> On 3 Jan 2019, at 13:24, ZmnSCPxj <zmnsc...@protonmail.com> wrote: > > 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. >
The initiator of the contract must deposit 1 WJT into the exchange before the exchange will create the contract. Therefore the opportunity costs are borne by the initiator. >> 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
