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FRM Part I · FRM Exam Part I

Options Markets for FRM Part I: Study Guide

Options markets cover contracts that give the holder the right, not the obligation, to buy (call) or sell (put) an asset at a strike price. To solve questions, draw the payoff, identify the inputs, apply the right formula (payoff, put-call parity, or strategy profit), and check the sign and direction.

What this chapter covers

This chapter covers how options work and how they are traded. You start with calls and puts, long and short positions, and payoff at expiry. Then you move to exchange-traded mechanics, such as margin, strike and expiry conventions, and adjustments for dividends and splits. After that you learn what drives option prices: the underlying price, strike, time to expiry, volatility, interest rates and dividends.

The second half links these pieces. Put-call parity ties European call and put prices together through no-arbitrage. Trading strategies then combine options and the underlying into spreads, combinations and covered positions. Exotic options close the chapter, showing how standard payoffs can be changed, for example through barriers, averaging or path dependence.

This chapter connects to the rest of Part I in several ways. Futures and forwards give you the cost-of-carry logic behind parity. Quantitative analysis supplies the probability and volatility ideas. Valuation and Risk Models builds on this with the Black-Scholes-Merton model, the Greeks and hedging. If you master the payoffs and parity here, those later topics become much easier.

Options show up across the exam, not just in this chapter. Payoff diagrams, parity and strategy questions are short, rule-based and quantitative, which makes them good places to collect marks quickly if you practise. The same ideas then return in valuation, the Greeks and risk-measurement questions. With 100 equally weighted questions in 4 hours, you cannot afford to spend several minutes re-deriving a payoff. Fluency here saves time everywhere else.

Options Markets: topics in the order to study them

  1. 1Option Basics and PayoffsEverything else rests on knowing the payoff and profit of long and short calls and puts.
  2. 2Option Trading Mechanics and Exchange-Traded OptionsOnce payoffs are clear, learn how contracts are specified, margined and adjusted in practice.
  3. 3Factors Affecting Option PricesYou need the direction of each driver before using parity or strategies.
  4. 4Put-Call ParityIt is the main no-arbitrage relationship and is easy to test numerically.
  5. 5Option Trading Strategies: SpreadsSpreads are built from the basic payoffs and teach you to add and subtract positions.
  6. 6Combinations and Covered StrategiesStraddles, strangles, covered calls and protective puts reuse the same payoff-building skill.
  7. 7Exotic OptionsStudy these last, since each exotic is a variation on standard options and needs the basics first.

How to prepare Options Markets

Treat this chapter as a skill, not a list of definitions. You should be able to sketch any payoff in under a minute.

  1. Learn the four basic payoffs by heart: long call = max(S_T − K, 0), long put = max(K − S_T, 0), and the short positions as their negatives. Then subtract the premium paid (or add the premium received) to get profit.
  2. Practise drawing payoffs for each position. Mark the strike, the break-even and the maximum gain and loss.
  3. Memorise the effect of each price driver on European and American calls and puts. Note the cases where the effect is not clear-cut, such as longer maturity on a European put.
  4. Write out put-call parity for European options on a non-dividend-paying stock: c + K·e^(−rT) = p + S₀. Then practise adding known dividends and checking for arbitrage in each direction.
  5. For every strategy, build the payoff by adding the legs at different values of S_T. Do this on paper until you can do it without prompts.
  6. Do timed practice questions in blocks. Aim for about two minutes per question and review every wrong answer for its cause, such as sign, formula or concept.
  7. Finish with exotics. For each one, write a one-line definition and the way it differs in value from a standard option.

Common mistakes in Options Markets

  • Confusing payoff with profit.

    Fix: Always ask whether the question wants payoff or profit. If profit, subtract the premium paid (or add the premium received) for the position.

  • Getting the sign wrong on short positions.

    Fix: Write the long payoff first, then flip the sign. Check that a short option's maximum gain equals the premium received.

  • Applying put-call parity to American options as an equality.

    Fix: Remember that the equality holds for European options. For American options there are only bounds, not an exact relationship.

  • Forgetting to discount the strike or adjust for dividends in parity.

    Fix: Check the question for the rate, the time and any dividend. Write the full parity equation before substituting numbers.

  • Stating price effects as always true.

    Fix: Learn which effects are certain and which depend on the case, such as European options with large dividends. Choose answers that match the exact conditions given.

  • Choosing the wrong strategy for the view described.

    Fix: Link each strategy to a view: direction, volatility or range. Sketch the payoff to confirm the match before you answer.

Last-day revision: Options Markets

  • Long call payoff = max(S_T − K, 0); long put payoff = max(K − S_T, 0).
  • Profit = payoff − premium paid for a long position; the short position is the mirror image.
  • A call gains from a higher underlying price; a put gains from a lower one.
  • Higher volatility raises the value of both calls and puts.
  • Higher interest rates raise call values and lower put values, other things equal.
  • Expected dividends lower call values and raise put values.
  • Put-call parity (European, no dividends): c + K·e^(−rT) = p + S₀.
  • With a known present value of dividends D: c + D + K·e^(−rT) = p + S₀.
  • Bull spread: long a lower strike, short a higher strike; bear spread is the reverse.
  • Straddle: long a call and a put at the same strike; it gains from a large move either way.
  • Covered call: long the stock and short a call; protective put: long the stock and long a put.
  • Barrier options are path dependent; Asian options depend on an average price.

Options Markets practice questions

Options Markets in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Options Markets: frequently asked questions

How should I start the Options Markets chapter for FRM Part I?

Start with the basic payoffs and profits of long and short calls and puts. Once you can sketch them quickly, the rest of the chapter, including parity and strategies, builds on them.

Do I need to memorise put-call parity?

Yes. Know the equation for European options without dividends and how to adjust for dividends. Practise it in both directions, since questions often ask you to find a missing price or spot an arbitrage.

Are exotic options heavily tested?

You should expect to know the main types and how they differ from standard options, not to price them by hand. Focus on definitions, what makes each one path dependent or customised, and how that changes its value.

Does this chapter link to other FRM Part I topics?

Yes. It supports futures and forwards, the Black-Scholes-Merton model and the Greeks in valuation and risk models, and it uses the volatility ideas from quantitative analysis.