Understanding the "Option Strategy"

Lesson -> Understanding the "Synthetic long & Arbitrages"

6.1 -Framework

Imagine you are required to hold both a short and long position on Nifty Futures simultaneously. Both positions would expire in the same series. What would you do?

In this chapter,We will discuss these questions. Let's first understand how it can be done. Then we will move on to why this is important (if you're curious, arbitrage might be the answer).

As you might have realized, options are versatile derivative instruments. You can use them to create any type of payoff structure, including futures (both short and long futures payoff).

This chapter will explain how options can be used to artificially duplicate a long-term payoff. Before we move on, it is worth reviewing the long Future's linear payoff.

Alternativ, you can also check out the quick overview at 

The breakeven point is the time at which the long futures position was initiated. The futures will move higher than the breakeven points, and you lose money if they move lower below it. A 10 point move up will make you a profit, while a move down will make you lose. This linearity in payoff is why the future is sometimes called a linear instrument.

Synthetic Longs are designed to create a similar long Future with options.

6.2 - Some Strategical Notes

It is easy to create a synthetic long.

  1. Get the ATM Call Option
  2. Put Option on the ATM

This is why it's important to ensure that -

  1. All options are part of the same underlying
  2. It belongs to the same expiry

Let's take an example to better understand the situation. Let's say Nifty is at 7399. This would give 7400 ATM strike. Synthetic Long would mean we need to be long on 7400 CE. The premium is Rs.107. We would also have to short 7400 PE at 80.

The net cash flow would be the difference in the premiums (i.e. 107 -80 =).27.

Considering further few scenarios of market expiry-

Scenario 1: Market closes at 7200 (below ATM).

The 7400 CE would become worthless at 7200. We would also lose the premium, i.e. Rs.107/-. The 7400 PE would still have intrinsic value.let's calculate this below-

Intrinsic value for Put Option = Max [Strike Spot, 0]

Max [7400-7200, 0]

=Max [200, 0, 0]

= 200

We would be losing money on the premium that we have already received, as we don't have this option. It would result in a loss of -

80-200 = -120

The total payoff for the short Call and long Put positions would be -

= -107 -120


Scenario 2: Market closes at 7400 (At ATM).

Both options would be worthless if the market closes at 7400.

  1. We lose the premium for the 7400 CE option, i.e. 107
  2. We retain the premium for the 7400PE option, i.e. 80
  3. Both positions would pay a net amount.-27e 80 -107

Note that 27 is the strategy's net cash outflow, which is the difference between the premiums.

Scenario 3: Market expires at 74227 (ATM + Difference Between the Two Premiums).

This is an interesting level. It is the breakeven point of the strategy. We don't make or lose any money at this point.

  1. 7400 CE - The option is ITM with an intrinsic value 27. We have also paid 107 premium, so we lose 80.
  2. 7400 PE - The option would expire OTM. Therefore, we retain the entire premium 80.
  3. One side we make 80, the other 80. We don't make or lose money. This is why 7427Breakeven pointThis strategy is recommended.

Scenario 4: Market closes at 7600 (above ATM).

The 7400 CE would be worth 200 at 7600. We would make -

Premium - Intrinsic Value

= 200 -107

= 93

We retain Rs.80 premium, so the 7400 PE would be worthless.

The strategy's total payoff would be -

= 93 +80

= 173

The above four scenarios show that the strategy is profitable when the market moves higher, and loses money when the market falls lower, much like futures. This does not mean that the payoff will be identical to futures. We need to evaluate the strategy's payoff in relation to the breakeven point. Let's say it is 200 points above or below that breakeven point. If the payoff is the same, it is clear that there is linearity in its payoff, which is similar to futures.

Let's get this out of the way.

This is the breakeven point.

ATM + Difference between the premiums

= 7400 + 27


This point should have a symmetric payoff. We will be considering7427 + 200 = 76227And7427-200 =7227This is how it works.

At 7627

  1. 7400 CE would have an intrinsic worth of 227. Therefore, we can make 227 + 107 = 120.
  2. We get to keep the whole premium of 80, as the 7400 PE would be worthless.
  3. All in all, we see a payoff between 120 and 80 =200

At 7227

  1. 7400 CE would have no intrinsic value and we lose all premium paid, i.e. 107
  2. 7400 PE would have an intrinsic worth of 7400 - 7227 = 17.3. Since we received 80 premium, the net loss would be 80 + 173 = -93.
  3. All things considered, we see a payoff between -93 and 107 =-200

There is a payoff symmetry surrounding the breakeven.Synthetic Long is a simulated long that mimics the long-term payoff.

