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Options pricing
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Understanding Options Basics

Options are financial contracts that give buyers the right, but not the obligation, to buy or sell an underlying asset at a predetermined price on or before a specified date. They are powerful tools for trading strategies and managing risk. Before diving into options trading strategies, it's important to understand some key options terminology and concepts:

Calls and Puts

The two main types of options contracts are calls and puts:

  • A call option gives the buyer the right to buy the underlying asset at a predetermined price, known as the strike price, before the expiration date. Buyers of call options hope the price of the asset will increase.

  • A put option gives the buyer the right to sell the underlying asset at the strike price before expiration. Buyers of put options hope the price of the asset will decrease.

Strike Price and Expiration Date

Every option contract specifies a strike price and an expiration date. The strike price is the price at which the underlying asset can be bought or sold according to the terms of the option. The expiration date is the last day the option can be exercised - meaning the holder can "use" their right to buy or sell at the strike price. After the expiration date passes, the option expires and ceases to exist.

Options Premium

Options have value - known as the premium - because they provide specific rights to buyers. Buyers pay this premium upfront when purchasing options contracts. The premium is determined by factors like the current price of the underlying asset, days until expiration, and the strike price. More time until expiration means higher premiums, since there's more time for the asset price to move favorably.

In the Money vs Out of the Money

An option is "in the money" if exercising it would result in a financial gain for the buyer. For call options, this means the strike price is below the current market price of the underlying asset. For put options, it means the strike price is above the current market price.

An option that is "out of the money" would not result in a gain if exercised immediately. The goal when buying options is being able to move out of the money options into profitable, in the money territory.

Options Pricing

While options pricing involves complex models, some key drivers of premium prices are:

  • Current price of the underlying asset - premiums increase when the price gets further from the strike price.

  • Time remaining until expiration - more time means higher premiums.

  • Volatility - higher volatility of the underlying asset means higher premiums.

  • Interest rates - increased rates drive call premiums up and put premiums down.

  • Dividends - dividends paid on the underlying asset decrease call premiums.

In summary, options are versatile trading instruments with many moving parts that affect their value and probability of profitability. Mastering the basics opens the door to effectively applying options in your own trading.

Options Trading Strategies

Now that we have a foundational understanding of what options are and how they work, we can explore some of the most common options trading strategies. As a reminder, we are focusing on conceptual overviews rather than technical details here.

Covered Calls

One popular options strategy is the covered call. Here's how it works:

  1. You already own shares of a particular stock.
  2. You then sell (or "write") call options on that same stock.
  3. The calls you sell give the buyer the right to purchase your stock shares at a specific price (the strike price) before a certain date.
  4. You collect a premium upfront when selling the calls.

Why do this? By writing covered calls, you can generate income from options premiums. However, you do limit your potential profit if the stock price rises rapidly.

For example, let's say you own 100 shares of XYZ stock currently trading at $50 per share. You then sell a call option with a $55 strike price and collect a premium of $1 per share. There are two potential outcomes when the option expires:

  • If XYZ is below $55, the calls expire worthless and you keep both the premium and your shares.
  • If XYZ is above $55, the calls are exercised and you must sell your 100 shares at $55. You keep the $1 premium but give up any additional profit above $55.

Covered calls work best when you expect a stock to have limited upside or trade sideways. The premiums collected can generate nice income. It caps your upside though.

Protective Puts

Protective puts involve buying put options as a hedge against potential losses. Here is how they work:

  1. You own shares of a stock (or another asset).
  2. You purchase put options on that same stock.
  3. The puts give you the right to sell shares at a specific price (the strike).
  4. This protects you if the stock price declines sharply.

For example, say you own 100 shares of ABC stock at $20. You are bullish on ABC but want to protect against a decline. You buy a put option with a $18 strike price for a premium of $1 per share.

Here are the scenarios:

  • If ABC stays above $18, the put expires worthless but you keep any gain on the shares.
  • If ABC falls below $18, you can exercise the put and sell your shares for $18, limiting losses.

The put premium paid acts like an insurance policy. Protective puts are popular for locking in gains or limiting potential downside.


Covered calls and protective puts represent two common beginner options strategies. They provide examples of how options can generate income and hedge risk under different market outlooks. There are many other strategies that use calls, puts, and combinations thereof to profit in options trading. But these two demonstrate core concepts like using options to capture premiums or protect holdings.

The Greeks

The "Greeks" refer to a set of metrics used to measure the sensitivity of an option's price to various factors. While options pricing models are complex, knowing the Greeks provides critical insights into how options may perform under different conditions. We will focus on four key Greeks - delta, gamma, theta, and vega - at a conceptual level.


