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Option Greeks

Conversion-Reversal Arbitrage

After learning Options Arbitrage, here we will understand the ‘Conversion Reversal Arbitrage.’


Conversion and reversal arbitrage is a strategy which takes advantage of differences in the value of synthetic positions and their equal in order to return a risk free profit. 


Conversion arbitrage is an options trading strategy to exploit inefficiencies that exist in option pricing. Conversion arbitrage is a risk-neutral strategy, where a trader buys a put and writes a covered call (on a stock that the trader already owns) with the same strike prices and expiration dates.


A trader will profit from a conversion strategy when the call option is overpriced or the put option is underpriced. This can be due to market inefficiencies, or from the effects of mispriced interest rate assumptions.


Conversion arbitrage is a strategy which can be carried out for riskless profit when options are either overpriced or underpriced.


Let me just mention how a synthetic position is created. There are six basic synthetic positions relating to combinations of put options, call options and their underlying stock:


  • Synthetic Long Stock = Long Call + Short Put
  • Synthetic Short Stock = Short Call + Long Put
  • Synthetic Long Call = Long Stock + Long Put
  • Synthetic Short Call = Short Stock + Short Put
  • Synthetic Short Put = Short Call + Long Stock
  • Synthetic Long Put =Long Call + Short Stock

In order for the synthetic trades to work, all options used together must be of the same expiration, strike and underlying.


Synthetic position allows an open option position to be synthetically squared off without selling the position itself. For example, a synthetic long stock can be squared off by shorting an equivalent amount of the actual stock. Synthetically closed positions are not subject to directional risk and hedges against short term price movement.


In simple words, a Conversion is when stock is being bought in order to synthetically close out a short stock position that is created synthetically by long put and short call of the same strike. Reversal is when stock is being shorted/ sold in order to synthetically close out a synthetic long stock position. However, conversion and reversal do not necessarily apply only to synthetic long and short stocks.


In fact, whenever a synthetically closed position involves a long stock, it is known as a Conversion and whenever it involves a short stock, it is known as a Reversal. For example, a synthetic call option (a long put and a long stock) can be synthetically squared off by shorting a call option. This is known as a conversion, as the entire position involves a long stock. A synthetic put option (a long call and short stock) can be synthetically squared off by shorting a put option. This is known as a reversal as it involves a short stock.



There are important risk factors to keep in mind for arbitrage conversions, like a hike in interest rates and the elimination of dividends.  

When a position is synthetically closed, it is exposed only to theta risk, which is time decay. When put-call parity is in force perfectly, the extrinsic value of the synthetic position should be just the same as the extrinsic value of the actual instrument.


For example, a synthetic long stock should have no extrinsic value at all as the premium of the put option cancels out the premium of the call option involved. A synthetic long call should have the same extrinsic value as the actual call option itself. However, there are conditions when 'Put Call Parity' is severely violated that a significant difference in extrinsic value exists between a synthetic position and its actual instrument. When such a position is synthetically closed out, it results in profit from that difference in extrinsic value on expiry. This is known as Conversion/Reversal Arbitrage.


Traders use conversions when options are relatively overpriced and use reversals when options are relatively underpriced. Conversion and Reversal can also be carried out between options and futures instead of the underlying stock. A well executed Conversion and Reversal Arbitrage has no chance of  loss, irrespective of how the underlying moves.

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