Good morning Lawrence, On re-reading your argument, no, you have misunderstood massively.

The two HTLCs together form a *single* American Call Option, issued by the exchange to the initiator of the "payment". It is not the initiator somehow issuing an American Call Option to itself by routing a payment to itself. It is the initiator forcing the exchange to give it the equivalent of an American Call Option by routing a payment to itself. In particular, the cost of locking the WJT asset is paid *by the exchange*, not the initiator of the contract. > If x_p = 0 then the issuer is guaranteed a loss. Therefore no rational > contract issuer will issue an American call option for free. This implies that the nobody will act as an exchange (since it could be coerced into issuing an American Call Option for free), hence the argument that Lightning Network will always have a single asset. Note that this is one trivial way for your conclusion: >lightning nodes do not offer premium-free American call options to be true, i.e. there will be no cross-asset nodes. Regards, ZmnSCPxj Sent with ProtonMail Secure Email. ‐‐‐‐‐‐‐ Original Message ‐‐‐‐‐‐‐ On Thursday, January 3, 2019 8:07 PM, Lawrence Deacon <lawre...@commerceblock.com> wrote: > 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. _______________________________________________ Lightning-dev mailing list Lightning-dev@lists.linuxfoundation.org https://lists.linuxfoundation.org/mailman/listinfo/lightning-dev