I’m trying to price something by building a chain of options that replicates the payoffs when exercised, and then summing the price of the options.
Basically, the payoffs involve 7 vanilla puts and calls, plus a bunch of cash. A colleage and I have different option combinations and come to different prices, and we’re trying to figure out why.
The law of one price says that investments with the same payoffs should have the same price. However, I know that certain option chains result in a net positive cash balance, whereas others result in a net negative cash balance, yet they have similar payoff streams. (e.g. put spreads and call spreads can be manufactured similarly, but I seem to recal some create a credit balance and others create a debit balance).
How does this square with the law of one price? I suspect that maybe there’s a self-funding assumption here, where borrowed amount + credit = different borrowed amount - debit, but I’m not sure how it works.
My colleague says that my figure adds up to his figure if he discounts my cash allocation by the RFR, but then we don’t get a true replication if the options are exercised early, which is very likely to happen (because these have a long time to expiry).
Anyway, some thoughts here would be useful. I used to know this stuff better, but I’m not a big options person and it’s been a while since I took L2 and L3.
I’m confused…are you saying you each have portfolios with the same terminal payoff but different market prices? Are you taking into account any marked pl? What do each of the positions reduce to? You’re right there is no arb any differences are funding, borrow, divs, bid/ask etc.
The payoff at expiration is the same in the equivalent long put spread v short call spread for example. Although one will initially be a debit and the other a credit.
ex) If you were bearish, buying the 55 strike put and selling the 50 put will be a net debit (55 puts are more expensive than the 50 puts), and the maximum payout will be the same as the max payout of selling a 50 strike call and buying a 55 call (50 calls are more expensive than the 55’s), so that would initially be a credit when you first put it on.
If you sold the 55/50 call spread for a net credit of $4, then you’d be indifferent to buying the 55/50 put spread for a net debit of $1, because if it closes below 50 at expiry, you keep the $4 credit on the call spread, or you make $4 on the put spread. Sometimes if you use the ‘midquote’ liquidity differences between calls and spreads will make the payout slightly different, but if you could actually get executed at those prices than you could arb, but chances of that are slim.
I can’t go into the details of the contract on a public forum, but I can tell you more in private message, LPoulin133, and maybe you can give me your take on it. This is more of a back-burner thing for me right now, but eventually it is going to be important.
Thanks for the confirmation on the credit/debit thing. I figured it must be something like that, but couldn’t remember how it works.