Options
Definition
Options are financial derivatives that give the buyer the right, but not the obligation, to buy or sell an underlying asset at a specified price on or before a specified date.
Types of Options
Underlying type: futures options, futures spread options, equity options, fx options, interest rate options
Payout Type: call, put, exotic
Settlement Type: cash settled, delivery
Exercise Time: European, American, Bermudan
Pricing Basics
How to determine option value?
Understanding option greeks
Option Specifications
In order to understand vanilla options pricing, we need to look at the following features:
- Strike price
- The specified price at which the underlying asset can be bought or sold
- Time to expiration
- The amount of time remaining until the option expires
Market data
Price of the underlying asset
Volatility of the underlying asset
- How much the price of the underlying asset is expected to fluctuate
These factors are used to calculate the theoretical value of an option using a mathematical model such as the Black-Scholes model. However, the actual price of an option may also be influenced by supply and demand in the market.
Example
- Strike: 100
- Time to expiration: 1 year
- Interest rate: 0%
- Volatility: 30%
Option Price and Payoff Charts
Numerical Result
| Underlying Price | Call Payoff | Put Payoff | Call Price | Put Price | Call Delta | Put Delta | Gamma | Theta |
|---|---|---|---|---|---|---|---|---|
| 1.00 | 0.00 | 99.00 | 0.00 | 99.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 2.00 | 0.00 | 98.00 | 0.00 | 98.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 3.00 | 0.00 | 97.00 | 0.00 | 97.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 4.00 | 0.00 | 96.00 | 0.00 | 96.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 5.00 | 0.00 | 95.00 | 0.00 | 95.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 6.00 | 0.00 | 94.00 | 0.00 | 94.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 7.00 | 0.00 | 93.00 | 0.00 | 93.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 8.00 | 0.00 | 92.00 | 0.00 | 92.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 9.00 | 0.00 | 91.00 | 0.00 | 91.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 10.00 | 0.00 | 90.00 | 0.00 | 90.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 11.00 | 0.00 | 89.00 | 0.00 | 89.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 12.00 | 0.00 | 88.00 | 0.00 | 88.