Option Valuation
Question: What are the components of Option Value?
Answer: The value of an Option is made up of two components, viz. Intrinsic Value and Time Value.
Question: What is Intrinsic Value?
Answer: The value that you will realize (as a buyer of an Option) on expiry or on exercise is the Intrinsic Value. For example, the Intrinsic Value of a Satyam 280 Call is Rs 11 when the Satyam share itself is quoting at Rs 291. You will realize Rs 11 if you exercise today.
Question: What is Time Value?
Answer: Time Value is the Total Option Value minus Intrinsic Value. For example, if the Satyam 280 Call above is quoting at Rs 25, Time Value will be Rs 25 minus Rs 11 i.e. Rs 14.
Question: How does Intrinsic Value correlate with Share Price?
Answer: In the case of Call Options, higher the Share Price, higher the Intrinsic Value. For example, if Satyam moves up from Rs 291 to Rs 301, the Intrinsic Value has moved up from Rs 11 to Rs 21. There is thus absolute correlation between the two. Obviously, if the Satyam share price moves down, the Intrinsic Value will move down to the same extent.
In the case of Puts, the correlation is absolutely negative. If Reliance is quoting at Rs 300, the Intrinsic Value of a Reliance 320 Put is Rs 20. If Reliance thereafter moves down from Rs 300 to Rs 295, the Intrinsic Value of the Reliance 320 Put will increase from Rs 20 to Rs 25.
Question: How does Time Value correlate with Share Price?
Answer: Time Value does not correlate with Share Price. It correlates with other factors, the principal ones being - Time left for Expiry and Volatility. If Time left for Expiry is high, the Time Value will be higher and vice versa. You will find, for example, that the Reliance 300 Feb Call Option will be cheaper than the Reliance 300 March Call Option. This is because, the March Options will have one more month to expire than the Feb Options.
Interestingly, Time left to expiry affects both Calls and Puts equally. Thus, long term Calls and Puts are priced more than short term Calls and Puts.
Volatility is a very interesting determining factor of Option Value. Higher the Volatility of the share, higher will be the values of both Calls and Puts. This is because, the probability of a highly volatile share moving up or down is much higher than that of a low volatile share. Option values are based on how much movement is possible or expected in the underlying share and higher this possible movement, higher the value of the Option.
Question: Can we summarise the factors determining Option Values?
Answer:
| Factor | Option Type | Impact on Option Value | Component of Option Value |
| Share price moves up | Call Option | Option Value will also move up | Intrinsic Value |
| Share price moves down | Call Option | Option Value will move down | Intrinsic Value |
| Share price moves up | Put Option | Option Value will move down | Intrinsic Value |
| Share prices moves down | Put Option | Option Value will move up | Intrinsic Value |
| Time to expire is high | Call Option | Option Value will be high | Time Value |
| Time to expire is low | Call Option | Option Value will be low | Time Value |
| Time to expire is high | Put Option | Option Value will be high | Time Value |
| Time to expire is low | Put Option | Option Value will be low | Time Value |
| Volatility is high | Call Option | Option Value will be high | Time Value |
| Volatility is low | Call Option | Option Value will be low | Time Value |
| Volatility is high | Put Option | Option Value will be high | Time Value |
| Volatility is low | Put Option | Option Value will be high | Time Value |
Question: Are there other factors determining Option Values?
Answer: Two other factors which affect Option Values are Interest rates in the economy and Dividends on stocks. These do not affect Option Values significantly. It is expected that higher Interest rates will result in higher Call Option Values and lower Put Option Values. Dividends have the impact of decreasing share prices. Accordingly, Call Option Values will decrease and Put Option Values will increase when Dividends are declared.
Question: How do I know whether a particular Option is correctly priced in the market or not?
Answer: There is a popular Black Scholes Model which provides the theoretical price of Options. Black Scholes Option Calculators are available on various websites. You need to key in the basic parameters which are the following:
- Current Share Price
- Option Strike Price
- Time left for Expiry
- Volatility
- Interest Rate
Given this data, the calculator will provide you with the price. You can then compare this price with the actual price prevailing in the market and find out whether the Option is being overpriced or underpriced.
Question: Will I face any practical difficulty in this process?
