{"type":"rich","version":"1.0","title":"Lawrence Deacon [ARCHIVE] wrote","author_name":"Lawrence Deacon [ARCHIVE] (npub1vy…yzn0r)","author_url":"https://yabu.me/npub1vyexeqgyhtssdgevhfedc0wf00s6wymrge0x7gn2w6nfyzgckrtqzyzn0r","provider_name":"njump","provider_url":"https://yabu.me","html":"📅 Original date posted:2019-01-03\n📝 Original message:\nDo cross-asset lightning nodes do not offer premium-free American call options?\n=============================================================\nI would argue that cross-asset lightning nodes do not offer premium-free American call options for the following reasons.\n\nSay I wanted to set up to purchase 1 WJT for P bitcoins at time t \u003c T where t is the time I close the contract and T is the expiry time.\n\nIn 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. \n\nI 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).\n\nIf S(t) is the spot price at time t and K = S(t) - P then the payoff for me is as follows:\n\nS(t) \u003e P:        K  - x_p  -  x_i1 \nS(t) \u003c P:        -x_i1 - x_p\n\n\nIf 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:\n\nS(t) \u003e P:        -K + x_p - x_i2\t\nS(t) \u003c P:         x_p  - x_i2\n\nIf x_p = 0 then the issuer is guaranteed a loss. Therefore no rational contract issuer will issue an American call option for free.\n\nIn the case where I am both recipient and issuer of the contract, to get the payoff we add the above payoffs:\n\nS(t) \u003e P:         -x_i1 - x_i2\nS(t) \u003c P:         -x_i1 - x_i2\n\nThis is a guaranteed loss.\n\nConclusion\n========\nLightning 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.\n-------------- next part --------------\nAn HTML attachment was scrubbed...\nURL: \u003chttp://lists.linuxfoundation.org/pipermail/lightning-dev/attachments/20190103/cc6cad95/attachment.html\u003e"}