Everything on Option Arbitrage

Option arbitrage trades can be used to make small profits and take on less risk. This is the act of buying and selling a similar commodity on two different markets. Put-call parities are a way to arbitrage options. You have the right to buy and sell with a call.

What's a Put-Call Parity?

It is the relationship between the value of put options and calls options from an equivalent class with an equal underlying asset and strike price and expiration date.

It suggests that holding both a short put and a long call of the same class will yield an equal return. This is because you have one forwarding contract for an identical asset with an equal expiration date and forward prices that are comparable to the Options' strike prices.

- If the prices of the call and put options diverge, this type of relationship is not valid, an arbitrage possibility exists. The traders can theoretically make a profit without risk.

- This equation expresses put-call parity as c+ Xe-rt= p+S

Where?

Call price c=

Strike Price = X

p = Price at the Put

S = Initial price of the underlying

r= Rates of interest

t = Time of expiry

e-rt = Discounting Factor

Arbitrage is available if this equality is not respected

Arbitrage Strategies through an Example:

- Let's say Stock ABC trades at Rupees90.

- Construct two portfolios portfolio A and portfolio B. Portfolio A consists of two items: a call option, and a zero-coupon bonds.

- In the protocol parity equation, portfolio A is represented on the left hand side, while B is on the right.

We buy portfolio A at Rs 8.56 and engage in zero-coupon bond trading activity at Rs. 88.56. The strike price is Rs 100.

Portfolio B - We buy stock and put options for two options. The put options are purchased at Rs 12 for the same underlying price of Rs 100, but priced at Rs 12.

Portfolio A consists of a call option as well as a 0 bond coupon option. It is worth:

c + Xe -rt= 8+ 100*e0.07*0.5=8 + 88.56 = R 96.56

p+S = 12 +90= Rs 102

We will see that portfolio A is different from portfolio B. This means that there is an arbitrage opportunity. We can profit from the difference in the prices of both portfolios which should essentially be equal.

To make a profit of Rs., we buy portfolio A that is cheaper and then sell portfolio B (expensive). 5.44

here's a list of different situations at Time of expiry.

Scenario 1 - Time expiration affects this strategy

- Stock price drops to zero at expiration

- Portfolio A's call option expires without any money and Portfolio B's put option is worth Rs. 100

- If the buyer of the option exercises it, we will have to pay Rs 100 to him. We have Rs. We have Rs. 100 bond that we can use for the payment of the put-option buyer.

This is how our net profit at Rs 5.44 remains unchanged

Scenario 2:

Suppose that the stock price is Rs. 200 at expiration.

- We have a bond worth Rs. 100, and the call option is in our money. 100 The putoption is no longer valid. We had already sold portfolio B stock, which now runs us Rs. 200

- To cover the short position Rs. We can use Rs. 100 from the call option, and Rs 100 from bond. This ensures that our profit stays the same at Rs. 5.44

The profit will be Rs 5.44. We will buy the less expensive portfolio and then sell it to make a profit on the difference in the prices.

Option Arbitrage Opportunities:

The Synthetic Position

These are also known as synthetic positions. These positions are the fundamental positions of underlying stocks.

- This means that the risk profile (Possible Loss & Profit) for any position is often exactly duplicated using different but more complicated methods.

- Synthetics should have identical strike value and expiration dates.

- To make synthetics, each underlying stock must have the same number of shares as the options.

To show a synthetic strategy, consider a relatively comfortable option position: The long decision. Your loss is limited to the premium you paid, but your potential gain is unlimitable once you make a decision.

Think about the synchronic purchase a put and 100 shares in the underlying stock. Your loss is limited to the premium you paid for the put. If the stock value goes up, your profit potential will be unlimited.

A long-put/long stock position is similar to owning a call option with a similar strike and expiration. A long-put/long/stock stock position is often referred to as "synthetic long calls".

Only difference between them is the amount of dividends that are paid over the entire holding period. Owners of stock would get the extra amount, but owners of long-call options would not.

Options arbitrage trades can be profitable without risk if the prices are out of alignment and the put-call paraity is being violated. You may lose if you place these trades at prices that are in alignment.