style="font-size:15px;"> ● OTM: 
● ATM:
For example, consider a 45 DTE put contract with a strike price of $100:
● Scenario 1 (ITM): The underlying price is $95. In this case, the intrinsic value of the put contract is $5 per share.
● Scenario 2 (OTM): The underlying price is $105. In this case, the put contract has no intrinsic value.
● Scenario 3 (ATM): The underlying price is $100. In this case, the put is also considered to have no intrinsic value.
The value of an option also depends on speculative factors, driven by supply and demand. The extrinsic value of the option is the difference between the current market price for the option and the intrinsic value of the option. Again, consider a 45 DTE put contract with a strike price of $100 on an underlying with a current price per share of $105. Suppose that, due to a period of recent market turbulence, investors are fearful the underlying price will crash within the next 45 days and create a demand for these OTM put contracts. The surge in demand inflates the price of the put contract to $10 per share. Therefore, because the put contract has no intrinsic value but has a market price of $10, the extrinsic value of the contract is $10 per share. If, instead, the price of the underlying is $95 and the price of the ITM put is still $10 per share, then the contract will have $5 in intrinsic value and $5 in extrinsic value.
The profitability of an option ultimately depends on both intrinsic and extrinsic factors, and it is calculated as the difference between the intrinsic value of an option and the cost of the contract. Mathematically, profit and loss (P/L) approximations for long calls and puts at exercise are given by the following equations:2
where the max function simply outputs the larger of the two values. For instance,
Example trade: A call with 45 DTE duration is traded on an underlying that is currently priced at $100
● Scenario 1: The underlying increases to $105 by the expiration date.
● Long call P/L:
● Short call P/L: +$100.
● Scenario 2: The underlying increases to $110 by the expiration date.
● Long call P/L:
● Short call P/L: –$400.
● Scenario 3: The underlying decreases to $95 by the expiration date.
● Long call P/L:
● Short call P/L: +$100.
The trader adopting the long position pays the seller the option premium upfront and profits when the intrinsic value exceeds the price of the contract. The short trader profits when the intrinsic value remains below the price of the contract, especially when the position expires worthless (no intrinsic value). The extrinsic value of an option generally decreases over the duration of the contract, as uncertainty around the underlying price and uncertainty around the profit potential of the option decrease. As a position nears expiration, the price of an option converges toward its intrinsic value.
Options pricing clearly plays a large role in options trading. To develop an intuitive understanding around how options are priced, understanding the mathematical assumptions around market efficiency and price dynamics is critical.
The Efficient Market Hypothesis
Traders must make a number of assumptions prior to placing a trade. Options traders must make directional assumptions about the price of the underlying over a given time frame: bearish (expecting price to decrease), bullish (expecting price to increase), or neutral (expecting price to remain relatively unchanged). Options traders also must make assumptions about the current value of an option. If options contracts are perceived as overvalued, long positions are less likely to profit. If options contracts are perceived as undervalued, short positions are less likely to profit. These assumptions about underlying and option price dynamics are a personal choice, but traders can formulate consistent assumptions by referring to the efficient market hypothesis (EMH). The EMH states that instruments are traded at a fair price, and the current price of an asset reflects some amount of available information. The hypothesis comes in three forms:
1. Weak EMH: Current prices reflect all past price information.
2. Semi‐strong EMH: Current prices reflect all publicly available information.
3. Strong EMH: Current prices reflect all possible information.
No variant of the EMH is universally accepted or rejected. The form that a trader assumes is subjective, and methods of market analysis available are limited depending on that choice. Proponents of the strong EMH posit that investors benefit from investing in low‐cost passive index funds because the market is unbeatable. Opponents believe the market is beatable by exploiting inefficiencies in the market. Traders who accept the weak EMH believe technical analysis (using past price trends to predict future price trends) is invalidated, but fundamental analysis (using related economic data to predict future price trends) is still viable. Traders who accept the semi‐strong EMH assume fundamental analysis would not yield systematic success but trading according to private information would. Traders who accept the strong EMH maintain that even insider trading will not result in consistent success and no exploitable market inefficiencies are available to anyone.
This book focuses on highly liquid markets, and inefficiencies are assumed to be minimal. More specifically, this book assumes a semi‐strong form of the EMH. Rather than constructing
The future value of the option should be used, but for simplicity, this approximates the future value as the current price of the option. The future value of the option premium is the current value of the option multiplied by the time‐adjusted interest rate factor.
