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How to do arbitrage using stock and index options

When we talk about arbitrage there are two thoughts that immediately come to mind. First is the age old practice of arbitraging the price differences between the NSE and the BSE. The second is the arbitrage between the spot and the future market, which is used quite popularly across most asset classes. But did you know that it is also possible to arbitrage the mispricing in options. So what are the arbitrage strategies using options and  how to do arbitrage in options? Let us understand risk arbitrage using options in greater detail..

There are broadly 2 common situations wherein you can actually do arbitrage in options and earn riskless profit.

1.  When there are discrepancies in the put / call parity
The concept of put call parity states that for given strike price on an underlying asset and the same strike price, the put and the call must have a static sustainable relationship. If this relationship is violated then it gives an arbitrage opportunity. Let us understand this concept by comparing a long call option with a protective put option..

ParticularsPay OffParticularsPay offStrategyLong on CallStrategyProtective put strategyCMP of RelianceRs.950CMP of RelianceRs.950Buy 950 CallRs.20Buy RIL Futures
Buy RIL 950 putRs.950

Let us assume that in the above case the parity is when the 950 call is available at 20 and the RIL 950 put is available at Rs.16. You can argue that the cost of buying the call is higher at Rs.20 but you need to remember that in the protective put we are combining a long future and a long put option. The difference of Rs.4 is accounted for by the cost of margin that you need to put for the long futures position. At this level of put call parity there is no arbitrage opportunity. But arbitrage could arise in 2 situations..

The markets may expect that the upside of the stock is limited. That will make the price of the 950 call come down from Rs.20 to Rs.14. This creates an arbitrage opportunity. You can buy the relatively underpriced call option and sell the combination of futures and put option. This is almost riskless arbitrage for you.

Alternatively, the imputed cost of futures may drop from Rs.4 to Rs.2 due to sharply lower cost of funds. This could result in an arbitrage where the combination of futures and put can be bought and the call option can be sold.

2.  Strike arbitrage in options
Strike arbitrage in options is available between two options on the same underlying but of different strikes. Normally, these price discrepancies do not last for too long as arbitrageurs come in and wipe away these differences. But this is how the strike arbitrage in options will typically work..

ParticularsOptionParticularsOptionSBI CMPRs.255SBI CMPRs.255SBI 255 CallRs.5SBI 250 call13Intrinsic Value0Intrinsic Value5Time Value5Time Value8Nature of OptionATMNature of OptionITMOption pricingRelatively UnderpricedOption PricingRelatively Overpriced Arbitrage by buying 1 lot of 255 SBI call and selling 1 lot of 250 SBI call Buy 1 lot 255 SBI Call-5Sell 1 lot 250 SBI Call+13If, SBI expires at 270+10 (Leg Profit)If SBI expires at Rs.270-7 (Leg Loss)The net profit on the above arbitrage will be Rs.3 if SBI expires at Rs.270/-If SBI expires at 220-5 (loss on option)If SBI expires at 220+13 (Let profit)The net profit on the above arbitrage will be Rs.8 if SBI expires at Rs.220/-

The above asymmetric options arbitrage is set up in such a way that irrespective of the price at which the underlying stock finally expires, the profit on the arbitrage will range between Rs.3 and Rs.8. That is profit range that you will lock in.

There are many more options arbitrage strategies
Actually, there are many more complex options strategies that you can use to create options arbitrage. There are strategies like Boxes, Conversions and Dividend arbitrage but the above mentioned strike arbitrage and Put Call Parity arbitrage are the most common.

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