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 13.00 | 0.00 | 87.00 | 0.00 | 87.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 14.00 | 0.00 | 86.00 | 0.00 | 86.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 15.00 | 0.00 | 85.00 | 0.00 | 85.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 16.00 | 0.00 | 84.00 | 0.00 | 84.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 17.00 | 0.00 | 83.00 | 0.00 | 83.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 18.00 | 0.00 | 82.00 | 0.00 | 82.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 19.00 | 0.00 | 81.00 | 0.00 | 81.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 20.00 | 0.00 | 80.00 | 0.00 | 80.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 21.00 | 0.00 | 79.00 | 0.00 | 79.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 22.00 | 0.00 | 78.00 | 0.00 | 78.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 23.00 | 0.00 | 77.00 | 0.00 | 77.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 24.00 | 0.00 | 76.00 | 0.00 | 76.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 25.00 | 0.00 | 75.00 | 0.00 | 75.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 26.00 | 0.00 | 74.00 | 0.00 | 74.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 27.00 | 0.00 | 73.00 | 0.00 | 73.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 28.00 | 0.00 | 72.00 | 0.00 | 72.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 29.00 | 0.00 | 71.00 | 0.00 | 71.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 30.00 | 0.00 | 70.00 | 0.00 | 70.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 31.00 | 0.00 | 69.00 | 0.00 | 69.00 | 0.00 | -1.00 | 0.0000 | -0.0000 |
| 32.00 | 0.00 | 68.00 | 0.00 | 68.00 | 0.00 | -1.00 | 0.0001 | -0.0000 |
| 33.00 | 0.00 | 67.00 | 0.00 | 67.00 | 0.00 | -1.00 | 0.0001 | -0.0000 |
| 34.00 | 0.00 | 66.00 | 0.00 | 66.00 | 0.00 | -1.00 | 0.0001 | -0.0000 |
| 35.00 | 0.00 | 65.00 | 0.00 | 65.00 | 0.00 | -1.00 | 0.0001 | -0.0000 |
| 36.00 | 0.00 | 64.00 | 0.00 | 64.00 | 0.00 | -1.00 | 0.0002 | -0.0000 |
| 37.00 | 0.00 | 63.00 | 0.00 | 63.00 | 0.00 | -1.00 | 0.0002 | -0.0000 |
| 38.00 | 0.00 | 62.00 | 0.00 | 62.00 | 0.00 | -1.00 | 0.0003 | -0.0001 |
| 39.00 | 0.00 | 61.00 | 0.00 | 61.00 | 0.00 | -1.00 | 0.0004 | -0.0001 |
| 40.00 | 0.00 | 60.00 | 0.01 | 60.01 | 0.00 | -1.00 | 0.0005 | -0.0001 |
