Options and their Uses¶

BUSI 722: Data-Driven Finance II¶

Kerry Back, Rice University¶

Options and Open Interest¶

  • A financial option is a right to buy or sell a financial security.

  • The right trades separately from the (underlying) security and usually even on a different exchange.

  • The rights are not (usually) issued by the companies who issue the underlying securities.

    • Instead, the rights are created when someone buys one from someone else.
    • Open interest is the number that exist at any time.

Example¶

  • When a contract is first opened for trading, open interest is zero.
  • Suppose Andy buys a contract from Chloe, and Brooke buys a contract from David.
    • Longs = Andy and Brooke
    • Shorts = Chloe and David
    • Open interest = 2
  • Suppose Andy then sells a contract to David.
    • Andy: long + short = no position
    • David: short + long = no position
    • Longs = Brooke
    • Shorts = Chloe
    • Open interest = 1

Clearinghouse¶

  • The long party has an option. The short party has an obligation.
  • After a trade is made, the option clearinghouse steps in the middle and becomes the counterparty to both sides.

Hedging, speculation, and income¶

  • You pay upfront to acquire an option.
    • The amount you pay is called the option premium.
    • It is not part of the contract but instead is determined in the market (like a stock price).
  • You buy options to hedge or to speculate. You sell options for income.
  • Sellers of options need to have sufficient equity in their accounts (margin). A buyer needs enough cash to pay the premium but no more (like buying a stock).

Calls, puts, and strikes¶

  • A call option gives the holder the right to buy an asset at a pre-specified price.

  • A put option gives the holder the right to sell an asset at a pre-specified price.

  • The asset is called the underlying asset or just the underlying.

  • The pre-specified price is called the exercise price or strike price.

American and European¶

  • An option is valid for a specified period of time, the end of which is called its expiration date or maturity date.

  • Most financial options can be exercised at any time the owner wishes, prior to maturity. Such options are called American.

  • There are some options that can only be exercised on the maturity date. They are called European. Both types are traded on both continents.

Moneyness¶

  • Borrowing language from horse racing, we say a call is

    • in the money if the underlying price is above the strike,
    • at the money if the underlying price equals the strike
    • out of the money if the underlying price is below the strike

  • The reverse for puts

  • Also, "deep in the money" and "deep out of the money"

Value of a call at maturity¶

  • At maturity, the value of a call is
$$\begin{cases} 0 & \text{if underlying < strike}\\ \text{underlying} - \text{strike} & \text{if underlying > strike} \end{cases} $$
  • Equivalently, the value of a call is
$$\max(\text{underlying price}-\text{strike}, 0)$$

Value of a put at maturity¶

  • At maturity, the value of a put is
$$\begin{cases} \text{strike} - \text{underlying} & \text{if underlying < strike}\\ 0 & \text{if underlying > strike} \end{cases} $$
  • Equivalently, the value of a put is
$$\max(\text{strike}-\text{underlying price}, 0)$$

