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Welcome to Tiger Academy - 「Options Academy Column」 Issue 9.

In the previous issue, we discussed that the seller of an option is required to deposit margin, while the buyer is not required to do so. The main source of profit for the seller is to earn the option's time value. With a high success rate, the earnings are stable. Today, let's discuss, since the time value of an option can bring profit to the seller and offer greater potential for the buyer, if the time value is negative, can both the buyer and the seller still make money?

1. Can the time value of an option be negative?

Speaking of the time value of options, we need to review the concepts we previously explained in the article "Day2.Unveiling the Secrets of Option Pricing with Apple and NVIDIA!" As we mentioned, the value of an option is divided into two parts: intrinsic value and time value.

The intrinsic value is the difference between the strike price and the current stock price. In simple terms, it's the value that the option buyer could immediately gain by exercising the option. For example, consider a call option with a strike price of $100 and a current stock price of $110. In this case, the intrinsic value of the call option is $110 - $100 = $10, meaning that the option buyer could immediately profit by $10 through exercising the option.

On the other hand, the time value represents the quantified value of all potential profits that could arise from future stock price fluctuations. Continuing with the previous example, if the option has an intrinsic value of $10 and its price (premium) is $15, then the time value of the option is $15 - $10 = $5.

This $5 essentially encapsulates the market's expectation of future volatility for the stock. The greater the expected volatility, the higher the time value. As the expiration date extends, the time value also increases. Under unchanged conditions, the more expensive the option is sold for, the higher its time value. Therefore, in theory, as long as the option has not expired and there is an expectation of future stock price fluctuations, the time value of the option must be a positive number.

However, why is it in practice that the time value of some options can be negative? For example, Tesla call options with strike prices below $130 often have negative time value.

First and foremost, it must be clarified that options with negative time value cannot possibly be out-of-the-money (OTM) options, as OTM options have an intrinsic value of 0. If the time value is negative, the option's price would be negative, which is theoretically not possible for an option's price.

Therefore, strictly speaking, it is only deep in-the-money (ITM) options that could potentially have negative time value. Why is that?

Let's address the direct reason first. If the option price is too low, as the option price equals intrinsic value plus time value, when the option price is less than the intrinsic value, the time value becomes negative.

Now, let's discuss the underlying reasons why an option price might be lower than its intrinsic value. This is primarily due to the cost of capital and expectations of future stock prices.

Consider an example: Suppose the current stock price is $1000, and investors generally anticipate that the future stock price will rise to around $1001. At this point, there are two call options: one with a strike price of $999 and the other with a strike price of $1. Both options would be profitable if exercised on the expiration date; the only difference is that one is slightly ITM, and the other is deeply ITM.

Assume that the call option with a strike price of $999 is priced at $1.5, and exercising it on the expiration date results in a profit of $2 ($1001 - $999). The return on investment (ROI) would be 33% (2/1.5 - 1).

Assume that the call option with a strike price of $1 is priced at $999, and exercising it on the expiration date results in a profit of $1000 ($1001 - $1). The ROI would be 0.1% (1000/999 - 1).

Therefore, as a high-risk derivative, the ROI of the latter option is much lower than that of the former, which is not attractive to investors in the market. Thus, in pricing, a significant discount would be necessary to increase the ROI of holding deeply ITM options. Consequently, the pricing of the latter option would often be below its intrinsic value of $999.

Suppose the call option with a strike price of $1 is priced at $900. In this case, let's calculate the ROI: 1000/900 - 1 = 11%. This ROI aligns with investor expectations. Relative to its intrinsic value of $999, the time value of the $900 option price becomes -99 ($900 - $999).

2.Can options with negative time value be profitable?

Since negative time value exists in practice, can both buyers and sellers capitalize on this to make a profit? The answer is yes.

When trading options of this kind, as a seller, even though we cannot obtain positive time value, the substantial premium income from deeply ITM options (high intrinsic value, expensive price) can offset the margin requirement for the seller to a great extent. This effectively allows the seller to acquire time value indirectly.

As a buyer, when initially purchasing an option, acquiring time value through a discounted price is possible. Under the condition of unchanged intrinsic value, patience in holding the option until expiration enables the buyer to capture this time value as income.

Given that both buyers and sellers can profit from the concept of negative time value, how can one side earn more profit than the other? This requires a better understanding of quantitative parameters related to options, such as delta, gamma, and others. For those interested, you are welcome to follow the second installment of our educational series on options, which will explain option Greek values.

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