Answer: Yes – you will. You will be able to key in all the above parameters into the Option Calculator except Volatility. This is not clearly known all the time. Further, Volatility can be understood and defined differently by different people. You need to understand Volatility well in order to determine Option Value correctly.
The other factors are clearly known – viz. the Current Share Price, Option Strike Price, Time left for Expiry are frozen anyway. Interest rate estimates can differ from person to person, but Interest rates do not affect Option Values very much, hence this does not matter.
Question: Are there other models also available?
Answer: Yes, there are other models apart from the Black Scholes model. The popular ones are the Binomial Model developed by Cox, Ross and Rubinstein and the Adison Whaley Model. These are slightly more sophisticated than the Black Scholes Model. However, the Option Values are not significantly different. For example, if one Model gives you a Value of Rs 14.12, another might come up with a Value of Rs 14.26. As a retail buyer of Options, you might find that the difference between the bid and the ask at any point of time is probably higher than the differences between Option Values of various Models.
Question: How do I learn about Volatility?
Answer: We will discuss that in our next Article.
Volatility - Significance for options Part-I
Question: Why is Volatility significant for Options?
Answer: The value of an Option, apart from other factors, depends upon the Volatility of the underlying. Higher the Volatility of the underlying, higher the Option Premium.
Question: What is Volatility?
Answer: Volatility is the fluctuation in the price of the underlying. For example, the movement in the price of Satyam is quite high as compared to the Sensex. Thus, Satyam is more volatile than the Sensex.
Question: How do you measure Volatility?
Answer: Volatility is the standard deviation of the daily returns on any underlying.
Question: This is too complicated ! What is Daily Return?
Answer: Ok – let me restate in simple language. Every day, every scrip moves up or down by a certain percentage. For example, if Satyam closed at Rs 280 yesterday and today it closed at Rs 285, the percentage change is 5/280 x 100 = +1.79%. This percentage is called ‘daily return’.
Let me make a slightly elaborate calculation and show you.
| Day | Satyam Closing Prices | Daily Return |
| 1 | 280 | |
| 2 | 285 | +1.79% |
| 3 | 272 | -4.56% |
| 4 | 292 | +7.33% |
| 5 | 287 | -1.71% |
Fine, what next?
Now you find out the standard deviation of these Daily Returns.
Question: What is Standard Deviation?
Answer: Standard deviation is a measure of dispersion and comes from statistics. Dispersion indicates how widely ‘dispersed’ a set of data is. For example, if you look at heights of adult males in India, you will find that the heights of various people are not too far off from each other. While the average male is about five and a half feet tall, the others are not too far off. While some may be one feet above this average, others might be one feet below.
You are unlikely to find people twenty feet tall, nor two feet tall. Thus, if you were to work out the Standard Deviation of this data, this figure will be a small number, because the data is not too dispersed.
On the other hand, if you try and plot the wealth of various Indian males, you might find a wide dispersion, as somebody might have a wealth of Rs 100 while somebody else might possess Rs 1 crore. Thus, standard deviation of wealth will be high.
Question: How is it calculated?
Answer: In these days of computerized living, it might be simpler to use an Excel spreadsheet and key in the formula for standard deviation. You will get the figure in a second.
The technical formula goes like this:
Identify the basic data (in our case the percentage daily returns)
Work out the average
Work out the deviations of each observation from the average (these deviations might be positive or negative)
Take a square of these deviations
Sum up these squares
Divide the sum by the number of observations
Work out the square root of this number
Let me show you from the above example:
| Day | Daily Return | Deviation | Square of Deviation |
| 2 | +1.79% | +1.08% | 0.011664% |
| 3 | -4.56% | -5.27% | 0.277729% |
| 4 | +7.33% | +6.62% | 0.438244% |
| 5 | -1.71% | -2.42% | 0.058564% |
| Average | +0.71% | Sum | 0.786201% |
Divide the sum by the number of observations: 0.1966%
Square root of above: 4.43%
Thus the standard deviation of the above data comes to 4.43%.
This is the daily standard deviation, as it is based on daily returns data.
I have heard that Volatility is 50%, 80% etc. Your volatility is far lower at only 4%.