| 41.00 | 0.00 | 59.00 | 0.01 | 59.01 | 0.00 | -1.00 | 0.0006 | -0.0001 |
| 42.00 | 0.00 | 58.00 | 0.01 | 58.01 | 0.00 | -1.00 | 0.0007 | -0.0002 |
| 43.00 | 0.00 | 57.00 | 0.01 | 57.01 | 0.00 | -1.00 | 0.0009 | -0.0002 |
| 44.00 | 0.00 | 56.00 | 0.02 | 56.02 | 0.00 | -1.00 | 0.0011 | -0.0003 |
| 45.00 | 0.00 | 55.00 | 0.02 | 55.02 | 0.01 | -0.99 | 0.0013 | -0.0003 |
| 46.00 | 0.00 | 54.00 | 0.03 | 54.03 | 0.01 | -0.99 | 0.0015 | -0.0004 |
| 47.00 | 0.00 | 53.00 | 0.04 | 53.04 | 0.01 | -0.99 | 0.0017 | -0.0005 |
| 48.00 | 0.00 | 52.00 | 0.05 | 52.05 | 0.01 | -0.99 | 0.0020 | -0.0006 |
| 49.00 | 0.00 | 51.00 | 0.06 | 51.06 | 0.01 | -0.99 | 0.0023 | -0.0007 |
| 50.00 | 0.00 | 50.00 | 0.07 | 50.07 | 0.02 | -0.98 | 0.0026 | -0.0008 |
| 51.00 | 0.00 | 49.00 | 0.09 | 49.09 | 0.02 | -0.98 | 0.0029 | -0.0009 |
| 52.00 | 0.00 | 48.00 | 0.11 | 48.11 | 0.02 | -0.98 | 0.0033 | -0.0011 |
| 53.00 | 0.00 | 47.00 | 0.13 | 47.13 | 0.02 | -0.98 | 0.0036 | -0.0013 |
| 54.00 | 0.00 | 46.00 | 0.16 | 46.16 | 0.03 | -0.97 | 0.0040 | -0.0014 |
| 55.00 | 0.00 | 45.00 | 0.19 | 45.19 | 0.03 | -0.97 | 0.0044 | -0.0017 |
| 56.00 | 0.00 | 44.00 | 0.23 | 44.23 | 0.04 | -0.96 | 0.0048 | -0.0019 |
| 57.00 | 0.00 | 43.00 | 0.27 | 43.27 | 0.04 | -0.96 | 0.0053 | -0.0021 |
| 58.00 | 0.00 | 42.00 | 0.31 | 42.31 | 0.05 | -0.95 | 0.0057 | -0.0024 |
| 59.00 | 0.00 | 41.00 | 0.36 | 41.36 | 0.05 | -0.95 | 0.0062 | -0.0027 |
| 60.00 | 0.00 | 40.00 | 0.42 | 40.42 | 0.06 | -0.94 | 0.0066 | -0.0029 |
| 61.00 | 0.00 | 39.00 | 0.48 | 39.48 | 0.07 | -0.93 | 0.0071 | -0.0033 |
| 62.00 | 0.00 | 38.00 | 0.55 | 38.55 | 0.07 | -0.93 | 0.0076 | -0.0036 |
| 63.00 | 0.00 | 37.00 | 0.63 | 37.63 | 0.08 | -0.92 | 0.0080 | -0.0039 |
| 64.00 | 0.00 | 36.00 | 0.72 | 36.72 | 0.09 | -0.91 | 0.0085 | -0.0043 |
| 65.00 | 0.00 | 35.00 | 0.81 | 35.81 | 0.10 | -0.90 | 0.0089 | -0.0047 |
| 66.00 | 0.00 | 34.00 | 0.92 | 34.92 | 0.11 | -0.89 | 0.0094 | -0.0050 |
| 67.00 | 0.00 | 33.00 | 1.03 | 34.03 | 0.12 | -0.88 | 0.0098 | -0.0054 |
| 68.00 | 0.00 | 32.00 | 1.15 | 33.15 | 0.13 | -0.87 | 0.0103 | -0.0059 |
| 69.00 | 0.00 | 31.00 | 1.29 | 32.29 | 0.14 | -0.86 | 0.0107 | -0.0063 |
| 70.00 | 0.00 | 30.00 | 1.43 | 31.43 | 0.15 | -0.85 | 0.0111 | -0.0067 |
| 71.00 | 0.00 | 29.00 | 1.58 | 30.58 | 0.16 | -0.84 | 0.0115 | -0.0071 |
| 72.00 | 0.00 | 28.00 | 1.75 | 29.75 | 0.17 | -0.83 | 0.0118 | -0.0076 |
| 73.00 | 0.00 | 27.00 | 1.93 | 28.93 | 0.18 | -0.82 | 0.0122 | -0.0080 |
