Lawrence Deacon [ARCHIVE] on Nostr: 📅 Original date posted:2019-01-03 📝 Original message: Do cross-asset lightning ...
📅 Original date posted:2019-01-03
📝 Original message:
Do cross-asset lightning nodes do not offer premium-free American call options?
=============================================================
I would argue that cross-asset lightning nodes do not offer premium-free American call options for the following reasons.
Say I wanted to set up to purchase 1 WJT for P bitcoins at time t < T where t is the time I close the contract and T is the expiry time.
In order to set up the contract I must pay P bitcoins to the contract, incurring an opportunity cost of x_i1. Assuming we set up the contract at time t_0=0, this will be equivalent to the money I could have earned by loaning the currency at interest during the period t.
I must also pay the issuer of the contract a premium x_p (in the case where I am both recipient and issuer, see further down).
If S(t) is the spot price at time t and K = S(t) - P then the payoff for me is as follows:
S(t) > P: K - x_p - x_i1
S(t) < P: -x_i1 - x_p
If x_i2 is the opportunity cost of paying 1 WJT to the contract for time t then the payoff for the other party (issuer) is as follows:
S(t) > P: -K + x_p - x_i2
S(t) < P: x_p - x_i2
If x_p = 0 then the issuer is guaranteed a loss. Therefore no rational contract issuer will issue an American call option for free.
In the case where I am both recipient and issuer of the contract, to get the payoff we add the above payoffs:
S(t) > P: -x_i1 - x_i2
S(t) < P: -x_i1 - x_i2
This is a guaranteed loss.
Conclusion
========
Lightning nodes do not offer premium-free American call options because whether or not the contract and issuer are the same person, setting up a premium free American call option using a HTLC guarantees a loss for one or both parties. Even if the opportunity costs were 0, then setting up a contract with myself would have a guaranteed 0 payoff.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.linuxfoundation.org/pipermail/lightning-dev/attachments/20190103/cc6cad95/attachment.html>;
📝 Original message:
Do cross-asset lightning nodes do not offer premium-free American call options?
=============================================================
I would argue that cross-asset lightning nodes do not offer premium-free American call options for the following reasons.
Say I wanted to set up to purchase 1 WJT for P bitcoins at time t < T where t is the time I close the contract and T is the expiry time.
In order to set up the contract I must pay P bitcoins to the contract, incurring an opportunity cost of x_i1. Assuming we set up the contract at time t_0=0, this will be equivalent to the money I could have earned by loaning the currency at interest during the period t.
I must also pay the issuer of the contract a premium x_p (in the case where I am both recipient and issuer, see further down).
If S(t) is the spot price at time t and K = S(t) - P then the payoff for me is as follows:
S(t) > P: K - x_p - x_i1
S(t) < P: -x_i1 - x_p
If x_i2 is the opportunity cost of paying 1 WJT to the contract for time t then the payoff for the other party (issuer) is as follows:
S(t) > P: -K + x_p - x_i2
S(t) < P: x_p - x_i2
If x_p = 0 then the issuer is guaranteed a loss. Therefore no rational contract issuer will issue an American call option for free.
In the case where I am both recipient and issuer of the contract, to get the payoff we add the above payoffs:
S(t) > P: -x_i1 - x_i2
S(t) < P: -x_i1 - x_i2
This is a guaranteed loss.
Conclusion
========
Lightning nodes do not offer premium-free American call options because whether or not the contract and issuer are the same person, setting up a premium free American call option using a HTLC guarantees a loss for one or both parties. Even if the opportunity costs were 0, then setting up a contract with myself would have a guaranteed 0 payoff.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.linuxfoundation.org/pipermail/lightning-dev/attachments/20190103/cc6cad95/attachment.html>;