Smart Derivatives: On-Chain Forwards for Digital Assets

Abstract

In this paper, we present a framework for the development of on-chain forwards (and futures). This utilises smart contracts to automate the custody of collateral and settlement of payouts on expiry. Importantly, our framework also enables forwards to be traded without counterparty risk or reliance on off-chain assets (such as fiat currencies). To achieve this, we build on our previous work on on-chain options and demonstrate how the relevant mathematical guarantees can be extended to forwards. In addition, we discuss recent trends in cryptoasset derivatives, capital requirements, and other design considerations (such as the use of split contracts). This paper will be of interest to academics and practitioners interested in financial smart contracts.

Appendices

A Appendix: Call Option

The diagram below shows the flow of payments for a physically settled, fully collaterised call option for 10 ETH (notional) with a strike price of $250, and a premium of 1.6 ETH (equivalent to $280 at the initial spot price).

Inflows/outflows at t = 0:

$$\begin{aligned} Long \textit{ call} = - premium \end{aligned}$$

(c1)

$$\begin{aligned} Short \textit{ call} = premium - notional \end{aligned}$$

(c2)

Inflows/outflows at t = expiry, if call option is ITM (finalPrice > strike):

$$\begin{aligned} Long \textit{ call} = notional - (notional * \frac{strike}{finalPrice}) \end{aligned}$$

(c3.1)

$$\begin{aligned} Short \textit{ call} = notional * \frac{strike}{finalPrice} \end{aligned}$$

(c4.1)

Inflows/outflows at t = expiry, if call option is ATM/OTM (finalPrice $\le$ strike):

$$\begin{aligned} Long \textit{ call} = 0 \end{aligned}$$

(c3.2)

$$\begin{aligned} Short \textit{ call} = notional \end{aligned}$$

(c4.2)

B Appendix: Put Option

The diagram below shows the flow of payments for a physically settled, fully collaterised put option for 10 ETH (notional) with a strike price of $70, and a premium of 0.2 ETH (equivalent to $35 at the initial spot price).

Inflows/outflows at t = 0:

$$\begin{aligned} Long \textit{ put} = - premium - notional \end{aligned}$$

(p1)

$$\begin{aligned} Short \textit{ put} = premium - notional * \frac{strike}{spot} \end{aligned}$$

(p2)

Inflows/outflows at t = expiry, if put option is ITM (finalPrice < strike):

$$\begin{aligned} Long \textit{ put} = 0 \end{aligned}$$

(p3.1)

$$\begin{aligned} Short \textit{ put} = notional \end{aligned}$$

(p4.1)

Inflows/outflows at t = expiry, if put option is ATM/OTM (finalPrice $\ge$ strike):

$$\begin{aligned} Long \textit{ put} = notional - (notional * \frac{strike}{finalPrice}) \end{aligned}$$

(p3.2)

$$\begin{aligned} Short \textit{ put} = notional * \frac{strike}{finalPrice} \end{aligned}$$

(p4.2)