| 74.00 | 0.00 | 26.00 | 2.12 | 28.12 | 0.20 | -0.80 | 0.0125 | -0.0084 |
| 75.00 | 0.00 | 25.00 | 2.32 | 27.32 | 0.21 | -0.79 | 0.0128 | -0.0089 |
| 76.00 | 0.00 | 24.00 | 2.54 | 26.54 | 0.22 | -0.78 | 0.0131 | -0.0093 |
| 77.00 | 0.00 | 23.00 | 2.77 | 25.77 | 0.24 | -0.76 | 0.0133 | -0.0097 |
| 78.00 | 0.00 | 22.00 | 3.01 | 25.01 | 0.25 | -0.75 | 0.0135 | -0.0102 |
| 79.00 | 0.00 | 21.00 | 3.27 | 24.27 | 0.26 | -0.74 | 0.0138 | -0.0106 |
| 80.00 | 0.00 | 20.00 | 3.53 | 23.53 | 0.28 | -0.72 | 0.0139 | -0.0110 |
| 81.00 | 0.00 | 19.00 | 3.82 | 22.82 | 0.29 | -0.71 | 0.0141 | -0.0114 |
| 82.00 | 0.00 | 18.00 | 4.12 | 22.12 | 0.30 | -0.70 | 0.0142 | -0.0118 |
| 83.00 | 0.00 | 17.00 | 4.43 | 21.43 | 0.32 | -0.68 | 0.0143 | -0.0122 |
| 84.00 | 0.00 | 16.00 | 4.75 | 20.75 | 0.33 | -0.67 | 0.0144 | -0.0125 |
| 85.00 | 0.00 | 15.00 | 5.09 | 20.09 | 0.35 | -0.65 | 0.0145 | -0.0129 |
| 86.00 | 0.00 | 14.00 | 5.45 | 19.45 | 0.36 | -0.64 | 0.0145 | -0.0132 |
| 87.00 | 0.00 | 13.00 | 5.82 | 18.82 | 0.38 | -0.62 | 0.0145 | -0.0136 |
| 88.00 | 0.00 | 12.00 | 6.20 | 18.20 | 0.39 | -0.61 | 0.0145 | -0.0139 |
| 89.00 | 0.00 | 11.00 | 6.60 | 17.60 | 0.41 | -0.59 | 0.0145 | -0.0142 |
| 90.00 | 0.00 | 10.00 | 7.01 | 17.01 | 0.42 | -0.58 | 0.0145 | -0.0145 |
| 91.00 | 0.00 | 9.00 | 7.44 | 16.44 | 0.43 | -0.57 | 0.0144 | -0.0147 |
| 92.00 | 0.00 | 8.00 | 7.88 | 15.88 | 0.45 | -0.55 | 0.0143 | -0.0150 |
| 93.00 | 0.00 | 7.00 | 8.34 | 15.34 | 0.46 | -0.54 | 0.0142 | -0.0152 |
| 94.00 | 0.00 | 6.00 | 8.81 | 14.81 | 0.48 | -0.52 | 0.0141 | -0.0154 |
| 95.00 | 0.00 | 5.00 | 9.29 | 14.29 | 0.49 | -0.51 | 0.0140 | -0.0156 |
| 96.00 | 0.00 | 4.00 | 9.79 | 13.79 | 0.51 | -0.49 | 0.0139 | -0.0157 |
| 97.00 | 0.00 | 3.00 | 10.30 | 13.30 | 0.52 | -0.48 | 0.0137 | -0.0159 |
| 98.00 | 0.01 | 2.01 | 10.83 | 12.83 | 0.53 | -0.47 | 0.0135 | -0.0160 |
| 99.00 | 0.08 | 1.08 | 11.37 | 12.37 | 0.55 | -0.45 | 0.0133 | -0.0161 |
| 100.00 | 0.40 | 0.40 | 11.92 | 11.92 | 0.56 | -0.44 | 0.0131 | -0.0162 |
| 101.00 | 1.08 | 0.08 | 12.49 | 11.49 | 0.57 | -0.43 | 0.0129 | -0.0163 |
| 102.00 | 2.01 | 0.01 | 13.07 | 11.07 | 0.59 | -0.41 | 0.0127 | -0.0163 |
| 103.00 | 3.00 | 0.00 | 13.66 | 10.66 | 0.60 | -0.40 | 0.0125 | -0.0164 |
| 104.00 | 4.00 | 0.00 | 14.27 | 10.27 | 0.61 | -0.39 | 0.0123 | -0.0164 |
| 105.00 | 5.00 | 0.00 | 14.88 | 9.88 | 0.62 | -0.38 | 0.0121 | -0.0164 |
