design. Verify against the current [soa.org](https://www.soa.org/) syllabus before your sitting.

### Apply put-call parity to relate European call and put prices

Setup

A European call price, strike, time to maturity, current stock price, and risk-free rate are given, and you must find the corresponding put price.

Approach

Use put-call parity: C - P = S - K e^{-rT} (for non-dividend stock) or C - P = S e^{-qT} - K e^{-rT} (with continuous dividend yield q). Solve for the unknown. Check that the put price is non-negative; if not, recheck the inputs and parity sign.

Key identity

C - P = S e^{-qT} - K e^{-rT} (European, continuous dividend q).

### Price options using one-period and multi-period binomial models

Setup

A stock can move up by u or down by d in each period with given probabilities, and you must price a European call or put using the binomial model.

Approach

Compute the risk-neutral probability p\* = (e^{rh} - d) / (u - d) per period. Walk back from terminal payoffs using p\* and discounting by e^{-rh} per step. For American options, take the max of the discounted expected continuation value and the exercise value at each node. Match h, u, d, and r to a consistent time unit.

Key identity

p\* = (e^{rh} - d) / (u - d); option price = e^{-rh} (p\* V\_u + (1 - p\*) V\_d).

### Use the Black-Scholes formula to price European calls and puts

Setup

Stock price, strike, time, volatility, risk-free rate, and dividend yield are given and you must price a European call or put.

Approach

Compute d\_1 = \[ln(S/K) + (r - q + σ^2/2) T\] / (σ √T) and d\_2 = d\_1 - σ √T. Look up N(d\_1) and N(d\_2) from a standard normal table. Call price = S e^{-qT} N(d\_1) - K e^{-rT} N(d\_2). Use put-call parity to get the put price if needed.

Key identity

C = S e^{-qT} N(d\_1) - K e^{-rT} N(d\_2); d\_1, d\_2 as above.

## Common exam traps on Option Pricing Fundamentals

Recurring patterns where candidates lose points on Option Pricing Fundamentals-style items. Each entry pairs the trap with the fix.

Trap

Using real-world probabilities instead of risk-neutral probabilities in the binomial pricer.

Fix

The actual probability of up/down is irrelevant; use p\* derived from the no-arbitrage condition.

Trap

Forgetting the dividend yield in put-call parity or Black-Scholes.

Fix

Include e^{-qT} on the stock side whenever a dividend yield is given.

Trap

Mixing time units between volatility (annual) and step size (often shorter).

Fix

Express σ, r, q, and h in consistent annualized units before plugging into formulas.

Trap

Pricing an American option with the European formula.

Fix

For American puts (and rarely American calls), step through the tree comparing exercise vs continuation at every node.

## Where to find Option Pricing Fundamentals in popular manuals

Pointers to where each major vendor covers this topic, so you can grab the right chapter without combing the full manual. We do not reproduce vendor content — just the location. Chapter and lesson numbers shift between editions; use these as a guide, not as a citation.

ASM

Option pricing chapter at the end of FAM manual

ACTEX

Derivatives and option pricing chapter

Coaching Actuaries

Learn modules on Option Pricing Fundamentals; Adapt category "Option Pricing"

The Infinite Actuary

Option pricing video block (binomial and Black-Scholes)

## 6-day Option Pricing Fundamentals micro plan

A focused 6-day sub-schedule for Option Pricing Fundamentals specifically, at roughly 1.5–2.5 hours per day. Drop it inside your full Exam FAM plan as a single coverage module.

Day 1

Read the option pricing chapter; build flashcards on put-call parity, binomial p\*, and Black-Scholes d\_1/d\_2.

Day 2

Drill 10 put-call parity problems with and without dividends.

Day 3

Binomial pricing — 8 problems on one and multi-period European trees.

Day 4

American options on binomial trees — 5 problems comparing exercise vs continuation.

Day 5

Black-Scholes drills — 10 problems computing call and put prices.

Day 6

Re-do flagged problems and write a one-page option pricing cheat sheet covering all three methods.

## How exclam.ai helps you master Option Pricing Fundamentals

### Flashcards from your manual

Upload your ACTEX Exam FAM digital edition, scanned ASM pages, TIA handouts, or your own notes. exclam.ai extracts the Option Pricing Fundamentals sections and generates flashcards automatically, tuned to the exam traps above.

### Worked-example drilling

Each per-objective approach above maps to a quiz template. exclam.ai re-surfaces missed items until you can recall both the setup and the key identity from cold.

### FSRS spaced repetition

Because Option Pricing Fundamentals is 5–10% of your exam, losing it during review costs you. FSRS brings it back at the optimal moment.

## Option Pricing Fundamentals in the Exam FAM context

SOA Exam FAM has 7 topic areas. Option Pricing Fundamentals is weighted at approximately 5–10% of the exam, here is where it sits relative to the other topics.

| Topic area | Weight |
| --- | --- |
| Insurance Coverages and Retirement Products | 5–10% |
| Severity, Frequency, and Aggregate Models | 15–20% |
| Parametric Estimation | 10–15% |
| Mortality and Survival Models | 10–15% |
| Life Insurance Pricing and Reserving | 15–20% |
| Short-Term Insurance Pricing and Reserving | 15–20% |
| → Option Pricing Fundamentals | 5–10% |

## Other Exam FAM topics

[Insurance Coverages and Retirement Products 5–10% Structure and features of common insurance and retirement products including life insurance, annuities, health, and short-term insurance. Study this topic](https://exclam.ai/actuarial/exam-fam/topics/insurance-coverages-and-retirement-products/index.md)

[Severity, Frequency, and Aggregate Models 15–20% Statistical models for individual loss severity, claim frequency, and aggregate loss distributions including compound distributions. Study this topic](https://exclam.ai/actuarial/exam-fam/topics/severity-frequency-aggregate-models/index.md)

[Parametric Estimation 10–15% Maximum likelihood and method of moments estimation for parametric models, including goodness of fit testing. Study this topic](https://exclam.ai/actuarial/exam-fam/topics/parametric-estimation/index.md)

[Mortality and Survival Models 10–15% Life table construction, force of mortality, select and ultimate mortality, and multiple-decrement models. Study this topic](https://exclam.ai/actuarial/exam-fam/topics/mortality-models/index.md)

[Life Insurance Pricing and Reserving 15–20% Pricing and reserving for life insurance and life annuity products using the equivalence principle and benefit reserves. Study this topic](https://exclam.ai/actuarial/exam-fam/topics/life-insurance-pricing-and-reserving/index.md)

[Short-Term Insurance Pricing and Reserving 15–20% Pricing, loss reserving, and credibility for short-term insurance products including property, casualty, and health. Study this topic](https://exclam.ai/actuarial/exam-fam/topics/short-term-pricing-and-reserving/index.md)