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Describe the types of option and what they are used for, and define moneyness.

FRM® Part I · Financial Markets and Products · Options Markets · FRM1.FM.12.a

The idea

A call option gives its holder the right, but not the obligation, to buy the underlying asset at the strike price. A put gives the right to sell at the strike. The writer takes the opposite side and carries the obligation. American options can be exercised at any time up to expiry, European options only at expiry. Options are used to hedge (a protective put limits losses on a long position), to speculate with leverage, and to earn income by writing. Moneyness compares the underlying price S with the strike K. A call is in the money when S > K, a put when S < K, and both are at the money when S equals K. Intrinsic value is max(S − K, 0) for a call and max(K − S, 0) for a put. The usual error is applying the call rule to a put.

Formulas

Time value of an option

time value = premium − intrinsic value

premium
the option's market price
intrinsic value
max(S − K, 0) for a call, max(K − S, 0) for a put

Intrinsic value is never negative. Using the call rule for a put is the usual moneyness error.

A practice question

From the question bank, with the reason each wrong option is wrong.

A pension fund holds a large diversified equity portfolio and wants protection against a market fall while keeping the gains if the market rises. Which option position is most suitable?

  1. Sell index call optionsWhy not: Writing a call earns a premium but gives up the upside and leaves most of the downside exposed, so it is not protection.
  2. Buy index put options - correct
  3. Buy index call optionsWhy not: A long call gains when the market rises, which adds to the fund's long exposure rather than hedging it.
  4. Sell index put optionsWhy not: A short put loses when the market falls, so it increases the fund's downside risk instead of reducing it.

A long put pays off when the index falls, offsetting losses on the portfolio, while the fund keeps the upside less the premium. This is a protective put.

A harder one

A stock trades at 62. Four options on it have the same expiry: a call with strike 60, a put with strike 60, a call with strike 65 and a put with strike 65. Which pair is in the money?

  1. The 60 call and the 65 callWhy not: The 65 call is out of the money because the stock price (62) is below its strike.
  2. The 60 put and the 65 callWhy not: Applies the call rule to the puts and the put rule to the calls, reversing the definitions.
  3. The 60 call and the 65 put - correct
  4. The 60 put and the 65 putWhy not: The 60 put is out of the money because the stock price is above its strike; only the 65 put qualifies.

A call is in the money when S > K (62 > 60) and a put when S < K (62 < 65). The 60 call and the 65 put are in the money; the other two are out of the money.

The hardest tier

A stock trades at 38. A put with strike 40 trades at a premium of 3.50. Which row gives the intrinsic value and the time value per share of the put?

  1. Intrinsic value 2.00; time value 1.50 - correct
  2. Intrinsic value 0.00; time value 3.50Why not: Uses the call formula max(S - K, 0) for a put, so the intrinsic value comes out as zero.
  3. Intrinsic value 3.50; time value 0.00Why not: Treats the whole premium as intrinsic value, ignoring that intrinsic value is set by S and K, not by the price paid.
  4. Intrinsic value -2.00; time value 5.50Why not: Computes S - K without flooring at zero and without using the put formula; intrinsic value cannot be negative.

Put intrinsic value = max(K - S, 0) = max(40 - 38, 0) = 2.00. Time value = premium - intrinsic value = 3.50 - 2.00 = 1.50.

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