Day3.Why do higher stock volatility lead to more expensive options?

Hello， everyone!

Welcome to Tiger Academy - 「Options Academy Column」episode 3.

In the previous article, we discussed how the time value of options is related to the expiration date. The longer the expiration date, the higher the time value. It is also related to volatility. The higher the volatility, the more expensive the options.

Some friends are not quite clear about the statement "the higher the volatility, the more expensive the options." With higher volatility, not only is there a greater possibility of an upward movement, but also a greater possibility of a downward movement. The opportunities are equal, so why are options necessarily more expensive?

Today I'm here to help you solve this question!

1. Why do options become more expensive with higher volatility?

Let's say you invest $10,000 in a financial product with a 50% chance of earning a profit of $10,000 and a 50% chance of losing $10,000. If it were you, would you choose to invest?

Many of you can probably see that in this case, the potential gains and losses are equal, with a 1/2 probability of making money and a 1/2 probability of losing money. For many risk-averse individuals, this is unacceptable.

However, if this product had a 50% chance of earning over $1 million and a 50% chance of losing $10,000, would you choose to invest? Even if you are a risk-averse investor, it would be hard not to be tempted because the potential losses are limited while the potential gains are unlimited.

Options are similar to the second scenario. Since the maximum loss (the premium) is limited, but the potential gains are theoretically unlimited, rational investors would prefer higher volatility because they can achieve unlimited gains with limited losses.

Now, here's the question: If higher volatility makes options more expensive, we encounter two types of volatility in practice: historical volatility and implied volatility.

2. What are historical volatility and implied volatility?

Let's provide another example: Jack is getting ready to go out today but is unsure if it will rain. So, Jack checks the historical weather data and finds that it has mostly rained on this day over the past ten years. Based on this historical data, Jack decides to take an umbrella with him today.

However, if Jack didn't find any clear patterns by checking the weather data and is uncertain about whether it will rain today, but instead observes that the prices of umbrellas suddenly rise while the prices of sunscreen suddenly drop, Jack speculates that there is a higher possibility of rain today and decides to take an umbrella with him.

In this example, the weather is analogous to the price fluctuations of options, and the historical weather data represents the historical price volatility of options, which is known as historical volatility. Historical volatility is based on past experiences and observations, representing data that has already occurred to some extent but may not necessarily reflect the future.

On the other hand, implied volatility is derived from the changes in market prices of umbrellas and sunscreen. It reflects the market's expectation of weather volatility for today, which is known as implied volatility. In simple terms, the implied volatility of an option is derived by inversely calculating it from the price information.

3. How to analyze historical volatility and implied volatility?

Since volatility is directly proportional to price, the key to trading options is to analyze volatility. Similar to stock prices, volatility also exhibits mean reversion characteristics. As mentioned earlier, since historical volatility may not be a reliable reference, we first look at implied volatility.

When implied volatility is high, the prices of the corresponding options are relatively expensive, indicating a higher probability of future volatility decreasing. This is suitable for selling options. Conversely, when implied volatility is low, it can be considered as a sign of relatively low volatility, and the prices of the corresponding options are relatively cheap. This suggests a higher probability of future volatility increasing, making it suitable for buying options.

Now, the question arises: How can we determine whether the current implied volatility is high or low? This is where historical volatility comes into play. By observing the historical volatility curve and comparing the current value of implied volatility with historical volatility values, if the difference between the two becomes significant, it indicates that the implied volatility is either too high or too low, which in turn suggests overpriced or underpriced options.

Taking Apple options as an example, there have been three recent instances where implied volatility deviated significantly from historical volatility, followed by a clear trend of reversion.

Of course, when the stock price isn't moving or the volatility is very low, do options prices still change?

The answer is yes, even when the stock price remains stagnant or volatility is low, options can still incur losses. Why does this happen?

I will reveal the secret in the next issue. In addition, for friends interested in option investment, here is a free Options tour course for you to learn.

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