Mercado de opciones

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Mechanics of Options Markets
Liuren Wu
Zicklin School of Business, Baruch College

Options Markets

(Hull chapter: 8)

Liuren Wu (Baruch)

Options Markets Mechanics

Options Markets

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Outline

1

Definition

2

Payoffs

3

Mechanics

4

Other option-type products

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Definitionsand terminologies
An option gives the option holder the right/option, but no obligation, to buy or sell a security to the option writer/seller for a pre-specified price (the strike price, K ) at (or up to) a given time in the future (the expiry date ) An option has positive value. Comparison: a forward contract has zero value at inception. Option types A call option gives the holder the right to buya security. The payoff is (ST − K )+ when exercised at maturity. A put option gives the holder the right to sell a security. The payoff is (K − ST )+ when exercised at maturity. American options can be exercised at any time priory to expiry. European options can only be exercised at the expiry.
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More terminologies
Moneyness:the strike relative to the spot/forward level An option is said to be in-the-money if the option has positive value if exercised right now:
St > K for call options and St < K for put options. Sometimes it is also defined in terms of the forward price at the same maturity (in the money forward): Ft > K for call and Ft < K for put The option has positive intrinsic value when in the money. Theintrinsic value is (St − K )+ for call, (K − St )+ for put. We can also define intrinsic value in terms of forward price.

An option is said to be out-of-the-money when it has zero intrinsic value.
St < K for call options and St > K for put options. Out-of-the-money forward: Ft < K for call and Ft > K for put.

An option is said to be at-the-money spot (or forward) when the strike is equal to thespot (or forward).

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More terminologies
The value of an option is determined by the current spot (or forward) price (St or Ft ), the strike price K , the time to maturity τ = T − t, the option type (Call or put, American or European), and the dynamics of the underlying security (e.g., how volatile the security priceis). Out-of-the-money options do not have intrinsic value, but they have time value. Time value is determined by time to maturity of the option and the dynamics of the underlying security. Generically, we can decompose the value of each option into two components: option value = intrinsic value + time value.
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Payoffs versus P&LsFor European options, the terminal payoff can be written as (ST − K )+ for calls and (K − ST )+ for puts at expiry date T . Since options have positive value, one needs to pay an upfront price (option price) to possess an option. The P&L from the option investment is the difference between the terminal payoff and the initial price you pay to obtain the option. Do not confuse the two. The textbooklikes to talk about P&Ls, but I like to talk about payoffs — Different perspectives: P&Ls: If I buy/sell an option today, how much money I can make under different scenarios? What’s my return? Payoffs: If I desire a certain payoff structure in the future, what types of options/positions I need to generate it?

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An example:Call option on a stock index
Consider a European call option on a stock index. The current index level (spot St ) is 100. The option has a strike (K ) of $90 and a time to maturity (T − t) of 1 year. The option has a current value (ct ) of $14. Is this option in-the-money or out-of-the-money (wrt to spot)? What’s intrinsic value for this option? What’s its time value? If you hold this option,...
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