Free lesson · Crypto derivatives

Perpetual funding as actual cash flows

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Start with the idea

Funding is a sequence of payments. The sign, assessment times and notional used for each payment matter more than a headline annual rate.

Symbols, units & horizon

C_fund: USD funding cash flow, positive received
k: funding event
K: event count
s_k: +1 long or −1 short
N_k: positive assessed USD notional
f_k: funding fraction per event
positive f means long pays in this convention

When and why to use this

Build a spot/perpetual carry ledger using actual eligible positions and funding events.

Funding is a sequence of payments. The sign, assessment times and notional used for each payment matter more than a headline annual rate.

Adopt an explicit teaching convention: a positive rate means longs pay shorts; position sign is positive for a long. Real venue rules can differ in assessment notional, caps and timing, so verify them before implementation.

Sum realized payments at each funding timestamp using the position that was eligible then. Future rates remain uncertain, and closing early can avoid or forfeit a scheduled payment depending on the rules.

C_{fund} = - \sum_{k = 1}^{K} s_{k} N_{k} f_{k}

Model assumptions, derivation and arithmetic

Perpetual funding as actual cash flows

At each assessment time identify side, eligible notional and rate.
Multiply −side×notional×rate to obtain signed payment.
Sum all event cash flows without multiplying by an arbitrary annualization factor.

Work it by hand

Short $10,000 assessed notional at rates .001, −.0005 and .0008 receives $10, pays $5 and receives $8: total +$13.

Apply it in a strategy

Build a spot/perpetual carry ledger using actual eligible positions and funding events.
Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
Stress this failure condition: Multiplying one observed rate by a year invents future funding and ignores changing notional and sign.

Research deliverable

Build and explain a perpetual funding as actual cash flows worksheet. Build a spot/perpetual carry ledger using actual eligible positions and funding events.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def funding_cash(sides,notionals,rates):
    if not(len(sides)==len(notionals)==len(rates)) or any(s not in (-1,1) for s in sides) or any(n<0 for n in notionals):
        raise ValueError("Aligned funding events required")
    return sum(-s*n*f for s,n,f in zip(sides,notionals,rates))

print(funding_cash([-1,-1,-1],[10000,10000,10000],[.001,-.0005,.0008]))

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Crypto Derivatives: Carry, Funding and Liquidation — all lessons

Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations