Two-Way Contracts for Difference (CfDs)

• Two-way CfDs are bilateral contracts that exchange payments based on the difference between a fixed strike price and a reference market price, mitigating revenue risk.
• They employ advanced methodologies like Dynkin games and DRBSDEs to model optimal stopping strategies and accurately value contract terms under stochastic price dynamics.
• Empirical studies indicate that while capacity-based CfDs offer lower revenue volatility, revenue-based designs better preserve market incentives and effective risk-sharing.

A two-way Contract for Difference (CfD) is a bilateral financial derivative designed to stabilize revenues or costs for participants exposed to price volatility, notably in electricity markets. Under a two-way CfD, payments are exchanged between two parties—typically a regulator or government entity and a power producer—based on the difference between a reference price and a fixed strike price, regardless of which direction the market moves. This mechanism insulates both generators and consumers from unfavorable price movements, typically striking a balance between risk mitigation and maintaining market incentives (Johanndeiter et al., 19 Dec 2025).

1. Definition and Basic Structure

A two-way CfD pays the net difference between a predetermined strike price $S$ and a realized reference price $P_{\rm ref}$, scaled by a contract quantity $Q$: $\Pi_{\rm CfD} = (P_{\rm ref} - S)\, Q$ If the reference price falls below the strike, the generator receives a payment; if it rises above, the generator must pay back the difference. This applies symmetrically, insulating both sides against adverse price movements. Common reference prices include the hourly spot price (price-based), annual average market value (revenue-based), or a uniform capacity payment (capacity-based). For energy contracts, $Q$ may be generation volume (MWh) or installed capacity (MW) (Johanndeiter et al., 19 Dec 2025).

In electricity markets, two-way CfDs may also embed cancellation provisions, allowing either party to exit early against a penalty; such features embed the contract into an optimal stopping game structure (Agram et al., 2 Mar 2025).

2. Game-Theoretic and Stochastic Modeling Approaches

The valuation and optimal design of two-way CfDs in energy markets have been rigorously modeled using Dynkin games—a class of zero-sum stochastic optimal stopping games—in combination with doubly-reflected backward stochastic differential equations (DRBSDEs) (Agram et al., 2 Mar 2025).

Electricity Price Dynamics

Suppose electricity spot prices $(P_s)_{s \ge 0}$ follow log-Ornstein-Uhlenbeck dynamics: $$dX_s = \kappa (\mu - X_s) ds + \sigma dB_s,\quad X_0 = x,\quad P_s = e^{X_s}$$ with mean-reversion rate $\kappa > 0$, long-run mean $\mu$, and volatility $\sigma$.

Contract Payoff and Termination

For $[t, T]$, the flow payoff is

$\varphi(s, P_s) = Q (K - P_s) e^{-\rho(s-t)}$

where $K$ is the strike price, $\rho$ is a discount rate.

Either party may trigger early termination—Player 1 (regulator) pays penalty $f_1(\tau_1, P_{\tau_1})$, Player 2 (producer) pays $f_2(\tau_2, P_{\tau_2})$, with $\gamma_1 > \gamma_2 > 0$ typically.

Game-theoretically, one seeks a Nash equilibrium in the choice of stopping times $(\tau_1, \tau_2)$ that maximize expected payoffs: \begin{align*} J_{t,x}(\tau_1, \tau_2) &= \mathbb{E}\Big[ \int_t^{\tau_1 \wedge \tau_2} \varphi(s,P_s) ds \ &\qquad + f_1(\tau_1,P_{\tau_1}){{\tau_1\le\tau_2,\,\tau_1<T}} \ &\qquad - f_2(\tau_2,P{\tau_2})_{{\tau_2<\tau_1}} \mid \mathcal{F}_t \Big] \end{align*} The unique value function $V(t,x)$ of this Dynkin game is characterized by a DRBSDE with time-dependent lower and upper barriers given by $-f_2$ and $f_1$ (Agram et al., 2 Mar 2025).