Option Data from Yahoo¶

  • You can get current trading prices of stock options from finance.yahoo.com.
  • You can click around and find it or use the yfinance library.
  • We'll look at CVX options.
In [10]:
import yfinance as yf
cvx = yf.Ticker("cvx")
  • cvx.options is the set of traded maturities
  • cvx.option_chain("some date") is an object containing call and put data
  • cvx.option_chain("some date").calls is a dataframe of call info
  • cvx.option_chain("some date").puts is a dataframe of put info
In [11]:
date = cvx.options[6]
cvx.option_chain(date).calls
Out[11]:
contractSymbol lastTradeDate strike lastPrice bid ask change percentChange volume openInterest impliedVolatility inTheMoney contractSize currency
0 CVX240315C00075000 2024-01-05 20:13:49+00:00 75.0 75.70 74.95 76.70 5.019997 7.102428 1.0 1 0.841798 True REGULAR USD
1 CVX240315C00080000 2023-11-22 15:29:20+00:00 80.0 63.85 71.95 72.65 0.000000 0.000000 24.0 24 1.053716 True REGULAR USD
2 CVX240315C00085000 2023-11-21 20:59:02+00:00 85.0 60.35 65.95 67.10 0.000000 0.000000 NaN 2 0.855226 True REGULAR USD
3 CVX240315C00090000 2023-12-26 18:31:02+00:00 90.0 63.65 60.10 61.55 0.000000 0.000000 2.0 40 0.644047 True REGULAR USD
4 CVX240315C00095000 2023-12-26 18:31:02+00:00 95.0 58.70 55.25 56.60 0.000000 0.000000 NaN 2 0.607914 True REGULAR USD
5 CVX240315C00100000 2023-12-26 17:50:05+00:00 100.0 53.80 50.25 52.30 0.000000 0.000000 1.0 36 0.611088 True REGULAR USD
6 CVX240315C00105000 2023-08-01 19:00:05+00:00 105.0 57.50 57.15 58.20 0.000000 0.000000 NaN 8 1.370609 True REGULAR USD
7 CVX240315C00110000 2023-12-22 15:15:35+00:00 110.0 42.75 40.35 41.60 0.000000 0.000000 2.0 15 0.531255 True REGULAR USD
8 CVX240315C00115000 2023-12-07 15:49:28+00:00 115.0 29.91 35.35 37.05 0.000000 0.000000 4.0 16 0.514897 True REGULAR USD
9 CVX240315C00120000 2024-01-03 20:21:15+00:00 120.0 34.00 30.55 31.90 0.000000 0.000000 2.0 119 0.440191 True REGULAR USD
10 CVX240315C00125000 2023-12-13 15:22:41+00:00 125.0 19.31 25.25 27.70 0.000000 0.000000 1.0 85 0.438482 True REGULAR USD
11 CVX240315C00130000 2024-01-04 17:12:59+00:00 130.0 22.61 21.40 22.00 0.000000 0.000000 7.0 199 0.328620 True REGULAR USD
12 CVX240315C00135000 2024-01-05 15:23:13+00:00 135.0 18.05 17.10 17.35 -0.400002 -2.168030 2.0 199 0.289924 True REGULAR USD
13 CVX240315C00140000 2024-01-05 15:19:40+00:00 140.0 13.80 12.95 13.20 0.200000 1.470587 33.0 489 0.268806 True REGULAR USD
14 CVX240315C00145000 2024-01-05 18:58:37+00:00 145.0 9.71 9.35 9.50 -0.410000 -4.051382 11.0 2687 0.251594 True REGULAR USD
15 CVX240315C00150000 2024-01-05 20:48:18+00:00 150.0 6.31 6.30 6.40 -0.340000 -5.112784 222.0 1784 0.237923 True REGULAR USD
16 CVX240315C00155000 2024-01-05 20:48:18+00:00 155.0 3.95 3.95 4.05 -0.400000 -9.195399 138.0 3496 0.229439 False REGULAR USD
17 CVX240315C00160000 2024-01-05 20:59:23+00:00 160.0 2.39 2.37 2.43 -0.240000 -9.125476 160.0 6179 0.225166 False REGULAR USD
18 CVX240315C00165000 2024-01-05 20:45:04+00:00 165.0 1.35 1.32 1.38 -0.150000 -9.999999 168.0 6916 0.222786 False REGULAR USD
19 CVX240315C00170000 2024-01-05 20:59:54+00:00 170.0 0.72 0.72 0.78 -0.110000 -13.253006 441.0 2295 0.224373 False REGULAR USD
20 CVX240315C00175000 2024-01-05 18:48:43+00:00 175.0 0.39 0.38 0.43 -0.090000 -18.750002 8.0 2638 0.226570 False REGULAR USD
21 CVX240315C00180000 2024-01-04 16:35:29+00:00 180.0 0.25 0.20 0.25 -0.010000 -3.846150 1.0 1560 0.232430 False REGULAR USD
22 CVX240315C00185000 2024-01-04 14:42:51+00:00 185.0 0.21 0.12 0.15 0.000000 0.000000 1.0 1061 0.238777 False REGULAR USD
23 CVX240315C00190000 2024-01-05 20:40:15+00:00 190.0 0.08 0.05 0.10 -0.030000 -27.272728 16.0 855 0.249031 False REGULAR USD
24 CVX240315C00195000 2024-01-05 14:31:45+00:00 195.0 0.05 0.04 0.07 -0.010000 -16.666664 1.0 780 0.259773 False REGULAR USD
25 CVX240315C00200000 2023-12-26 17:20:21+00:00 200.0 0.05 0.00 0.11 -0.020000 -28.571426 10.0 634 0.297859 False REGULAR USD