You have heard correct. What we have calculated above is the Daily Volatility. If you want to know the Annual Volatility, you should multiply with the square root of the number of working days in a year. For example, if one year has 256 working days, square root of 256 days is 16 days. Thus in the above case the Annual Volatility is 4.43% x 16 = 70.88%.
In a similar manner, if you want to know the Volatility of the next 9 days, the 9-day Volatility will be 4.43% x 3 = 13.29%.
Question: Having derived the Volatility, how do I interpret it?
Answer: The concept of Normal Distribution states that you can derive a deep understanding of possible movements in the share price from this figure of Volatility. The movement will be within 1 standard deviation 66% of the time, within 2 standard deviations 95% of the time and within 3 standard deviations 99% of the time.
Question: Can you elaborate using examples?
Answer: If Satyam’s closing price today is Rs 287, expected movement in the next one day can be tabulated as under:
| Number of Standard Deviations | Percentage | Price Movement | Lower Price | Higher Price | Probability |
| One | 4.43% | 13 | 274 | 300 | 66% |
| Two | 8.86% | 26 | 261 | 313 | 95% |
| Three | 13.29% | 38 | 325 | 249 | 99% |
Similarly possible movement over the next nine days can be forecasted as under:
| Number of Standard Deviations | Percentage | Price Movement | Lower Price | Higher Price | Probability |
| One | 13.29% | 38 | 325 | 249 | 66% |
| Two | 26.58% | 76 | 211 | 363 | 95% |
| Three | 39.87% | 114 | 173 | 401 | 99% |
Question: What are we predicting here?
Answer: Predicting is a rather difficult science. First of all, we are not looking at direction at all. We are not saying whether Satyam will move up or down. Secondly, we are forecasting possible maximum swing in magnitude irrespective of direction.
For example, we are saying that Satyam will close between Rs 249 to Rs 325 tomorrow and the probability of this happening is 99%. The implication is that the probability of Satyam closing below Rs 249 or above Rs 325 is 1%.
Question: How many days of data should we consider for calculating Volatility?
Answer: There is a difference of opinion among traders as to the number of days that should be considered. In the Indian context, we currently find that Options are available for 3 months. However, most of the trading happens in the first month. Thus, the relevant period for forecasting is one month or lower. Accordingly, it would be sensible to consider Volatility based on the past 10 trading days and for the past 20 trading days. Longer periods would perhaps not be relevant in the present context.
Question: How do we use Volatility in our trading strategies?
Answer: We will discuss this in our next column.
Volatility - Significance for options Part-II
Question: Can we summarise our discussion last time?
Answer: In our last Article, we discussed the concept of Volatility, how is it calculated, how is it interpreted and what period of time should be reckoned for such calculations.
Question: How can these learnings be applied?
Answer: Study of past prices of a scrip will enable you to arrive at ‘historical’ volatility. Option prices as you are aware, depend on Volatility to a high degree. However, Option prices may or may not reflect ‘historical’ volatility.
Study of past prices of a scrip will enable you to arrive at ‘historical’ volatility. Option prices as you are aware, depend on Volatility to a high degree. However, Option prices may or may not reflect ‘historical’ volatility.
Question: Why not?
Answer: It is possible that market participants believe that Volatility in future is expected to rise. Thus, historical Volatility may have been 50%, but it is widely believed that the scrip will become more Volatility resulting in a higher level of say 60%. Accordingly, the Option might be priced on the basis of 60% forecasted Volatility.
Question: How will I know this?
Answer: If you study the price of the Option as actually quoted in the market, you will realize what is the ‘implied’ Volatility. For example, if the following Option is theoretically studied:
Stock Price Rs 280
Strike Price Rs 260
Volatility 50% annual
Days to Expiry 20 days
Interest Rate 12% annual
The price of the Option applying Black-Scholes Model comes to Rs 26.28. But the actual price of that Option in the market might be (say) Rs 29.50.
Question: What does this imply?
Answer: This could imply that the market is not going by the historical Volatility of 50%, but is imputing another Volatility to that Option going forward. You can use the same calculator, but now instead of providing the Volatility figure yourself, you can provide the Option price instead. Now if you work backwards and find out what is the Volatility that would support the price of Rs 29.50, that Volatility comes to 65%.
Question: So how can I use this understanding?
