Option Basics
Right (not obligation) to buy (call) or sell (put) the underlying asset on or before a certain day in the future.
- Options traded on exchanges can be settled physically or by cash
- Can be traded OTC and are sometimes called exotics
- Warrants are a type of option
Long Call and Long Put
- Long Call: 适用于预期基础资产价格上涨的场景，通过支付期权费获得在未来以固定价格买入资产的权利，潜在收益无限，最大损失是期权费。
- 定义: 购买一个看涨期权。
- 预期: 你认为基础资产的价格会上涨。
- 权利: 在到期日或之前，以固定价格购买基础资产。
- 风险: 最大损失是支付的期权费。
- 潜在收益: 无限，因为资产价格可以无限上涨。
- Long Put: 适用于预期基础资产价格下跌的场景，通过支付期权费获得在未来以固定价格卖出资产的权利，潜在收益是行权价格减去期权费，最大损失是期权费。
- 定义: 购买一个看跌期权。
- 预期: 你认为基础资产的价格会下跌。
- 权利: 在到期日或之前，以固定价格卖出基础资产。
- 风险: 最大损失是支付的期权费。
- 潜在收益: 最大收益是行权价减去期权费，当资产价格跌至零时。
Short Call and Short Put
- Short Call: 适用于预期基础资产价格不会上涨的场景，通过卖出看涨期权赚取期权费，但面临无限的潜在损失风险。
- 定义: 卖出一个看涨期权。
- 预期: 你认为基础资产的价格不会大幅上涨（看跌或中性）。
- 义务: 如果买方行权，你必须以固定价格卖出基础资产。
- 风险: 无限，因为资产价格可以无限上涨。
- 收益: 收到的期权费。
- Short Put: 适用于预期基础资产价格不会下跌的场景，通过卖出看跌期权赚取期权费，但面临有限的潜在损失风险（基础资产价格跌到零时）。
- 定义: 卖出一个看跌期权。
- 预期: 你认为基础资产的价格不会大幅下跌（看涨或中性）。
- 义务: 如果买方行权，你必须以固定价格买入基础资产。
- 风险: 有限，但当基础资产价格跌至零时，最大损失是行权价减去期权费。
- 收益: 收到的期权费。
Risk Offset
Option 的风险结构
Black-Scholes Option Pricing Model
The Black-Scholes Model, developed by Fischer Black, Myron Scholes, and Robert Merton, is one of the most famous models for pricing European options. It provides a theoretical estimate of the price of European-style options and is based on several assumptions.
Assumptions:
- The option is European and can only be exercised at expiration.
- No dividends are paid out during the life of the option.
- Markets are efficient (market movements cannot be predicted).
- No commissions or transaction costs.
- The risk-free rate and volatility of the underlying asset are known and constant.
- The returns on the underlying asset are normally distributed.
Formula:
The Black-Scholes formula for a call option is:
Calculation Example
Option Pricing Model
The Greeks
1. Delta (Δ)
- Definition: Delta measures the sensitivity of an option's price to changes in the price of the underlying asset.
- Call Option: Delta ranges from 0 to 1.
- Put Option: Delta ranges from -1 to 0.
- Interpretation: If a call option has a delta of 0.5, for every $1 increase in the underlying asset's price, the option's price is expected to increase by $0.50.
- Usage: Delta is used to gauge the directional exposure of an option position. It also helps in creating delta-neutral strategies where the overall delta is zero, reducing the impact of small price movements.
As hedge ratio
Futures equivalents
2. Gamma (Γ)
- Definition: Gamma measures the rate of change of delta with respect to changes in the underlying asset's price.
- Interpretation: Gamma is highest for at-the-money options and decreases for in-the-money and out-of-the-money options.
- Usage: Gamma helps in understanding the stability of delta. High gamma indicates that delta is highly sensitive to price changes, which can lead to significant adjustments in hedging strategies.
3. Theta (Θ)
- Definition: Theta measures the sensitivity of an option's price to the passage of time, also known as time decay.
- Interpretation: Theta is usually negative for both call and put options, meaning options lose value as they approach expiration.
- Usage: Theta helps traders understand how much value an option is expected to lose each day, aiding in the management of time-sensitive positions.
4. Vega (ν)
- Definition: Vega measures the sensitivity of an option's price to changes in the volatility of the underlying asset.
- Interpretation: A high Vega means the option's price is highly sensitive to changes in volatility. Vega is the same for both call and put options.
- Usage: Vega is crucial for assessing the impact of volatility on option prices. Traders use Vega to manage positions in volatile markets and to take advantage of changes in implied volatility.
5. Rho (ρ)
- Definition: Rho measures the sensitivity of an option's price to changes in the risk-free interest rate.
- Call Option: Rho is positive, meaning call option prices increase with rising interest rates.
- Put Option: Rho is negative, meaning put option prices decrease with rising interest rates.
- Usage: Rho is less significant compared to other Greeks but is important for long-term options where interest rate changes can have a more pronounced effect.
Hedging strategy
Covered call
最适合使用 Covered Call 的情景
✅ 情景 1：你看好股票，但认为短期不会大涨（温和看涨）
比如：你持有英伟达（NVDA），觉得它长期会涨，但未来 1~2 个月可能在 180~200 区间震荡。
这时候卖出一个行权价 200 的 Call，赚权利金，相当于“给股票额外分红”。
✅ 情景 2：市场震荡，波动率较高（IV 高）
当隐含波动率（IV）高时，期权价格贵 → 权利金收入更高。
你相当于“高价卖保险”，即使股价不动，也能赚时间价值。
✅ 情景 3：你想降低持仓成本 or 增强收益
权利金可以抵消部分下跌损失，或提前锁定卖出价格。
很多退休投资者用这策略“收租”，替代部分股息收入。
✅ 情景 4：你愿意在某个价位卖出股票
比如：你成本是 150，现在股价 180，你愿意在 200 卖出。
卖出行权价 200 的 Call，如果被行权，你就按 200 卖出 + 白拿权利金，一举两得。
1. Definition
A covered call involves selling (writing) a call option on a stock you already own.
You’re “covered” because if the buyer exercises the call, you already have the shares to deliver.
Position structure:
- Long 100 shares of stock
- Short 1 call option on the same stock
2. Objective
The main goal is to generate extra income from the option premium while holding a stock you expect to remain neutral or slightly bullish in the short term.
You earn money if:
- The stock stays flat or rises slightly, so the call expires worthless or is exercised near your target price.
3. Payoff Mechanics
Let’s use an example:
Component | Action | Details |
Stock | Buy 100 shares at $50 | Cost = $5,000 |
Option | Sell 1 call with strike $55 for $2 | Receive $200 |
Possible outcomes at expiration:
a) Stock below $55
- The call expires worthless.
- You keep the $200 premium.
- Effective cost basis = $50 − $2 = $48 per share.
b) Stock above $55
- The call is exercised.
- You must sell your stock at $55, even if it rises to $60.
- Profit = ($55 − $50) × 100 + $200 = $700 total.
- You forfeit further upside beyond $55.
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