Here is the payoff at different expiry levels:

When we plot the Net Profitoff, we see a payoff structure that is very similar to long-call futures.

After we have figured out how to set-up a Synthetic long, it is time to determine the most common circumstances in which a synthetic long might be required.

6.3 - What is "Fish market arbitrage"?

Let's assume you are familiar with Arbitrage. Arbitrage can be described as the opportunity to purchase goods/assets in a cheaper market, and then sell them in more expensive markets. You get the profit. Arbitrage trades can be risk-free if executed correctly. Let me give you an example of an arbitrage opportunity.

Let's suppose you live near a city that has a lot of fresh fish. The rate at which fish can be sold in your area is low. A neighboring city, 125kms away, has a large demand for the same fresh seafish. The same fish can be purchased in the neighboring city for Rs.150 per Kg.

If you are able to purchase fish in your city for Rs.100, and then sell it in your neighboring city for Rs.150, you will get Rs.50. You will need to pay for transport and logistics. However, Rs.50 per Kg is still possible. It is still a great deal, and it is typical of arbitrage in the fish markets!

This looks great, but it's not risky.

It is risk-free and nothing will change. However, if the circumstances change, your profitability will also change. Let me tell you a few things that could happen.

  1. No Fish (opportunity Risk)Imagine that you decide to go to the market one day to buy fish for Rs.100. But you find out there are no fish on the market. You will lose Rs.30/-.
  2. No Buyers (liquidity Risk)Suppose you buy fish for Rs.100, then go to a neighboring town to try to sell it at Rs.150. But you find that there are no buyers. The bag is full of dead fish that are literally worthless.
  3. Bad bargaining (execution risk)Arbitrage is based on the fact that you can always bargain to buy at Rs.100 but sell at Rs.150. What happens if you buy 110 and sell 140 on a bad day? It is still necessary to transport 20 Rupees. This means that instead of 30 Rupees profit, you will make only 10 Rupees. If this continues, the arbitrage opportunity may become less appealing and you might not want to continue.
  4. Transport becomes costly (cost of transaction).This is another important factor that will determine the profitability of arbitrage trade. What if transportation costs go up from Rs.20 to rs.30? As execution costs rise, arbitrage opportunities become less attractive. The cost of transaction is the key factor that determines whether an arbitrage opportunity will be successful or not.
  5. Concurrence Kicks in (Who can drop lower?)You are more likely to be surrounded by competition because the world is highly competitive. Imagine this:
    1. You are currently the only person who is doing this trade.
    2. Your friend sees that you make a profit and wants to follow you. This is a free market, so you can't stop him.
    3. You both buy it for Rs.100 and transport it for Rs.20. Then you try to sell it in the nearby town.
    4. Potential buyers walk in and see a new seller selling the same fish. Which of the two is more likely to sell the fish?
    5. If the fish is the same quality, the buyer will purchase it from the seller who sells it at a lower price. Let's say you are looking to buy the client and lower the price to Rs.145/.
    6. Your friend drops the price and offers to buy fish at Rs.140/KG. This will spark a price war. The price continues to drop and arbitrage opportunities are lost.
    7. How low can it drop? It can drop to Rs.120 (cost for transport and fish) It is not a good idea to operate the business beyond 120.
    8. In a highly competitive world, eventually competition will kick in and arbitrage opportunities cease to exist. In this scenario, the price of fish in a neighboring town would fall to Rs.120 or an equivalent price.

I trust the above discussion has given you an overview of arbitrage. Any arbitrage opportunity can be described mathematically. Let's take the fish example as an example.

[Cost of selling fish to town B - Cost for buying fish in the town A] = 20

Arbitrage opportunities exist when there is an imbalance in any of the equations. Arbitrage opportunities exist in all markets, including the stock market, fish market, agrimarket, currency market and currency market. They are all governed using simple arithmetic equations.

6.4 - What is "The Options arbitrage"?

