Options

Question 1

What is an option?

Answer 1

A contract giving the holder the right (but not the obligation) to buy/sell an asset at a specified price (strike price) on or before a specified date (expiration date). The buyer must pay the seller a premium for the option.

Question 2

What is a call option?

Answer 2

An option contract giving the holder the right to buy the asset.

Question 3

What is a put option?

Answer 3

An option contract giving the holder the right to sell the asset.

Question 4

What is an in-the-money, at-the-money, or out-the-money option?

Answer 4

At the money:
S = X
In-the-money option has intrinsic value:
S > X (call option)
S < X (put option)
Out-the-money option has no intrinsic value:
S < X (call option)
S > X (put option)

Question 5

What is the delta of a stock option?

Answer 5

The ratio of the change in the price of a stock option to the change in the price of the underlying stock. It is the number of units of the stock we should hold for each option shorted in order to create a riskless portfolio. The delta of a call option is positive whereas the delta of a put option is negative. The delta measures the sensitivity of the option price to the price of the underlying asset when small changes are considered.

Question 6

What are the key differences between American and European options?

Answer 6

EARLY EXERCISE/FLEXIBILITY: American options can be exercised at any time before expiration, and are thus more flexible and expensive.
European options can only be exercised at expiration.
If a stock pays dividends, American call options might be exercised early to capture dividends. European options cannot be exercised early, so their valuation is adjusted for dividends.
European options are simpler to price and are priced using models like Black-Scholes, while American options often require binomial trees.

Question 7

What is the main difference between futures and options?

Answer 7

Obligation vs Right:
- A futures contract obligates both buyer and seller to execute the trade at a set
price on a future date.
- An option contract gives the buyer the right, but not the obligation, to buy
(call) or sell (put) at a set price before or at expiration.
Payoff Symmetry:
- Futures have symmetric payoff - both sides have unlimited profit/loss.
- Options have asymmetric payoff - the buyer’s loss is limited to the premium,
but profit is unlimited (for calls).
Upfront Cost:
- Futures generally require no premium (just margin).
- Options require an upfront premium payment.