3. CfD Design Variants in Electricity Markets

Three principal two-way CfD designs have been analyzed for their distinct effects on risk and market incentives (Johanndeiter et al., 19 Dec 2025):

Design	Reference Price Definition	Payment Unit
Price-based ("basic")	$P_{\rm ref}(t)=p_t$, the hourly spot price	Annual generation (MWh)
Revenue-based ("2way")	$P_{\rm ref}(t)=v$, the annual market value, $$v = \frac{\sum_{t,i} q_{t,i} p_t}{\sum_{t,i} q_{t,i}}$$	Annual generation (MWh)
Capacity-based ("financial")	$P_{\rm ref}=r$, annual zone-averaged value per MW capacity	Capacity (MW)

Empirical findings in high-renewables scenarios demonstrate that capacity-based CfDs yield the lowest revenue volatility but can distort long-term investment signals by delinking remuneration from marginal market value (Johanndeiter et al., 19 Dec 2025).

4. Analytical Derivation of Optimal Strike Price

The optimal strike price $S^*$ for a risk-neutral investor in a two-way CfD is derived from a zero-profit condition: $$E[\Pi(S^*)] = 0 \implies S^* = \frac{E\left[\sum_t q_t p_t\right] + E[P_{\rm ref} Q] - C}{Q}$$ where $C$ is total cost (variable and capital), and the expectations are taken over joint scenarios for spot prices and generation profiles. For all three CfD styles, closed-form or second-order approximations to $S^*$ can be constructed, accounting for the variance and covariance structure in simulated market scenarios (Johanndeiter et al., 19 Dec 2025).

5. Risk-Sharing and Bilateral Negotiation under Asymmetric Funding

Beyond the single-market-principal framework, two-way CfDs between general financial agents involve joint optimization of the contract price and collateralization to accommodate differences in funding costs, risk preferences, and default risk (Lee et al., 2019).

Agents A and B maximize the weighted sum of expected utilities: $$\max_{p,m}\ \mathbb{E}\left[U_A(\cdot) + \lambda U_B(\cdot)\right]$$ Optimal price adjustment and collateral (variation margin) processes balance loss-given-default (LGD), funding spreads, and bargaining power. The optimal margin is fully posted only in the limit of zero funding spread and perfect delta hedging. Practical implementation for CfDs follows by treating the mark-to-market value as the running exposure and applying the risk-sharing recipe to determine ex-ante payment and dynamic margin requirements (Lee et al., 2019).

6. Numerical Methods and Calibration

Modern computation of the DRBSDE characterizing complex CfD contracts leverages deep learning-based solvers. The procedure involves time discretization, simulation of the underlying price process, and the use of feedforward networks to represent the value and control processes $(Y, Z)$. A backward induction procedure with batch training and explicit barrier enforcement ensures the solution remains within prescribed boundaries. Parameters are calibrated from historical forward price time series using maximum-likelihood estimation of the Ornstein-Uhlenbeck model, as exemplified by calibration to French baseload power data yielding parameters $(\hat\mu, \hat\sigma, \hat\kappa)$ representative of market conditions (Agram et al., 2 Mar 2025).

7. Empirical Impact and Economic Trade-Offs

Two-way CfDs substantially reduce inter-scenario cost-recovery volatility for generators: coefficient of variation (CV) typically drops from 25–30% (no CfD) to below 7% with revenue- or price-based CfDs, and under 4% for capacity-based designs (Johanndeiter et al., 19 Dec 2025). The reduction in consumer price volatility is more modest. A significant design trade-off emerges: while capacity-based CfDs minimize investor risk (lowest CV), they erode investment incentives aligned with locational or system value. Revenue-based CfDs preserve more price signals and thus better align with system optimization objectives, at the expense of marginally increased revenue volatility.

In contracts with early-exit penalties, optimal strategies and contract values are rigorously determined by the solution of a DRBSDE, and sensitivity analysis reveals that larger penalties suppress exit probabilities while higher underlying price volatility increases contract value and causes stopping boundaries to approach each other (Agram et al., 2 Mar 2025).

These findings suggest that the design of two-way CfDs must balance investor risk reduction, consumer price stability, and the preservation of market incentives for efficient generation and investment (Johanndeiter et al., 19 Dec 2025, Lee et al., 2019, Agram et al., 2 Mar 2025).