| 106.00 | 6.00 | 0.00 | 15.51 | 9.51 | 0.63 | -0.37 | 0.0118 | -0.0164 |
| 107.00 | 7.00 | 0.00 | 16.15 | 9.15 | 0.65 | -0.35 | 0.0116 | -0.0163 |
| 108.00 | 8.00 | 0.00 | 16.80 | 8.80 | 0.66 | -0.34 | 0.0113 | -0.0163 |
| 109.00 | 9.00 | 0.00 | 17.47 | 8.47 | 0.67 | -0.33 | 0.0111 | -0.0162 |
| 110.00 | 10.00 | 0.00 | 18.14 | 8.14 | 0.68 | -0.32 | 0.0108 | -0.0162 |
| 111.00 | 11.00 | 0.00 | 18.83 | 7.83 | 0.69 | -0.31 | 0.0106 | -0.0161 |
| 112.00 | 12.00 | 0.00 | 19.52 | 7.52 | 0.70 | -0.30 | 0.0103 | -0.0160 |
| 113.00 | 13.00 | 0.00 | 20.23 | 7.23 | 0.71 | -0.29 | 0.0101 | -0.0159 |
| 114.00 | 14.00 | 0.00 | 20.95 | 6.95 | 0.72 | -0.28 | 0.0098 | -0.0157 |
| 115.00 | 15.00 | 0.00 | 21.67 | 6.67 | 0.73 | -0.27 | 0.0096 | -0.0156 |
| 116.00 | 16.00 | 0.00 | 22.41 | 6.41 | 0.74 | -0.26 | 0.0093 | -0.0154 |
| 117.00 | 17.00 | 0.00 | 23.15 | 6.15 | 0.75 | -0.25 | 0.0091 | -0.0153 |
| 118.00 | 18.00 | 0.00 | 23.91 | 5.91 | 0.76 | -0.24 | 0.0088 | -0.0151 |
| 119.00 | 19.00 | 0.00 | 24.67 | 5.67 | 0.77 | -0.23 | 0.0086 | -0.0149 |
| 120.00 | 20.00 | 0.00 | 25.44 | 5.44 | 0.78 | -0.22 | 0.0083 | -0.0148 |
| 121.00 | 21.00 | 0.00 | 26.22 | 5.22 | 0.78 | -0.22 | 0.0081 | -0.0146 |
| 122.00 | 22.00 | 0.00 | 27.01 | 5.01 | 0.79 | -0.21 | 0.0078 | -0.0144 |
| 123.00 | 23.00 | 0.00 | 27.80 | 4.80 | 0.80 | -0.20 | 0.0076 | -0.0142 |
| 124.00 | 24.00 | 0.00 | 28.61 | 4.61 | 0.81 | -0.19 | 0.0074 | -0.0140 |
| 125.00 | 25.00 | 0.00 | 29.42 | 4.42 | 0.81 | -0.19 | 0.0071 | -0.0137 |
| 126.00 | 26.00 | 0.00 | 30.24 | 4.24 | 0.82 | -0.18 | 0.0069 | -0.0135 |
| 127.00 | 27.00 | 0.00 | 31.06 | 4.06 | 0.83 | -0.17 | 0.0067 | -0.0133 |
| 128.00 | 28.00 | 0.00 | 31.89 | 3.89 | 0.83 | -0.17 | 0.0065 | -0.0131 |
| 129.00 | 29.00 | 0.00 | 32.73 | 3.73 | 0.84 | -0.16 | 0.0063 | -0.0128 |
| 130.00 | 30.00 | 0.00 | 33.57 | 3.57 | 0.85 | -0.15 | 0.0061 | -0.0126 |
| 131.00 | 31.00 | 0.00 | 34.42 | 3.42 | 0.85 | -0.15 | 0.0058 | -0.0124 |
| 132.00 | 32.00 | 0.00 | 35.28 | 3.28 | 0.86 | -0.14 | 0.0057 | -0.0121 |
| 133.00 | 33.00 | 0.00 | 36.14 | 3.14 | 0.86 | -0.14 | 0.0055 | -0.0119 |
| 134.00 | 34.00 | 0.00 | 37.01 | 3.01 | 0.87 | -0.13 | 0.0053 | -0.0117 |
| 135.00 | 35.00 | 0.00 | 37.88 | 2.88 | 0.87 | -0.13 | 0.0051 | -0.0114 |
| 136.00 | 36.00 | 0.00 | 38.76 | 2.76 | 0.88 | -0.12 | 0.0049 | -0.0112 |
| 137.00 | 37.00 | 0.00 | 39.64 | 2.64 | 0.88 | -0.12 | 0.0047 | -0.0109 |
