# [Lightning-dev] An Argument For Single-Asset Lightning Network

```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

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.```
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