Option Pricing: The Mathematics of Probability

In the previous modules, we learned that options are essentially insurance contracts. But how does an insurance company decide what to charge you for a policy? They look at the risk, the duration, and the value of the asset. Option pricing follows the exact same logic.

Option pricing is not just about supply and demand. It is a mathematical output based on the probability of the stock reaching a certain price by a certain time. This is where we move from "trading" to "financial engineering."

1. The Two Components of Premium

As we briefly touched upon in Module 05, the premium you see on your terminal is actually the sum of two very different values. Understanding the "DNA" of the premium is crucial for picking the right strike.

A. Intrinsic Value (The "Real" Worth)

Intrinsic value is the tangible value an option would have if it expired right this second. Only In-the-Money (ITM) options have intrinsic value.

• Formula: Spot Price - Strike Price (for Calls).
• If Nifty is at 22,500 and you have a 22,400 Call, the intrinsic value is ₹100. Even if time stops, that ₹100 is yours.

B. Extrinsic Value (The "Time" Worth)

Also known as Time Value, this is the amount by which the premium exceeds its intrinsic value. It is essentially the "premium" you pay for the *possibility* of the stock moving further in your favor. At-the-Money (ATM) and Out-of-the-Money (OTM) options are made entirely of extrinsic value.

2. The Five Factors Affecting Price

The **Black-Scholes Model** is the gold standard for calculating these prices. While you don't need to know the complex calculus, you must understand the five inputs that feed the engine.

3. Volatility: The Market's Uncertainty

Volatility is the most misunderstood component of pricing. Think of it this way: If a stock moves only ₹1 a day, the chance of it hitting a target ₹50 away is nearly zero. Therefore, the option will be very cheap. But if the stock moves ₹20 a day, hitting that ₹50 target is highly likely. Therefore, the option will be expensive.

Implied Volatility (IV): This is the volatility currently "priced in" by the market. If IV is high, you are paying a lot for the option. If IV crashes (e.g., after a major event like a budget or earnings report), the option premium can crash even if the stock price stays same. This is known as an "IV Crush."

4. Time Decay (Theta): The Silent Killer

Options are "wasting assets." Every day you hold an option, it loses a portion of its value simply because one less day remains for the stock to reach your target.

Notice the curve above. Time decay is not linear. It is slow when there are 30 days left, but it accelerates massively in the last 7 days of expiry. This is why "buying" options just before expiry is extremely risky—you need a massive, immediate move to overcome the rapid loss of time value.

5. Option Pricing as a Probability

Professional traders don't look at an option and say "This is a good bet." They look at the Delta. If an option has a Delta of 0.20, the market is effectively saying there is a 20% chance of this option expiring ITM.

Pricing is the market's way of balancing the scales so that, over thousands of trades, the "Insurance Seller" (Option Writer) and "Insurance Buyer" (Option Holder) have a fair game—though the house (Seller) usually has a slight mathematical edge due to Time Decay.

Summary of Module 07

• Premium = Intrinsic Value + Time Value.
• Intrinsic Value only exists for ITM options.
• Volatility (IV) is the market's expectation of future movement. High IV = Expensive options.
• Theta (Time Decay) accelerates as expiry approaches.
• Understand IV Crush: Don't buy expensive options just before big events.

Now that you understand what makes an option's price tick, how do you see all these prices for different strikes at once? We use a powerful map called the Option Chain. In the next module, we learn how to read this map to find support and resistance levels.