Arbitrage opportunities are available in nearly every market. To spot them and make a profit, one must be an attentive observer of the market. Stock market-based arbitrage opportunities can allow you to lock down a small but guaranteed profit and keep it no matter what the market does. Arbitrage trades are a popular choice for risk-tolerant traders.

Here is a simple case of arbitrage that I'd like to talk about. Its roots lie in the idea of"Put Call Parity". I won't be discussing the Put Call Parity Theory, but will instead illustrate one of its applications.

This arbitrage equation is based on Put Call Parity.

Short Synthetic Long Futures + Long Synthetic Long Futures = 0

This can be further elaborated to:

Long ATM Call + Short AT Put + Short Futures = 0.

According to the equation, the P&L at expiry due to holding a long synthesized long and short future should equal zero.Well the Put call Parity is the answer to this.

If the P&L has a value other than zero, we have an opportunity to arbitrage.

To understand this let's take an example-

21 st January, the Nifty spot was at 7304 and Nifty Futures traded at 7316.


79.5 and 73.5 respectively traded the 7300 CE (ATM options) and 7300 PE (CE). All the contracts are from the January 2016 series.

If one executes the trade according to the above arbitrage equation, the positions will be -

  1. Long 7300 CE @ 79.5
  2. 7300 PE Short @ 73.85
  3. Futures Short Nifty @ 7316

Note that the first two positions form a long synthetic lengthy. As per the arbitrage equation, the positions should expire with a zero P&L.

Scenario 1 - Expiry at 7200

  • We would lose the premium we paid for 7300 CE, so the 7300 CE would be worthless.79.5
  • The intrinsic value of the 7300 PE is 100. However, we are short at 72.85 so the net payoff would only be 73.85 + 100.-26.15
  • We are short on futures at 7316 which would result in an increase of 116 points (7316-7200).
  • Net payoff would be 79.5 - 26.15 + 11 =+10.35

We are now experiencing a positive, non-zero P&L, rather than a 0 payoff.

Scenario 2 - Expiry at 7300

  • We would lose the premium we paid for 7300 CE, so the 7300 CE would be worthless.79.5
  • We retain 73.85 because the 7300 PE would be worthless.
  • We are short on futures at 7316 which would result in a 16 point profit (7316-7300).
  • The net payoff would be -79.5 +73.85+16+10.35

Scenario 3 - Expiry at 7400

  • The 7300 CE would have an intrinsic worth of 100 and the payoff would therefore be 100 - 79.5 = 20.5
  • We retain 73.85 because the 7300 PE would be worthless.
  • Futures are currently short at 7316. This would lead to a loss of 84 points (7316-7400).
  • Net payoff would then be 20.5 + 73.285 - 84 =+10.35

This could be used to test the market for any expiry value, meaning that markets can move in any direction. However, you're likely to get 10.35 points.upon expiry.This is what I want to emphasize again: arbitrage allows you to make 10.35 upon expiry.

Below is the payoff structure for different expiry dates.


Isn't it intresting?you may think what's the catch?

Transaction fees

You must consider the cost of execution to determine if the trade is still worth it. This is how it works:

  • BrokerageIf you trade with a traditional broker, you will be charged a percentage which will reduce your profits. On the one hand, you earn 10 points but may end up paying 8-10 points for brokerage. If you trade this trade with a discount broker such as Stock market box, the breakeven point would be approximately 4-5 points.
  • STTRemember that the P&L is realized upon expiry. Therefore, you will need to keep your positions open until expiry. If you have an ITM option that is long, you will need to pay a substantial STT upon expiry. This will further reduce your profits. Please doThis is what you need to knowLearn more
  • Other taxes applicable -You also need to account for stamp duty, service tax, and other taxes

Considering these costs, it may not be a good idea to try to trade arbitrage for 10 points. It would make sense if the reward was higher, perhaps 15 or 20 points. You can maneuver the STT trap with 15 to 20 points. However, it will only shave off a few points.

Key points-

  1. Options can be used to duplicate futures payoffs
  2. The long-term payoff of a synthetic long is replicated by a synthetic long
  3. Simultaneously selling ATM Put and buying ATM Call creates a synthetic lengthy
  4. The synthetic long's breakeven point is the ATM strike + Net Premium Paid
  5. Arbitrage opportunities are created when synthetic long + short futures have a positive, non-zero P&L at expiry
  6. Only execute the arbitrage trade if the P&L at expiry makes sense after accounting expenses.