Answer: You are facing a situation where historical Volatility of the scrip is 50%, but the implied Volatility is 65%. Various possibilities for this divergence can emerge. One possibility is that the market is expecting the future Volatility of the scrip to increase and is accordingly factoring in such expectations. Another possibility is that the market is mis-pricing the Option and that the Option value will come back to around Rs 26.28 shortly. The third possibility could be that there is some news about the company that could affect the price favourably and this news is being reflected in the Options become more expensive to begin with and in a short time, the underlying scrip will also reflect this phenomenon.
Depending on what you see from these possibilities (and there could be others too), you could take an appropriate stand.
For example, if you believe that Volatility will rise, you could go in for Option Strategies that could suit such an event happening. If you believe that the Option is being mispriced, as an aggressive player, you could sell such Options with a belief that you could buy them back at a later date. Such a strategy would need to be supported by a hedging strategy as mere selling of Options will leave with unlimited risk.
If you believe that there is some positive ‘news’, you might be tempted to buy the Options inspite of high Volatility (or buy the underlying).
Question: What if the Implied Volatility is lower than Historical Volatility?
Answer: This is also possible. It could indicate that the Option itself is being underpriced in the market (which could make it a good buy on its own merit). It could indicate that the market believes that the days of high Volatility in that scrip are over and it will now trade a lower level. Another possibility is that there is some bad news whereby the underlying stock price is expected to move down and the Option has first started reflecting this possibility.
Question: What should I do to fine tune my understanding?
Answer: If you are a serious derivatives market player, you should track historical Volatility very closely. It is recommended that you work out 10 day and 20 day moving Volatilities on a continuous basis. A moving daily trend would be very useful.
Once you have this set of numbers, you could compare with Implied Volatility to arrive at a more definitive conclusion. For example, you could find the following information:
10 day Volatility Today (of last 10 days): 61%
20 day Volatility Today (of last 20 days): 57%
Max 10 day Volatility in the last 6 months: 62%
Max 20 day Volatility in the last 6 months: 59%
Implied Volatility Today: 71%
This set of data reveals that the current Implied Volatility is way beyond historical levels and the likelihood of some positive news in the scrip is probable. If you plan to sell the Option on the assumption that it is overpriced, that strategy is dangerous and should be dropped.
On the other hand, if the data shows up as under:
10 day Volatility Today (of last 10 days): 51%
20 day Volatility Today (of last 20 days): 47%
Max 10 day Volatility in the last 6 months: 72%
Max 20 day Volatility in the last 6 months: 67%
Implied Volatility Today: 61%
This would indicate the possible overpricing of the Option at current levels, but as the Implied Volatility is within the maximum levels reached in the recent past, there does not appear to be abnormal behaviour in the price. Advanced players could consider selling such Options which have a ‘statistical edge’ and if necessary covering the position with some other Option or Future. Selling such Options needs further discussion, which we will try and explore in later articles in this series.
If you are anyway considering selling the Option (for reasons other than Volatility reasons enumerated here), you could think that this is an appropriate time for selling the Option as the edge will help you in increasing your profit to a small degree.
Question: How much does Volatility affect an Option’s price?
Answer: It does affect the price quite significantly. Some examples are provided below:
Days to expiry: 30 days
Interest Rate: 12% per annum
At The Money Option:
Stock Price: 260
Strike Price: 260
| Volatility Annualised | Option Price |
| 50% | 16.09 |
| 60% | 19.03 |
| 70% | 21.98 |
| 80% | 24.92 |
In the Money Option:
Stock Price: 300
Strike Price: 260
| Volatility Annualised | Option Price |
| 50% | 45.46 |
| 60% | 47.44 |
| 70% | 49.69 |
| 80% | 52.14 |
Out of the Money Option:
Stock Price: 240
Strike Price: 260
| Volatility Annualised | Option Price |
| 50% | 7.15 |
| 60% | 9.72 |
| 70% | 12.35 |
| 80% | 15.03 |
You can see that the price of the Option is significantly affected in all three types of Options.
Question: What are the Advanced applications of Volatility trading?
Answer: Volatility trading is a subject in itself. Strategies like delta neutral and gamma neutral fall within its ambit. We will discuss them after understanding basic strategies.
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