Option Arbitrage

by: Jesse Chen

Of all the options analysis strategies, Arbitrage trades seem to

be one of the most intriguing and elusive strategies.  Arbitrage is officially defined

as the buying and selling of a financial instrument in order to profit from the price

differential.  This traditionally occurs between two different exchanges, possibly between

a domestic and foreign exchange where one exchange has not adjusted for the

constantly changing currency rates.  Arbitrage was made famous in the movie "Rogue

Trader" in which Nick Leason was supposedly making his millions arbitraging the

Nikkei index between the Singapore and UK exchanges. 


Option Arbitrage involves the simultaneous buying and selling of options either between

exchanges or the same exchange.  We will cover six different types of options strategies

in this article: strike, calendar, intra-market, and conversions, boxes, and straddles.

Please take into account when trading arbs that there can be early assignment of any in the money options

for all American Style Exercise Options (exercise before expiration).

Also, possible dividend liability exists on any exercised short puts during dividend dates.


Calendar Option Arbitrage

A calendar arbitrage involves the buying and selling of options with the same underlying options, strike, and type (call or put), but different

months where the nearer month is sold for more than the further month is bought.

Calendar arbitrages, may require longer periods in order to realize the small profit.


Strike Option Arbitrage

A strike arbitrage involves buying and selling the same underlying options,  month, and type (call or put) but different strikes

where the strike difference is less than the premium difference.  When this occurs, a risk less trade can be formed.

Intra-market Arbitrage

A intra-market arbitrage invoices buying and selling the same underlying options, month, strike, and type (call or put) but

different exchanges (cboe, philadelphia, pacific, or american).


A conversion consists of buying a put, selling a call, and buying the underlying.

The put and call are the same underlying option, strike, and month.

There is also a short conversion which is the opposite of this:  Sell Put + Buy Call + Sell Underlying = Short Conversion

Box Conversion

A box conversion is Buy Call (strike1) + Sell put (strike1) + Buy Put (strike2) + Sell Call (strike2)
Essentially a box is two conversions without the underlying.

You can also have conversions and boxes with different strike prices which may produce arbitrages:

There a 6th arb known as the a Straddle Arb with a net negative time value on the call and put options.

These six options arbitrages can be summarized in the following table:

Option Arbitrage Matrix

  Calendar Strike Intra Mkt Conversion Box Straddle
Underlying same same same same same same
Month different same same same same same
Strike same different same same different same
Option type (call/put) same same same different different different
Exchange same same different same same same

Here are some arbitrage examples generated by Optionstar - Options Analysis Software.


ARB SCAN:  OEX on 9/1/06  2:10pm cst

STRIKE ARB:     OEX on 9/1/06 2:10pm @ 602.03.. . 
Buy Call + Sell Call (further in the money)
(buy 585c@21) + (sell 580c@26.15)        

STRIKE ARB2:     SPX on 9/05/06 10:15am @ 1309.52.. 
Sell Call (strike1) + Buy Call (strike2) 
(sell 1360c@.40) + (buy 1355c@.2) 

CONVERSION SPREAD1:     OEX on 9/1/06 3:15pm @ 602.03..  
Sell Call (strike1) + Buy Put (strike1) + Buy Underlying
(sell 555c@48.1) + (buy 555p@.1) + (buy oex@602.03)

CONVERSION SPREAD2:     OEX on 9/1/06 3:15pm @ 602.03.. 
Sell Put (strike1) + Buy Call (strike2) + Sell Underlying
(sell 620p@18.55) + (buy 615p@.6) + (sell oex@602.03)

BOX SPREAD1:     OEX on 9/1/06 3:15pm @ 602.03.. 
Sell Call (strike1) + Buy Put (strike1) + Buy Call (strike2) + Sell Put(strike2)
(sell 555c@48.1) + (buy 555p@.1) + (sell 620p@18.55) + (buy 620c@.2)

BOX SPREAD2:     OEX on 9/1/06 3:15pm @ 602.03.. 
Sell Call (strike1) + Buy Put (strike1) + Buy Call (strike2) + Sell Put(strike3)
(sell 555c@48.1) + (buy 555p@.1) + (buy 615c@.6) + (sell 620p@18.55)

BOX SPREAD3:     OEX on 9/1/06 3:15pm @ 602.03.. 
Sell Call (strike1) + Buy Put (strike2) + Buy Call (strike3) + Sell Put(strike4)
(sell 545c@57.8) + (buy 555p@.1) + (buy 615c@.6) + (sell 620p@18.55)


Strike Arbitrage

A scan done on 3/28/02 shows a Strike arbitrage between QQQ Jan-03
14 and 16 calls for a 2.00 arb credit.


Synthetic Spread Arbitrage

On 7/26/02, we did a scan for msft and came up with the following synthetic spread arbitrages.  A synthetic spread Arb is simply a (buy call + sell put + buy underlying) which is greater than zero.  The call and put have to be the same strike price and month.  As you can see, the selected spread generates a net credit of 1.05

It consists of selling a Jan-04 60call for 5.7bid + buying a Jan-03 70put for 19.3ask + buying MSFT for 45.35
At expiration, you stand to make $105 at any price.

Copyright 2006 Star Research, Inc.

No reprinting or retransmission permitted without express permission from Star Research, Inc.