| 138.00 | 38.00 | 0.00 | 40.53 | 2.53 | 0.89 | -0.11 | 0.0046 | -0.0107 |
| 139.00 | 39.00 | 0.00 | 41.42 | 2.42 | 0.89 | -0.11 | 0.0044 | -0.0105 |
| 140.00 | 40.00 | 0.00 | 42.32 | 2.32 | 0.90 | -0.10 | 0.0042 | -0.0102 |
| 141.00 | 41.00 | 0.00 | 43.22 | 2.22 | 0.90 | -0.10 | 0.0041 | -0.0100 |
| 142.00 | 42.00 | 0.00 | 44.12 | 2.12 | 0.91 | -0.09 | 0.0039 | -0.0098 |
| 143.00 | 43.00 | 0.00 | 45.03 | 2.03 | 0.91 | -0.09 | 0.0038 | -0.0095 |
| 144.00 | 44.00 | 0.00 | 45.94 | 1.94 | 0.91 | -0.09 | 0.0036 | -0.0093 |
| 145.00 | 45.00 | 0.00 | 46.86 | 1.86 | 0.92 | -0.08 | 0.0035 | -0.0091 |
| 146.00 | 46.00 | 0.00 | 47.78 | 1.78 | 0.92 | -0.08 | 0.0034 | -0.0088 |
| 147.00 | 47.00 | 0.00 | 48.70 | 1.70 | 0.92 | -0.08 | 0.0032 | -0.0086 |
| 148.00 | 48.00 | 0.00 | 49.63 | 1.63 | 0.93 | -0.07 | 0.0031 | -0.0084 |
| 149.00 | 49.00 | 0.00 | 50.55 | 1.55 | 0.93 | -0.07 | 0.0030 | -0.0082 |
| 150.00 | 50.00 | 0.00 | 51.49 | 1.49 | 0.93 | -0.07 | 0.0029 | -0.0080 |
| 151.00 | 51.00 | 0.00 | 52.42 | 1.42 | 0.94 | -0.06 | 0.0028 | -0.0078 |
| 152.00 | 52.00 | 0.00 | 53.36 | 1.36 | 0.94 | -0.06 | 0.0026 | -0.0075 |
| 153.00 | 53.00 | 0.00 | 54.30 | 1.30 | 0.94 | -0.06 | 0.0025 | -0.0073 |
| 154.00 | 54.00 | 0.00 | 55.24 | 1.24 | 0.94 | -0.06 | 0.0024 | -0.0071 |
| 155.00 | 55.00 | 0.00 | 56.19 | 1.19 | 0.95 | -0.05 | 0.0023 | -0.0069 |
| 156.00 | 56.00 | 0.00 | 57.13 | 1.13 | 0.95 | -0.05 | 0.0022 | -0.0067 |
| 157.00 | 57.00 | 0.00 | 58.08 | 1.08 | 0.95 | -0.05 | 0.0022 | -0.0066 |
| 158.00 | 58.00 | 0.00 | 59.04 | 1.04 | 0.95 | -0.05 | 0.0021 | -0.0064 |
| 159.00 | 59.00 | 0.00 | 59.99 | 0.99 | 0.96 | -0.04 | 0.0020 | -0.0062 |
| 160.00 | 60.00 | 0.00 | 60.95 | 0.95 | 0.96 | -0.04 | 0.0019 | -0.0060 |
| 161.00 | 61.00 | 0.00 | 61.90 | 0.90 | 0.96 | -0.04 | 0.0018 | -0.0058 |
| 162.00 | 62.00 | 0.00 | 62.86 | 0.86 | 0.96 | -0.04 | 0.0018 | -0.0057 |
| 163.00 | 63.00 | 0.00 | 63.82 | 0.82 | 0.96 | -0.04 | 0.0017 | -0.0055 |
| 164.00 | 64.00 | 0.00 | 64.79 | 0.79 | 0.96 | -0.04 | 0.0016 | -0.0053 |
| 165.00 | 65.00 | 0.00 | 65.75 | 0.75 | 0.97 | -0.03 | 0.0015 | -0.0052 |
| 166.00 | 66.00 | 0.00 | 66.72 | 0.72 | 0.97 | -0.03 | 0.0015 | -0.0050 |
| 167.00 | 67.00 | 0.00 | 67.69 | 0.69 | 0.97 | -0.03 | 0.0014 | -0.0049 |
| 168.00 | 68.00 | 0.00 | 68.66 | 0.66 | 0.97 | -0.03 | 0.0014 | -0.0047 |
| 169.00 | 69.00 | 0.00 | 69.63 | 0.63 | 0.97 | -0.03 | 0.0013 | -0.0046 |
