rich1.0Lawrence Deacon [ARCHIVE] (npub1vy…yzn0r)https://yabu.me/npub1vyexeqgyhtssdgevhfedc0wf00s6wymrge0x7gn2w6nfyzgckrtqzyzn0rnjumphttps://yabu.me📅 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>