**PREMIUM Khanewala **

**Who is a Premium Khanewala? **

In India, options have existed since many years and Indian options market has its own dictionary. Option writers are typically called as *Khanewalas, * and Option buyers are known as *Laganewalas.* The import is that Option writers ‘eat away’ the premiums they earn, while Option buyers apply their funds towards purchasing possibly valuable rights of appreciation or depreciation in stock prices.

Players who consistently write Options and believe in eating up premiums most of the time are known as *Khanewalas.*

**Is that not a high risk proposition? **

Yes, that is a high risk proposition, but some players like risk, can handle risk and have the knowledge and wherewithal to hedge their positions if risk rises beyond acceptable levels. For such players, premium *khana *is an exciting lunch.

**How are premiums determined and what level of premiums can be exciting for such players? **

One of the key determinant of Option prices is the volatility in share prices. If prices are volatile, Option prices tend to move higher. Further, if the market is trended and most players are of the opinion that market is moving up, then demand for calls will rise. When demand rises, buyers will be willing to pay a higher Option price resulting in higher implied volatility levels. When call volatility levels rise, put prices also rise sympathetically.

**What is meant by volatility and how can prices of options rise in a volatile market and also in a trended market? **

Yes, it does appear that Option prices react by moving up in rather dissimilar situations, viz – one – when the market is volatile and – two – when the market is trended. Let us understand volatility. If market is moving up and down, up and down severely, volatility levels will go up. In such a situation, option prices will also be higher.

Buyers of options are likely to gain more if prices move up or down (up for call buyers and down for put buyers). Hence, they are likely to pay more premium causing a rise in prices.

If the market is trended, most players will look for further movement in the direction of the trend and hence be willing to pay higher for options in that direction.

**Why should put prices rise if call prices rise? **

There is a basic put call parity equation. As per text books on the subject, cash market prices are taken to define this equation. However, I believe text books adopt that approach because stock futures are not available (or till recently were not available in most developed countries). In India, this put call parity equation can be defined as under:

**Strike Price + Call Value – Put Value = Futures Price **

This should be true. For example if Satyam 220 strike call is available for Rs 9 and put for Rs 12, then Satyam Futures price should be Rs 217 (220 + 9 – 12).

**If that is not so, what will happen? **

If that is not so, an arbitrage opportunity will arise and prices will start moving in such a way that the above equation becomes valid. For example, if Satyam is available not at Rs 217 but at Rs 214, then arbitrageurs will buy the right hand side of the equation and sell the left hand side of the equation.

That is, they will take the following actions:

- Buy Satyam Futures at Rs 214
- Sell Satyam Calls at Rs 9
- Buy Satyam Puts at Rs 12
- Net Cash outflow on day of transacting Rs 3

By doing so, they would have made a risk free profit of Rs 3.

**How will that be achieved? Satyam could move to say Rs 240 by the close of the month or Rs 180 by the close of the month. **

Let us examine the two situations closely. Suppose Satyam moves to Rs 240, what is the payoff?

- Satyam Futures – Profit of Rs 26 (240 closing price minus 214 cost)
- Satyam Calls – Payout of Rs 20 (240 closing price minus 220 strike price)
- Satyam Puts – No payout (Satyam closes above 220)
- Net Cash Inflow – Rs 6
- Net Cash Outflow on Day of transacting – Rs 3
- Hence, Net Profit – Rs 3

On the other hand, if Satyam moves to Rs 180, what is the payoff?

- Satyam Futures – Loss of Rs 34 (180 closing price minus 214 cost)
- Satyam Calls – No Payout (Satyam closes below 220)
- Satyam Puts – Receipt of Rs 40 (220 Strike minus 180 Closing)
- Net Cash Inflow – Rs 6
- Net Cash Outflow on Day of transacting – Rs 3
- Hence, Net Profit – Rs 3

Thus, irrespective of wherever Satyam moves, the arbitrageur will make a profit of Rs 3.

**What if the left hand side of the equation is lower? **

Consider a situation where call and put prices are the same as above, but Satyam futures are quoting at Rs 219.

In this case, the arbitrageur will buy the left hand side of the equation and sell the right hand side. That is, he will take the following actions:

- Buy Satyam Call at Rs 9
- Sell Satyam Put at Rs 12
- Sell Satyam Futures at Rs 219
- Net Cash Inflow on Day of transacting: Rs 3

**What is the assured profit and how do we establish it if Satyam moves to say Rs 245 or Rs 195 at close of the month? **

The assured profit is Rs 2 (as per the equation Satyam Futures should have quoted at Rs 217, but it is actually quoting at Rs 219 – hence the difference is Rs 2).

If Satyam closes at Rs 245, let us check the payoff on the last day.