| 170.00 | 70.00 | 0.00 | 70.60 | 0.60 | 0.97 | -0.03 | 0.0012 | -0.0044 |
| 171.00 | 71.00 | 0.00 | 71.57 | 0.57 | 0.97 | -0.03 | 0.0012 | -0.0043 |
| 172.00 | 72.00 | 0.00 | 72.55 | 0.55 | 0.97 | -0.03 | 0.0011 | -0.0041 |
| 173.00 | 73.00 | 0.00 | 73.52 | 0.52 | 0.98 | -0.02 | 0.0011 | -0.0040 |
| 174.00 | 74.00 | 0.00 | 74.50 | 0.50 | 0.98 | -0.02 | 0.0010 | -0.0039 |
| 175.00 | 75.00 | 0.00 | 75.48 | 0.48 | 0.98 | -0.02 | 0.0010 | -0.0038 |
| 176.00 | 76.00 | 0.00 | 76.45 | 0.45 | 0.98 | -0.02 | 0.0010 | -0.0036 |
| 177.00 | 77.00 | 0.00 | 77.43 | 0.43 | 0.98 | -0.02 | 0.0009 | -0.0035 |
| 178.00 | 78.00 | 0.00 | 78.41 | 0.41 | 0.98 | -0.02 | 0.0009 | -0.0034 |
| 179.00 | 79.00 | 0.00 | 79.40 | 0.40 | 0.98 | -0.02 | 0.0008 | -0.0033 |
| 180.00 | 80.00 | 0.00 | 80.38 | 0.38 | 0.98 | -0.02 | 0.0008 | -0.0032 |
| 181.00 | 81.00 | 0.00 | 81.36 | 0.36 | 0.98 | -0.02 | 0.0008 | -0.0031 |
| 182.00 | 82.00 | 0.00 | 82.34 | 0.34 | 0.98 | -0.02 | 0.0007 | -0.0030 |
| 183.00 | 83.00 | 0.00 | 83.33 | 0.33 | 0.98 | -0.02 | 0.0007 | -0.0029 |
| 184.00 | 84.00 | 0.00 | 84.31 | 0.31 | 0.99 | -0.01 | 0.0007 | -0.0028 |
| 185.00 | 85.00 | 0.00 | 85.30 | 0.30 | 0.99 | -0.01 | 0.0006 | -0.0027 |
| 186.00 | 86.00 | 0.00 | 86.29 | 0.29 | 0.99 | -0.01 | 0.0006 | -0.0026 |
| 187.00 | 87.00 | 0.00 | 87.27 | 0.27 | 0.99 | -0.01 | 0.0006 | -0.0025 |
| 188.00 | 88.00 | 0.00 | 88.26 | 0.26 | 0.99 | -0.01 | 0.0006 | -0.0024 |
| 189.00 | 89.00 | 0.00 | 89.25 | 0.25 | 0.99 | -0.01 | 0.0005 | -0.0023 |
| 190.00 | 90.00 | 0.00 | 90.24 | 0.24 | 0.99 | -0.01 | 0.0005 | -0.0023 |
| 191.00 | 91.00 | 0.00 | 91.23 | 0.23 | 0.99 | -0.01 | 0.0005 | -0.0022 |
| 192.00 | 92.00 | 0.00 | 92.22 | 0.22 | 0.99 | -0.01 | 0.0005 | -0.0021 |
| 193.00 | 93.00 | 0.00 | 93.21 | 0.21 | 0.99 | -0.01 | 0.0004 | -0.0020 |
| 194.00 | 94.00 | 0.00 | 94.20 | 0.20 | 0.99 | -0.01 | 0.0004 | -0.0020 |
| 195.00 | 95.00 | 0.00 | 95.19 | 0.19 | 0.99 | -0.01 | 0.0004 | -0.0019 |
| 196.00 | 96.00 | 0.00 | 96.18 | 0.18 | 0.99 | -0.01 | 0.0004 | -0.0018 |
| 197.00 | 97.00 | 0.00 | 97.17 | 0.17 | 0.99 | -0.01 | 0.0004 | -0.0018 |
| 198.00 | 98.00 | 0.00 | 98.16 | 0.16 | 0.99 | -0.01 | 0.0004 | -0.0017 |
| 199.00 | 99.00 | 0.00 | 99.16 | 0.16 | 0.99 | -0.01 | 0.0003 | -0.0016 |
| 200.00 | 100.00 | 0.00 | 100.15 | 0.15 | 0.99 | -0.01 | 0.0003 | -0.0016 |
Greeks
- Delta: measures the sensitivity of an option’s price to changes in the underlying asset’s price.
