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What is an option?

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    Benton Li
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Foreword: This blog is a brief introduction to options. Here we mainly focus on the vanilla equity option. Topics like option pricing and bizarre options (e.g. Asian options) will be explained in separate blogs. Also, this is the option in the context of finance, not the option in CS.

What is an option?

To buy, or not to buy, that is the option. — William Sachspeare

As mentioned in a previous blog on derivatives, the option is a genre of derivatives.

Definition: An option is a contract, that gives you the right to (but not an obligation) to buy, sell, or enter a swap at a specific price at a future moment.

That is a long sentence that makes no goddam chicken sense, init? Well, you only need to keep a few keywords in mind: right, specific price, and future moment.

To better understand this, just think of it as a coupon for a lock-in price in the future.

Option specification:

Expiration date: also known as the maturity date. After this date, your option goes void.

Type:

Style: we never talk about when you can exercise your right, right? It depends on its style.

Here are 3 common types:

  • European: the vanilla; You can only exercise your option on the expiration date.
  • American: the dominative; You can exercise your option anytime before or on the expiration date;
  • Bermudan: a mixture of European and American; You can exercise your option at any time within a specified time window. (e.g. Exercisable from 9 AM - 5 PM on any Friday after September 12th but before the expiration date)

Note: the name has nothing to do with the place or currency, i.e. you can originate or trade an American option in Europe too.

Strike price: also known as the exercise price.

Premium: “That’s the price you pay” for the option

Underlying asset: What exactly will you buy/sell? It can be a variety of things: a stock, a bond, or even another derivative!

The underlying assets of certain options (like interest rate options) are not buyable/sellable. In that case, you compute a value based on the difference between strike rate and the spotted rate.

Quantity: e.g number of stock shares, notion amount for interest rate

Settlement:

  • Physical settlement: you get/give physical goods like foreign currencies, stocks, and bonds.
  • Cash settlement:
    • you receive/pay cash based on untouchable numbers like interest rates, and equity indexes (or your standing in your girlfriend’s scoring system).
    • Physical goods can be cash settled too.

Pseudo code in C++:

typedef enum {EUROPEAN, AMERICAN, BERMUDAN} OptionStyle;
typedef enum {PUT, CALL, CAPLET, FLOORLET} OptionType;
typedef enum {CASH, PHYSICAL} Settlement;
class OptionContract: public Derivative{
		std::time expiration_date;
		OptionStyle style;
		OptionType type;
		QuantLib::Instrument underlying_asset;
		Settlement Settlement;
		float amount;
		float strike;
		float premium;
		// More info e.g. stock dividend...
};

Moneyness:

Moneyness entails the probability if you exercise the option. In other words, it is how much you gain/loss if you exercise your option right now.

There are three kinds:

  • In the money (ITM): You are paying(or receiving) a price lower(or higher) than the market price.
  • At the money (ATM): You are paying/receiving a price same as the market price
  • Out of the money (OTM): You are paying(or receiving) a price higher(or lower) than the market price

Notice that moneyness only depends on spotted price (S) and strike price (K). Premium does not affect moneyness.

Example of an option:

Today, DeezNuts company’s common stock price is $100.

You, a little chipmunk, speculate that DeezNuts will go up to $120 next month.

So you bought a European call option of 100 shares of that expires next month at the exercise price of $101. It costs you $10 * 100 = $1k.

Quick check:

  • Strike price (K)? - $101
  • Underlying asset? - DeezNuts common shares
  • Quantity? - 100 shares
  • Will you be buying or selling? - buying, because it’s a call.
  • When can you exercise? - A month from now.
  • Premium? - $1000 ($10/share)
  • Who are you? A speculative chipmunk.

Next month:

If your speculation is right.

Spot price(S) = $120. If you exercise. It will be ITM, because $101 < $120

In total, your gain is 100 * ($120 - $101) - $1000 = $900

Yay, now you can buy some peanuts.

If the stock price rises to $101

It will be ATM because spotted price ($101)= strike price($101)

Notice that although the spotted price and strike are the equal, it doesn’t mean ATM options are useless. Why so?

  1. Exercising option usually doesn’t charge fees, whereas buying from the market usually does.
  2. Your counterparty has the obligation to give you the asset upon exercise. When the underlying asset is scarce or illiquid in the market, your ATM option gives you wings.

If the stock price drops to $98

It will be OTM because spotted price ($98) < strike price($101)

Notice that sometimes it’s still reasonable to exercise OTM options. For example, you can potentially get a fat dividend if you own this stock, but it’s not liquid in the market or the transaction fee is too high.

If the stock price rises to $106

It will be ITM because spotted price ($106) > strike price($101)

Net gain if exercise: 100 * ($106 - $101) - $1000 = - $500

Notice that even if exercising gives you an overall loss, the option is still ITM.

However it’s still better to exercise. Because the loss for not exercising will be $1000 > $500

Remark

This is a every simple example. When we trade or make strategy in real world, we also need to take account for factors like risk-free rate, stock dividends, capital cost, volatility, liquidity, etc.

Read more:

Black–Scholes model - Wikipedia