Delta measures how much an option's price is expected to change based on a $1 movement in the price of the underlying asset. Call options with deltas of 0.40 would gain $0.40 when the underlying stock price rises $1.00. Put options work oppositely.

  • Delta ranges from 0 to 1 for calls and 0 to -1 for puts.
  • Higher deltas mean the option price is more sensitive to underlying price changes.

For example, say a call option has a delta of 0.50. If the underlying stock price rises from $50 to $51, the call premium would increase by $0.50 (50% of the $1 price move).

Delta helps gauge the probability an option will expire in the money. Higher deltas indicate a greater chance of profitability but also higher risk.


While delta measures sensitivity to the underlying asset price, gamma measures sensitivity of delta itself. Gamma indicates how much delta may change when the underlying price moves.

  • Gamma is highest when options are at the money.
  • Gamma impacts options more as expiration nears.

For example, an at the money option with a gamma of 0.10 means its delta could increase 0.10 if the underlying price rises $1.00. This accelerates gains from favorable price moves.

Traders sometimes buy options with high gamma to capitalize on large price swings in the underlying asset. Gamma risk management is also important.


Theta measures how much an option's price declines as expiration approaches, all else equal. Options lose value over time as there are fewer days for the underlying price to move favorably.

  • Theta increases as expiration nears (time decay accelerates).
  • Far out of the money options have lower theta.

For example, an option with a theta of -0.10 would lose $0.10 per day from time decay, assuming no other price changes. Managing theta decay by rolling options or closing profitable trades is key.


Vega indicates an option's price sensitivity to changes in the underlying asset's volatility. Volatility measures size and frequency of price fluctuations.

  • Higher vega means larger gains if volatility rises.
  • Vega approaches zero as expiration nears.

For example, an option with a vega of 0.10 would increase $0.10 if volatility rose 1 percentage point. Traders may buy options expecting volatility increases.


The Greeks help assess how options prices may change under different conditions. While complex mathematically, their conceptual meaning provides important trading insights. Calculating and comparing the Greeks is a vital skill in options trading.

Applying Options Trading Fundamentals

Now that we have covered the basics of options terminology, pricing, trading strategies, and Greeks, let's discuss some key takeaways and action steps for applying options trading fundamentals as a beginner.

Start Small and Manage Risk

When first getting started in options, it is advisable to start small with a minimal amount of capital at risk. Options provide leverage, but also greater risk if used improperly. Define a maximum loss per trade and overall investing capital you feel comfortable with. Diversify across multiple trades. Use stop losses. Consider trading options on ETFs rather than individual stocks when starting out.

Focus on High Probability Setups

Look for options trading opportunities that have defined areas of support or resistance in the technical chart patterns of the underlying asset. This makes it easier to identify price levels to set your strikes around. Trade options with at least 30-45 days until expiration to give time for your thesis to play out. Pick strike prices that align with your market outlook. For example, if bullish, choose out of the money call strikes.

Understand Your Risks and Rewards

When entering any options trade, be clear on the maximum risk, maximum reward, and probability of profit by analyzing the Greeks. Maximum risk is the premium paid. Maximum reward depends on strike selection. Higher probability trades tend to have lower reward. Define the market conditions needed for profitability. Monitor positions closely and have an exit plan.

Learn from Experience

Paper trade options contracts for practice before using real capital. Start by buying long calls or puts to get experience trading directionally. Then explore more advanced strategies like spreads or writing covered calls. Review your losing trades to improve. A trading journal helps identify mistakes and successes to replicate. Experience over time is the best teacher.

Know the Tax Implications

Options trades typically generate short term capital gains or losses since most options are open less than one year. This can impact your tax planning. Consult a tax professional when needed. Also be aware of wash sale rules if selling options on securities you own at a loss. Do your due diligence on the tax implications.

Continue Your Education

Keep expanding your knowledge even after getting started trading options. Read books, take courses, or work with a mentor/coach. The options world is complex with endless nuances. Be wary of over complicating though - stay focused on high probability setups. Never stop learning as markets evolve.

Maintain Discipline and Patience

Stick to your trading plans and pre-defined risk points. Don't chase trades or deviate from your strategy. Patience is key - wait for prime opportunities meeting your criteria. Avoid over trading by being selective with only the best setups. Staying disciplined is challenging but pays off over time.

In summary, applying options trading fundamentals requires prudence, preparation, and persistence. But the journey can be rewarding. Follow these tips and continue educating yourself to put the odds of success in your favor. Options offer a versatile toolkit once mastered through practice. With the right foundation, you can use options to generate income, hedge risk, and capitalize on market opportunities.