Gamma: measures the rate of change in an option’s delta to changes in the underlying asset’s price.
Vega: measures the sensitivity of an option’s price to changes in the volatility of the underlying asset.
Theta: measures the sensitivity of an option’s price to the passage of time.
Rho: measures the sensitivity of an option’s price to changes in the interest rate.
Delta Charts
Gamma and Theta Charts
Hedging
Hedging reduces exposure for possible future scenarios. Price changes are the main risk factor.
Static hedge: hedged portfolio’s risk profile does not change materially over possible future scenarios.
futures vs physical exposure.
put-call parity: call - put = underlying - strike
Dynamic hedge: delta hedging and re-hedging as required
- futures option vs futures.
Dynamic Hedging
Positive gamma lead to natural buy low sell high re-hedging trades and produce hedging profit.
Option loses time value as time to expiration reduces.
Gamma vs Theta trade-off
Option increase in value as volatility/uncertainty increases.
Implied volatility vs realized volatility
Benefits
Payoff asymmetry: limited loss from long options
Leverage: option premium is a fraction of underlying asset price
Express view of any market condition: bull, bear, range bounding
Risks
Unlimited loss
Margin calls
Complexity
WTI Option
WTI (West Texas Intermediate, a US light sweet crude oil blend) futures provide direct crude oil exposure
Hedge against adverse oil price moves or speculate
Price discovery
American style call/put
Source CME WTI Option Specs
Crude Oil Futures Settlements
Crude Oil Futures Option Settlements
Natual Gas Option
Natual Gas Futures Settlements
Natural Gas Futures Option Settlements
Corn Option
Deliverable into Corn Futures, American style call/put
Listed Contracts:
- Monthly contracts listed for 4 consecutive months and:
- 3 monthly contracts of Mar listed in July
- 3 monthly contracts of May listed in September
- 3 monthly contracts of Sep listed in March
- 7 monthly contracts of Jul and Dec listed in November
Source CME Corn Option Specs
Corn Futures Settlements
Corn Futures Option Settlements
Soybean Option
Soybean Futures Settlements
Soybean Futures Option Settlements
Live Calculator
Source CME
Strategies
Combinations of various options and underlying asset can be used to meet different payoff requirements
Common Strategies
covered calls
call spreads
straddle/strangle
Covered call example
Source CME
Trading
- Who trades options?
- How to trade options?
Market mechanism
Listed vs OTC market
Market Participants
Margin Requirements
Exercising / Assignments
Open Interest
Source CME
Commitments of Traders Report
- Producer/Merchant/Processor/User
- A “producer/merchant/processor/user” is an entity that predominantly engages in the production, processing, packing or handling of a physical commodity and uses the futures markets to manage or hedge risks associated with those activities.
- Swap Dealer
- A “swap dealer” is an entity that deals primarily in swaps for a commodity and uses the futures markets to manage or hedge the risk associated with those swaps transactions. The swap dealer’s counterparties may be speculative traders, like hedge funds, or traditional commercial clients that are managing risk arising from their dealings in the physical commodity.
- Money Manager
- A “money manager,” for the purpose of this report, is a registered commodity trading advisor (CTA); a registered commodity pool operator (CPO); or an unregistered fund identified by CFTC.7 These traders are engaged in managing and conducting organized futures trading on behalf of clients.
Conclusion
- What is option
- Option pricing factors
- Benefits and risk
- Option market