What is the difference between Local Balance and Remote Balance in a Lightning channel?

A Lightning payment channel represents a 2-of-2 multisig UTXO on the Bitcoin base chain. Local Balance represents the satoshis owned by the node operator, which dictates outbound payment capacity. Remote Balance represents satoshis owned by the channel counterparty, which dictates inbound payment reception capacity. Sending payments shifts liquidity from local to remote; receiving payments shifts liquidity from remote to local.

How are multihop routing fees calculated on the Lightning Network?

Routing node operators set two fee parameters: a fixed Base Fee (typically 1 satoshi per forward) and a proportional rate measured in Parts Per Million (PPM, where 1,000 PPM = 0.10%). Total Routing Fee = Base Fee + (PPM / 1,000,000) * Forwarded Amount.

Model #41 • Desk 7: Digital Assets & Crypto Derivatives

Bitcoin Lightning Network Payment Channel & Routing Liquidity Simulator

A deterministic Layer-2 payment channel simulator and multihop graph routing engine. Model 2-of-2 multisig funding balances, directional local vs. remote liquidity exhaustion, multihop Hash Time-Locked Contract (HTLC) fee accrual, Submarine Swap rebalancing economics (Loop In / Loop Out), and unilateral force-close CSV penalty timelocks.

Channel Presets:

Payment Channel Liquidity Distribution (2-of-2 Multisig UTXO) 5,000,000 Sats Total

Local 50%

Remote 50%

• Local Outbound Balance: 2,500,000 Sats ($1,625) • Remote Inbound Balance: 2,500,000 Sats ($1,625)

Channel Parameters LIGHTNING L2

Spot Bitcoin Benchmark ($) $65,000

Current institutional spot benchmark price.

Channel Total Capacity (Sats) 5,000,000 Sats

Total locked 2-of-2 multisig funding transaction size.

Local Balance Allocation (%) 50.0%

Outbound sending liquidity vs inbound receiving liquidity.

HTLC Routing & Forwarding Fees

Fixed Base Routing Fee (Sats) 1 Sat

Fixed fee charged per successfully routed HTLC payment hop.

Proportional Fee Rate (PPM) 350 PPM (0.035%)

Parts Per Million charged on forwarded payment volume (1k PPM = 0.1%).

Daily Forwarded Routing Volume 45 Payments / Day

Number of HTLC payments routed through this channel daily.

Average Payment Size (Sats) 250,000 Sats

Median satoshi size per forwarded Lightning payment invoice.

L1 On-Chain Settlement Friction

Bitcoin L1 Mempool Fee Rate (Sat/vB) 35 Sat/vB

Base chain mining fee required for channel open/close & swaps.

Channel Performance & Routing P&L HUD ROUTING YIELD

Annualized Routing Fee Yield 5.81% APY +290,449 Sats / Year

Daily Routing Income +$0.52 / day +796 Sats / Day

Submarine Loop Rebalance Cost $12.42 19,105 Sats (0.4% Fee + L1)

Force-Close L1 Penalty Cost $7.05 10,850 Sats (310 vB @ 35 Sat/vB)

HTLC Forwarding Economics & Channel Balance Analysis

Channel Metric	Satoshi Amount	USD Equivalent	Channel Share
Local Outbound Sending Capacity	2,500,000 Sats	$1,625.00	50.0%
Remote Inbound Receiving Capacity	2,500,000 Sats	$1,625.00	50.0%
Single Forward Routing Fee Earned	88.5 Sats	$0.0575	1 Sat Base + 350 PPM
Gross Daily Routing Volume Forwarded	11,250,000 Sats	$7,312.50	2.25x Channel Turnover
Annual Gross Forwarding Fees Earned	290,449 Sats	+$188.79	5.81% APR
Submarine Loop Rebalance (500k Sats)	-19,105 Sats	-$12.42	Loop Out to Cold UTXO
Unilateral Force-Close Breakeven Run	10,850 Sats	$7.05	144 Blocks CSV Timelock

Routing Sensitivity: PPM Rate vs. Daily Forwarding Volume

Quantitative Formulation: Lightning Network Graph Routing & Channel Physics

The Bitcoin Lightning Network functions as a directed graph of bidirectional payment channels anchored to Bitcoin Layer-1 via 2-of-2 multisignature UTXOs. Channel capacity is strictly conserved: payments do not create new satoshis, but shift ownership between local and remote commitment balances.

$$\text{Routing Fee} = \text{Base Fee} + \left(\frac{\text{PPM}}{1,000,000} \times \text{Forwarded Amount}\right)$$

Where $\text{PPM}$ represents Parts Per Million (e.g. $500\text{ PPM} = 0.05\%$). Routing nodes maximize yield by operating at high velocity and setting fees dynamically to balance inbound and outbound channels.

$$\text{Submarine Swap Cost} = (S_{\text{swap}} \cdot f_{\text{provider}}) + (\text{TxSize}_{\text{vB}} \cdot \text{FeeRate}_{\text{sat/vB}})$$

When a channel becomes outbound-depleted ($\text{Local} \approx 0$), the node can no longer route payments. Node operators execute Submarine Swaps (Loop Out) to atomically exchange off-chain channel liquidity for on-chain UTXO cold storage, incurring base-chain sat/vB fees.

$$\text{Breach Penalty: } \Delta t = 144 \text{ Blocks} \quad \Longleftrightarrow \quad \text{Revocation Key Punishes Fraud}$$

If a peer attempts to broadcast an outdated commitment state, the node operator uses the revocation secret within the CheckSequenceVerify (CSV) timelock window to seize 100% of the channel's funds as a punitive fraud remedy.