arXiv subjects

Christian P. Fries

Publications and source records attributed to Christian P. Fries.

7 recordsLinked to original sources

arXiv2026

Replication-Consistent Liquidity Forecasting for Derivatives -- Forward Funding Sensitivities and a Liquidity Valuation Adjustment for Settlement Lags

We study cash-flow forecasting for derivatives used in liquidity management and clarify its relation to risk-neutral valuation and replication. While it is well known that expectations under different measures (e.g., $\mathbb{P}$ vs. $\mathbb{Q}$) can yield different undiscounted cash-flows, further inconsistencies arise when payment times are stochastic. We show that using discounting sensitivities (funding-curve hedge ratios) instead of "expected cash-flows" aligns forecasting with the self-financing replication strategy and avoids measure-mixing/aggregation issues. We then illustrate how a standard valuation model delivers pathwise funding requirements and propose a simple liquidity valuation adjustment to capture settlement lags and related timing frictions. The note provides implementation hints (American Monte Carlo with adjoint differentiation) and clarifies when "expected cash-flows" are informative and when sensitivities should be used instead.

q-fin.PR↗

arXiv2025

Stateless and Secure Delivery versus Payment across Blockchains

We propose a secure, stateless and composable transaction scheme to establish delivery-versus-payment (DvP) across two (or more) blockchains without relying on time-locks, centralized escrow, or stateful intermediaries. The method minimizes coordination overhead and removes race conditions via a stateless decryption oracle that conditionally releases cryptographic keys. Specifically, the scheme requires: 1) a decryption oracle service (either centralized or using threshold decryption) that decrypts transaction-specific encrypted messages, and 2) a payment contract on the payment chain that executes conditional payments via transferAndDecrypt and emits the appropriate key, depending on transaction outcome (finality). The decrypted key then deterministically enables follow-up transactions - such as asset delivery or cancellation - on a separate blockchain. The protocol is lightweight and compatible with existing blockchain infrastructure (e.g., Ethereum), and avoids timeouts or pre-defined orderings. Our approach improves atomic cross-chain settlement and can serve as a blueprint for decentralized inter-chain financial markets. The protocol allows for multi-party DvP across multiple chains. A multi-party delivery versus payment is a valuable trade feature as it allows to bound multiple trade into a single atomic unit, effectively reducing liquidity requirements.

cs.CR↗

arXiv2025

Intergenerational Equitable Climate Change Mitigation: Negative Effects of Stochastic Interest Rates; Positive Effects of Financing

Climate mitigation decisions today affect future generations, raising questions of intergenerational equity. Integrated assessment models (IAMs) rely on discounting to evaluate long-term policy costs and benefits. Using the DICE model, we quantify how optimal pathways distribute abatement and damage costs across cohorts. Unconstrained optimization creates intergenerational inequality, with future generations bearing higher costs relative to GDP. Extending the model with stochastic discount rates, we show that discount-rate uncertainty significantly amplifies this inequality. We consider two independent extensions: the financing of abatement costs and the modeling of nonlinear financing costs under large damages. Both extensions can materially improve intergenerational equity by distributing mitigation efforts more evenly. As an illustration, we present a modified DICE model whose optimal pathway limits generational costs to 3 % of GDP, leading to more equitable effort sharing. Our proposed model extensions are model-agnostic, applicable across IAMs, and compatible with alternative intergenerational equity metrics.

q-fin.MF↗

arXiv2024

Implied CO$_{\textbf{2}}$-Price and Interest Rate of Carbon

By its nature, the so-called social cost of carbon (SCC(t)) will likely not cover the cost induced by climate change (damage cost and abatement cost) if it is used as a CO$_2$-price. It is a marginal price only. We define an implied CO$_2$-price that covers the climate change-induced costs. The price can be interpreted as a \textit{polluter pays principle}. A numerical analysis using a classical DICE model reveals that the cost-implied CO$_2$ price is around 500 \$/tCO$_2$, while the corresponding price associated with the SCC is about 50 \$/tCO$_2$. In addition, we define the internal rate of return of carbon abatement and calculate it for the classical DICE model. This rate is much higher than the model's discount rate, which may suggest the advantage of financing abatement by loans.

q-fin.MF↗

arXiv2021

Non-Linear Discounting and Default Compensation: Valuation of Non-Replicable Value and Damage: When the Social Discount Rate may become Negative

In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a discounting when discount factors cannot be derived from market products. That is, a risk-neutralising trading strategy cannot be performed. This is the case when one needs a risk-free (default-free) discounting, but default protection on funding providers is not traded. For this case, we derive a default compensation factor that describes the present value of a strategy to compensate for default (like buying default protection would do). In a second part of the paper, we introduce a model where the survival probability, and hence the discount factor, depends on the notional. This model introduces an effect not present in the classical modelling of a time-dependent survival probability. Our model allows that large liquidity requirements are more likely to default instantly than small ones. Combined, the two models build a framework where discounting (and hence valuation) is non-linear: discount factors depend on the amount to be discounted. Our approach builds on top of the classical theory of discounting (which may either be given as market-implied or be derived from a model of utility, consumption and production). In that sense, it is rather a generalisation than an alternative. The modelling approach has specific relevance for climate models, where discounting is an important aspect in assessing the severity of future events. Our model may result in non-decaying discount factors (negative discount rates) for certain scenarios.

q-fin.MF↗

arXiv2019

Stochastic Algorithmic Differentiation of (Expectations of) Discontinuous Functions (Indicator Functions)

In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. The finite difference approximation of a partial derivative of a Monte-Carlo integral of a discontinuous function is known to exhibit a high Monte-Carlo error. The issue is evident since the Monte-Carlo approximation of a discontinuous function is just a finite sum of discontinuous functions and as such, not even differentiable. The algorithmic differentiation of a discontinuous function is problematic. A natural approach is to replace the discontinuity by continuous functions. This is equivalent to replacing a path-wise automatic differentiation by a (local) finite difference approximation. We present an improvement (in terms of variance reduction) by decoupling the integration of the Dirac delta and the remaining conditional expectation and estimating the two parts by separate regressions. For the algorithmic differentiation, we derive an operator that can be injected seamlessly - with minimal code changes - into the algorithm resulting in the exact result.

q-fin.CP↗

arXiv2017

Automatic Backward Differentiation for American Monte-Carlo Algorithms (Conditional Expectation)

In this note we derive the backward (automatic) differentiation (adjoint [automatic] differentiation) for an algorithm containing a conditional expectation operator. As an example we consider the backward algorithm as it is used in Bermudan product valuation, but the method is applicable in full generality. The method relies on three simple properties: 1) a forward or backward (automatic) differentiation of an algorithm containing a conditional expectation operator results in a linear combination of the conditional expectation operators; 2) the differential of an expectation is the expectation of the differential $\frac{d}{dx} E(Y) = E(\frac{d}{dx}Y)$; 3) if we are only interested in the expectation of the final result (as we are in all valuation problems), we may use $E(A \cdot E(B\vert\mathcal{F})) = E(E(A\vert\mathcal{F}) \cdot B)$, i.e., instead of applying the (conditional) expectation operator to a function of the underlying random variable (continuation values), it may be applied to the adjoint differential. \end{enumerate} The methodology not only allows for a very clean and simple implementation, but also offers the ability to use different conditional expectation estimators in the valuation and the differentiation.

q-fin.CP↗