26 CVX240315C00210000 2024-01-03 19:18:15+00:00 210.0 0.09 0.00 0.09 0.000000 0.000000 1.0 313 0.332038 False REGULAR USD
27 CVX240315C00220000 2023-11-14 15:07:21+00:00 220.0 0.03 0.00 0.08 0.000000 0.000000 10.0 6 0.365241 False REGULAR USD
28 CVX240315C00230000 2023-12-07 15:26:41+00:00 230.0 0.01 0.00 0.08 0.000000 0.000000 30.0 470 0.401373 False REGULAR USD
29 CVX240315C00240000 2023-12-12 19:44:58+00:00 240.0 0.01 0.00 0.08 0.000000 0.000000 31.0 457 0.435553 False REGULAR USD
In [12]:
cvx.option_chain(date).puts
Out[12]:
contractSymbol lastTradeDate strike lastPrice bid ask change percentChange volume openInterest impliedVolatility inTheMoney contractSize currency
0 CVX240315P00075000 2023-12-06 15:46:27+00:00 75.0 0.04 0.00 0.08 0.000000 0.000000 5.0 610 0.613285 False REGULAR USD
1 CVX240315P00080000 2023-12-11 20:18:41+00:00 80.0 0.02 0.00 0.08 0.000000 0.000000 8.0 362 0.560551 False REGULAR USD
2 CVX240315P00085000 2023-12-11 20:18:01+00:00 85.0 0.05 0.00 0.08 0.000000 0.000000 7.0 36 0.511724 False REGULAR USD
3 CVX240315P00090000 2023-11-29 15:07:37+00:00 90.0 0.06 0.00 0.09 0.000000 0.000000 1.0 93 0.509771 False REGULAR USD
4 CVX240315P00095000 2023-11-17 20:52:56+00:00 95.0 0.15 0.02 0.11 0.000000 0.000000 2.0 70 0.473638 False REGULAR USD
5 CVX240315P00100000 2024-01-04 20:13:42+00:00 100.0 0.05 0.02 0.11 0.020000 66.666670 5.0 49 0.425787 False REGULAR USD
6 CVX240315P00105000 2023-12-26 15:01:51+00:00 105.0 0.08 0.03 0.14 0.000000 0.000000 10.0 188 0.394049 False REGULAR USD
7 CVX240315P00110000 2024-01-03 20:32:23+00:00 110.0 0.11 0.10 0.14 0.000000 0.000000 10.0 325 0.349128 False REGULAR USD
8 CVX240315P00115000 2024-01-04 16:45:21+00:00 115.0 0.18 0.17 0.21 0.000000 0.000000 14.0 1131 0.326179 False REGULAR USD
9 CVX240315P00120000 2024-01-05 16:06:39+00:00 120.0 0.28 0.29 0.33 -0.010000 -3.448272 1.0 1166 0.306159 False REGULAR USD
10 CVX240315P00125000 2024-01-05 20:45:47+00:00 125.0 0.50 0.49 0.54 0.050000 11.111114 7.0 2354 0.289314 False REGULAR USD
11 CVX240315P00130000 2024-01-05 16:06:39+00:00 130.0 0.88 0.85 0.91 0.220000 33.333330 6.0 2348 0.275886 False REGULAR USD
12 CVX240315P00135000 2024-01-05 19:38:09+00:00 135.0 1.48 1.47 1.54 -0.050000 -3.267971 17.0 3836 0.265266 False REGULAR USD
13 CVX240315P00140000 2024-01-05 20:47:28+00:00 140.0 2.49 2.45 2.51 -0.020000 -0.796812 148.0 4685 0.254890 False REGULAR USD
14 CVX240315P00145000 2024-01-05 19:47:28+00:00 145.0 4.00 3.90 4.00 0.150000 3.896107 423.0 5311 0.247566 False REGULAR USD
15 CVX240315P00150000 2024-01-05 20:51:45+00:00 150.0 6.00 5.95 6.05 0.200000 3.448272 263.0 2792 0.239998 False REGULAR USD
16 CVX240315P00155000 2024-01-05 18:08:00+00:00 155.0 8.45 8.65 8.80 0.210000 2.548544 207.0 1256 0.235481 True REGULAR USD
17 CVX240315P00160000 2024-01-04 15:14:14+00:00 160.0 10.65 12.05 12.60 0.000000 0.000000 3.0 2578 0.250679 True REGULAR USD
18 CVX240315P00165000 2024-01-05 17:09:24+00:00 165.0 16.23 16.15 16.45 1.250000 8.344460 6.0 1412 0.248909 True REGULAR USD
19 CVX240315P00170000 2024-01-05 19:55:53+00:00 170.0 21.08 20.05 20.90 1.629999 8.380458 1.0 222 0.261482 True REGULAR USD
20 CVX240315P00175000 2023-12-06 19:53:37+00:00 175.0 31.85 24.50 26.15 0.000000 0.000000 720.0 239 0.318122 True REGULAR USD
21 CVX240315P00180000 2023-11-07 17:42:29+00:00 180.0 37.90 36.00 38.05 0.000000 0.000000 1.0 0 0.653080 True REGULAR USD
22 CVX240315P00185000 2023-09-11 16:42:38+00:00 185.0 21.67 25.35 26.00 0.000000 0.000000 3.0 6 0.000010 True REGULAR USD
23 CVX240315P00190000 2023-09-22 17:34:23+00:00 190.0 24.91 25.45 26.00 0.000000 0.000000 NaN 10 0.000010 True REGULAR USD
24 CVX240315P00200000 2023-09-06 17:47:50+00:00 200.0 33.55 37.70 38.95 0.000000 0.000000 10.0 0 0.000010 True REGULAR USD
25 CVX240315P00230000 2023-10-27 19:27:37+00:00 230.0 86.42 83.65 85.50 0.000000 0.000000 2.0 0 0.894532 True REGULAR USD

