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Options Arbitrage

by Irving Rivera on April 15, 2014 · 0 comments

Options Arbitrage

What is Options Arbitrage?

This post is going to be the first in a series of articles where we are going to discuss the multiple types, strategies and advantages of options arbitrage.  For the most part I am going to assume that you already have a serious understating of how options work and that I don’t have to cover the basics of this financial instrument with you.  If you are really interested in options arbitrage you must understand the simple key differences between a call and a put options, if not please review this website first.  However, let me define in general terms what options are and how we are going to use them regarding our arbitrage strategy.

Options are a derivative financial product from equities which represent a contract to the rights, but not the obligation, to sell or buy a bulk of 100 shares of a given stock.

The key aspects that makes this instrument unique are:

  •  Having an expiration date; which will let us arbitrage across time. (Contango & Backwardation)
  • Having a strike price; which will let us arbitrage across price inefficiencies.
  •  Having define market volatility; which will let us arbitrage across the Greek variables and the statistical difference.
  • Having leverage 100:1, which will let us arbitrage with little capital.

Lastly, being versatile; did you know there are more than 110 options strategies and hedges, here is a short list of them:

Bullish StrategiesBearish StrategiesNeutral Strategies
Call BuyingPut BuyingRatio Spread
Bull Call SpreadBear Put SpreadThe Straddle
The CollarPut BackspreadThe Strangle
Call BackspreadCovered PutsThe Butterfly
Bull Calendar SpreadNaked CallsThe Condor
Covered CallsThe Iron Butterfly
Naked PutsThe Iron Condor
Covered StraddleCalendar Straddle

 “but now for the topic at hand of how to arbitrage”

I plan to explain to you over 5 different tactics and techniques of options arbitrage, in our usual way, definition “the what”, the execution “the how to”, the practical example “the case study (including calculators and spreadsheets)” and finally the bottom line “what this mean to you (where is the money)”; but individually in their own single post; but for now let me quickly introduce you to the best practices I know with a quick definition and a brief how to guide:


Put Call Parity: this one is the most complex of all the strategies, because it involve European style options, bonds (t-bills), the company stock (best when they don’t pay dividends) and call and put contracts. Basically, an arbitrageur will try to profit from the price conversion of buying the 100 shares of Xco, by shorting a t-bill “borrowing capital / funds” (or naked margin), and selling a call option and buying a put contract. To determent how this trade going to be profitable follow this equation:

T-bill + Call = Put + Stock

Conversion and Reversal Arbitrage: this technique is very simple and if identified properly can be very lucrative. Here you try to purchase an underlying equity while at the same time buying a put and shorting an upside call, both with the same strike price and expiration date.  The purpose of this trade is to lock-in the gains from the time premium of the options “time decay”.


Arbitrage by the Greeks’ Volatility: thanks to the Black-Scholes pricing model; options contracts have 14 price variables; that runs in the effect of first, second and third order. Here the best way to uncover inefficiencies is to compare the relative prices and intrinsic volatility of the option contract to the general market S&P500 Beta.  Shorting high premiums and buying low ones.


Box Spread Arbitrage: is very similar to the conversion tactic, but here you will sell double the calls with a spread between them; while doing the same thing with the puts.


Dividend Date Arbitrage: here we try to hedge the price loss that happens when a stock goes ex-dividend date, by buying a put of lower cost than the dividend payout. A riskless return when following this equation:

Put Cost < Payout


Intra-Market Exchange Arbitrage: this happens when same option contracts sell for different prices at different exchanges. Let say you can buy a GOOG call in the CBOE for $5.00 and sell it at the NASDAQ for $5.01, booking that one cent profit.


Strike Arbitrage: is done when calls of lower strike price trade for less than one with a higher strike price, inversely the same is true for puts.


Maturity ‘Calendar Spread” Arbitrage:  done when an option of a shorter time expiration is trading for more than one with the same strike price but with a longer expiration date.

Sell the short time – by the longer date


Replicating Portfolio: here we try to create a portfolio with zero capital, using margin. The basic idea is to short an equity and utilized that cash and then lent out the same amount of money, (buying a bond). The key characteristic of this hedge is that both the long bond and the short stock need to have equivalent cash-flow principals; enhance the term replacing portfolio. Well I just explained you the term with equities so a quick example will be:

Shorting shares of a utility company – buying t-bill of the same

But if you do this using the derivatives like options you can leverage a higher income.


Synthetic Stock and Option Arbitrage: is based on the typical table of synthetic conversion and by that you can determent what options are trading at a premium or at a discount relative to the equivalent position. A synthetic call should cost the same as an actual call, if they don’t you are free to arbitrage. Reference the following table for better understating of their relationships:

Synthetic long stockLong call + short put
Synthetic long call optionLong underlying + long put
Synthetic short call optionShort underlying + short put
Synthetic long put optionShort underlying + long call
Synthetic short stockLong put + short call
Synthetic short put optionLong underlying + short call

Bottom Line

Don’t get intimidated by the complexity and all the moving pieces of an option arbitrage position. If done properly they could generated riskless returns; with little capital upfront.

Facebook Thoughts

Which of all the strategies interest you the most? Leave a comment below.

November ReportOn March 2014, book some gains and rebalanced the portfolio.

I share my results with you mainly for three reasons:

  • The Benefit of Full Disclosure
  • Share the Knowledge
  • Track Performance

 “No one should talk about investing; if they are not willing to show their actual holdings and performance.”

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Annual Report Three years has passed since I started my Arbitrage Investment Strategy; and I want to share my results with you…

“No one should talk about investing; if they are not willing to show their actual holdings and performance.”

Let’s start with a recap of my holdings and performance of my Roth IRA. [Read More…]