- Satyam Futures – Loss of Rs 26 (219 sale price minus 245 closing price)
- Satyam Calls – Receipt of Rs 25 (245 closing price minus 220 strike)
- Satyam Puts – No Payout (Satyam closes above 220 strike)
- Net Cash Outflow – Re 1
- Net Cash Inflow on Day of transacting – Rs 3
- Hence, Net Profit – Rs 2

If Satyam closes at Rs 195, let us check the payoff on the last day.

- Satyam Futures – Profit of Rs 24 (219 sale price minus 195 closing price)
- Satyam Calls – No Payout (Satyam closes below 220 strike price)
- Satyam Puts – Payout Rs 25 (220 strike minus 195 closing price)
- Net Cash Outflow – Re 1
- Net Cash Inflow on Day of transacting – Rs 3
- Hence, Net Profit – Rs 2

**What does this establish? **

The put call parity equation establishes that call and put prices have to move together in a disciplined manner. In any given market, if call prices shoot up (due to trending, higher volatility, expectations of any news or any other factor), put prices will necessarily respond.

**What are the risks in the put call parity arbitrage that we discussed above? **

The first risk is execution risk. While the computerized trading systems may show the prices as in my example, the prices might change with fraction of a second, so that when you actually execute you do not get the arbitrage difference as expected. You might get slightly less or sometimes even more.

Secondly, if you have sold calls or puts, these might be exercised sometime before expiry. In that case, you will receive the exercise notice after the close of trading hours. You will have to reinstate the same position in the morning tomorrow, but by that time the scrip might have moved away. This could result in a cost (or a gain), but in any case you face overnight risk.

Third, such arbitrages are not easily available and you need to watch the market closely.

Fourth, such arbitrages might not be available in large volumes. Hence, if you a large player, you might find not enough opportunities on a regular basis.

**What does the Khanewala desire? **

The *Khanewala* desires that he should sell options when volatility levels are high so that his premium income is maximized. He will be delighted if volatility levels fall after he completes his sales.

Most Khanewalas look at Option prices in a simplistic manner taking the Option prices as a percentage of the stock prices. They might for example comment that Satyam calls are generating 4% premium per month and this is interesting. Some people equate this with earning interest on a principal so to say and a 4% monthly return might translate into a 48% annual return which is very exciting considering other investment avenues available today. Obviously, this is a simplistic method of looking at premiums but is done commonly.

**How is this simplistic percentage return related to volatility? **

If we run a simulation on Black Scholes, taking a 30 day period to expiry and a zero percent interest rate, the following interesting pattern emerges:

Implied Volatility % |
Option Premium % to Stock Price |
Incremental Option Premium % |

15% | 1.72% | |

20% | 2.29% | 0.57% |

25% | 2.86% | 0.57% |

30% | 3.43% | 0.57% |

35% | 4.00% | 0.57% |

40% | 4.57% | 0.57% |

45% | 5.14% | 0.57% |

50% | 5.71% | 0.57% |

55% | 6.28% | 0.57% |

60% | 6.85% | 0.57% |

Thus, the simplistic Option Premium increases by 0.57% for every 5% point increase in Implied Volatility.

**What is Implied Volatility? **

In the Black Scholes model, Option prices are based on six variables:

- Stock Price
- Strike Price
- Volatility
- No of Days to expiry
- Interest Rate
- Dividends

The current Option price would reflect a certain level of Volatility automatically. This level of Volatility is said to ‘implied’ in the Option price. For example, if Satyam is at Rs 217 and the 220 Call trades at Rs 9 when there are 30 days to expiry with a Interest rate of zero percent and a dividend of zero, then what is the volatility level which results in the price being Rs 9? If you run it on the Black Scholes calculator, you find the volatility is 42%. This 42% is the Implied Volatility.

**Is there any other kind of Volatility? **

Yes, the volatility actually shown by the stock in the past is called Historical Volatility (also referred to as Statistical Volatility by some people). This is based on the actual movement in the stock over a certain period of time. For example, you could take up the movements over the past ten days and work out the volatility level.

Technically, the steps involved are as under:

- Put down the stock prices in an Excel column
- Work out the daily change in prices (today’s price minus yesterday)
- Express the daily change in percentage terms (Daily change upon yesterday’s price)
- Work out the standard deviation of this daily change percentage column

The resulting figure is the ten day volatility of Satyam.

**Is there a relationship between the two? **

Yes, there would be a vague positive correlation between the two indicating that if Satyam has been volatile in the recent past, the market will expect it to stay volatile in the short term and hence options will be quoting higher. On the other hand, if Satyam has been rather dull in the recent past (ten days in our example), market will expect no great moves immediately and hence option premiums will drift downwards.

However, if some news is expected, market will start factoring this into the premium and you may well find that implied volatility levels are rising inspite of dull historical volatilities. Sometimes, inside information may be acting in the market as a result of which implied volatilities might suddenly rise.

This can be a pointer to news and can be acted upon if you are active in the market.