đ
Original date posted:2019-01-03
đ Original message:
> On 3 Jan 2019, at 13:24, ZmnSCPxj <ZmnSCPxj at 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.
>
> âââââââ Original Message âââââââ
> On Thursday, January 3, 2019 8:07 PM, Lawrence Deacon <lawrence at 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.
>
>
Lawrence Deacon [ARCHIVE] /
npub1vyâŚyzn0r
2023-06-09 12:53:44
in reply to nevent1qâŚxzjp
Author Public Key
npub1vyexeqgyhtssdgevhfedc0wf00s6wymrge0x7gn2w6nfyzgckrtqzyzn0rPublished at
2023-06-09 12:53:44Event JSON
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Original date posted:2019-01-03\nđ Original message:\n\u003e On 3 Jan 2019, at 13:24, ZmnSCPxj \u003cZmnSCPxj at protonmail.com\u003e wrote:\n\u003e \n\u003e Good morning Lawrence,\n\u003e \n\u003e On re-reading your argument, no, you have misunderstood massively.\n\u003e \n\u003e The two HTLCs together form a *single* American Call Option, issued by the exchange to the initiator of the \"payment\".\n\u003e \n\u003e It is not the initiator somehow issuing an American Call Option to itself by routing a payment to itself.\n\u003e It is the initiator forcing the exchange to give it the equivalent of an American Call Option by routing a payment to itself.\n\u003e In particular, the cost of locking the WJT asset is paid *by the exchange*, not the initiator of the contract.\n\u003e \n\nThe 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.\n\n\u003e\u003e If x_p = 0 then the issuer is guaranteed a loss. Therefore no rational contract issuer will issue an American call option for free.\n\u003e \n\u003e 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.\n\u003e Note that this is one trivial way for your conclusion:\n\u003e \n\u003e\u003e lightning nodes do not offer premium-free American call options\n\u003e \n\u003e to be true, i.e. there will be no cross-asset nodes.\n\u003e Regards,\n\u003e ZmnSCPxj\n\u003e \n\u003e \n\u003e Sent with ProtonMail Secure Email.\n\u003e \n\u003e âââââââ Original Message âââââââ\n\u003e On Thursday, January 3, 2019 8:07 PM, Lawrence Deacon \u003clawrence at commerceblock.com\u003e wrote:\n\u003e \n\u003e\u003e Do cross-asset lightning nodes do not offer premium-free American call options?\n\u003e\u003e \n\u003e\u003e =============================================================\n\u003e\u003e \n\u003e\u003e I would argue that cross-asset lightning nodes do not offer premium-free American call options for the following reasons.\n\u003e\u003e \n\u003e\u003e Say 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\u003e\u003e \n\u003e\u003e 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. \n\u003e\u003e \n\u003e\u003e 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).\n\u003e\u003e \n\u003e\u003e If S(t) is the spot price at time t and K = S(t) - P then the payoff for me is as follows:\n\u003e\u003e \n\u003e\u003e S(t) \u003e P: K - x_p - x_i1 \n\u003e\u003e S(t) \u003c P: -x_i1 - x_p\n\u003e\u003e \n\u003e\u003e 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:\n\u003e\u003e \n\u003e\u003e S(t) \u003e P: -K + x_p - x_i2\n\u003e\u003e S(t) \u003c P: x_p - x_i2\n\u003e\u003e \n\u003e\u003e If x_p = 0 then the issuer is guaranteed a loss. Therefore no rational contract issuer will issue an American call option for free.\n\u003e\u003e \n\u003e\u003e In the case where I am both recipient and issuer of the contract, to get the payoff we add the above payoffs:\n\u003e\u003e \n\u003e\u003e S(t) \u003e P: -x_i1 - x_i2\n\u003e\u003e S(t) \u003c P: -x_i1 - x_i2\n\u003e\u003e \n\u003e\u003e This is a guaranteed loss.\n\u003e\u003e \n\u003e\u003e Conclusion\n\u003e\u003e ========\n\u003e\u003e 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.\n\u003e \n\u003e",
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