Put-Call Arbitrage in Practice

Discussion in 'Order Execution' started by RPEX, Apr 24, 2009.

  1. RPEX


    A newbie question on the practical aspects of how one actually carries out options arbitrage from a flat book position, and without venturing into wilder strategies to make it possible.

    I'd be really grateful for any answers/referrals, i've been thinking about it for a while:

    Suppose a market maker is using Put-Call parity to price an option. Suppose he can sell a call for more than he can buy the long future + the put (so the deltas will cancel out) = free money. But what are the actual mechanics of this? Like if someone buys that call, our MM immediately goes to cover by buying the future and the put BUT THEN WHAT?...does he have to hold onto that inventory of {1 short call, 1 put, 1 future} until the options expire? If so, that sounds like a hell of a lot of capital for a long time for miniscule profits (taking the real interest rate into account potentially negative profits).

    This is the specific case i'm interested in, rather than simple cash/spot product market making where one just looks to balance ones book as opposed to hedge everything. I'm thinking mainly of the algorithms of the big banks and the Euronext.Liffe market makers, which work on such a large scale they couldn't possibly accumulate a correspondingly massive inventory. I'm basically interested in the mechanics of a put-call parity style arbitrage.

  2. Read Cottle's book, it goes into this quite a bit... The price that is being implied from the market legs (i.e. banker wants to sell the call, so he has a floating offer for the call that is derived from the put & underlying price) includes the interest rate factor. Unplanned circumstances can occur with the interest rates too, turning what seemed like a "risk free" trade into a very risky trade.

    In the book, it details that when people have a ton of these and they want to get them off their books, they sometimes just offer the conversion/or reversal in the pit at fair value, and if someone wants to trade with you, you can get flat, otherwise, you're stuck.
  3. cvds16


    you have lots of positions in your books, ones often ofsetting others. In practice you will never be able to do a conversion or reversal in itself just part of the legs that later become the conversion or reversal if the other part of the leg becomes mispriced. In the meantime you delta-hedge and try to keep hedged while the greeks are moving. An option book is a dynamic thing that changes by the minute, probably why they call it dynamic delta neutral hedging. You never thought market making was as easy as doing reversals en conversions did you ?
  4. Sintra


    Hi rpex,

    I want to add something. A reversal and a conversion is not free money! There is still a interest risk(which one can try to hedge) and a dividend risk(which one can't hedge). I have witnessed the last myself when a company increased dividend by 50%. This sucks when you are mainly in a reversal. Think of all the companies that cuts dividend last year......

    Second put-call parity is not true for american style options. Still your idea is the same.
    The only time I did set up a conversion or a reversal with profit where the ones that appeared in a market maker combination screen(all mm have electronic eyes on this to autotrade) which not every one can see or in a prof market.
    If you can trade a "synthetic" then the profit will be very very small because there is a low risk or you will have a big profit per synthetic but you are only trading like 1 -10 so the total profit will be small too. It could be that another MM must get rid of his/her short stock position, but still the trade will be even or half a cent better then theoretical.
    It is more like cvds16 says, it is proces that takes time.

    It does take a lot of capital. But when you position is very good hedge-ed then you can have more options in you inventory(low haircut low premium where key figures in my experience, it is different with every clearing)

  5. Can you expand on the "combination screen" please?


  6. Sintra


    If I am not mistaken retail broker accounts and even some prof accounts can't see this. When someone want to trade a straddle he sees the combination bid and offers of the seperate legs. For example both legs are 1-1.05 then he/she sees the straddle quote as 2-2.1. When you want to buy it at 2.05 then a mm can see that directly(in the combination screen a new line appears, with your quote and without the combination of market quotes so very clear that somebody wants to trade a straddle). A mm can create the straddle without quoting it, so letting others mm know that he wants a price(they probably ignore it), normal broker accounts won't show this. I am not 100 % sure but even when he quotes to sell the straddle at 2.05 then a broker account still show you the market quotes 2-2,1 because they don't have this info. All this information could make a trade easier.

    The electronic eye part is based on greeks. A mm quotes the legs at 1-1,05 with a theoretical value of 1,01. Now you bid for the straddle 2,05. His theoretical value is 2,02. But because he wants to sell vega and it has a no delta value he could be happy with only 2,04 instead of 2,1. A smaller profit per leg but trading both at the same time could be good for him. So if you quote 2,05 then the electronic eye automatically trades it.

    A mm has a advantage as well in the opening. trading options in it (limit order) could be instantly 0,15 worse then theo. He knows this at front but you don't. in other words the bid and offer 1 second before the open doesn't have to be the real bid-offer.

    I hope it is a bit clear. Some things are easy for me to write down but hard for anyone else to understand.

  7. RPEX


    Cheers for everyone's help, that's thrown a lot more light on the matter. Does anyone know if Cottle's book is still available? I can only see an out of print one from 1996 on amazon (priced over £100 second hand!), and i can't seem to find 'hidden reality' anywhere.
  8. You betcha...


    riskdoctor.com is his official site... Honestly, the design of the site looks like any other snake oil site, but the stuff in the book is gold.