Buying Calls to Bet on a Stock¶

  • Investing in call options is similar to buying shares - you win when the stock goes up - but the % gains and losses are amplified
  • It is similar to buying stocks with very high leverage
  • The amount of "leverage" is greater for out of the money call
  • Example: stock trading at 100. Might buy calls with a strike of 110 or 120.
  • Don't have to hold to maturity. If the stock goes up, the price of the call will go up, and you can sell and take the profit.

Buying Puts to Bet Against a Stock¶

  • Investing in puts is similar to shorting a stock - you win when the stock goes down - but the % gains and losses are amplified.
  • The amplification is greater for out of the money puts.
  • Example: stock trading at 100. Might buy puts with a strike of 90 or 80.
  • Again, don't have to hold to maturity.

Limited Liability¶

  • Buying options is different in one way from buying stocks on margin or short selling - your maximum loss is capped with options.
  • You can lose everything that you invest but not more than that.
  • It is possible, though rare, to lose more than you've invested when buying a stock on margin or short selling.
  • On the other hand, sellers of options have unlimited liability.

Buying Puts for Protection¶

  • If you own a stock, you might buy a put for insurance.
  • You normally buy out-of-the-money puts for protection.
  • Example: you own a stock trading at 100 and buy a put with a strike of 80.
  • Your downside on the stock is now limited at 80, because you have an option to sell it at 80.
  • Usually, you wouldn't exercise the put. If the stock falls, you make a profit on the put that offsets some of your loss on the stock.

Selling Calls for Income¶

  • If you own a stock, you might sell a call option on it for income. This is called selling a covered call.
  • You normally sell out-of-the-money calls.
  • Example: you own a stock trading at 100 and sell a call with a strike of 120.
  • If the stock doesn't go up beyond 120, you'll be happy you sold the call.

Collars¶

  • It is common to buy a put for insurance and to sell a call to pay for the put.
  • You are selling off some of your upside to protect your downside.
  • Example: you own a stock trading at 100 and buy a put with a strike of 80 and sell a call with a strike of 120.
  • The portfolio value is collared between 80 and 120.