arXiv subjects

Damien Ackerer

Publications and source records attributed to Damien Ackerer.

9 recordsLinked to original sources

arXiv2023

Perpetual Futures Pricing

Perpetual futures are contracts without expiration date in which the anchoring of the futures price to the spot price is ensured by periodic funding payments from long to short. We derive explicit expressions for the no-arbitrage price of various perpetual contracts, including linear, inverse, and quantos futures in both discrete and continuous-time. In particular, we show that the futures price is given by the risk-neutral expectation of the spot sampled at a random time that reflects the intensity of the price anchoring. Furthermore, we identify funding specifications that guarantee the coincidence of futures and spot prices, and show that for such specifications perpetual futures contracts can be replicated by dynamic trading in primitive securities.

q-fin.PR↗

arXiv2021

A Game-Theoretic Analysis of Cross-Ledger Swaps with Packetized Payments

We propose a game-theoretic framework to study the outcomes of packetized payments, a cross-ledger transaction protocol, with strategic and possibly malicious agents. We derive the transaction failure rate and demonstrate that without disciplinary mechanisms, packetized payments are likely to be incomplete. Our analysis suggests that collateral deposits can prevent malicious agents from taking advantage of the protocol. We further infer that the deposit amount should depend on the underlying asset price volatility or that it should be dynamically adjusted as the price changes.

cs.GT↗

arXiv2021

A Game-Theoretic Analysis of Cross-Chain Atomic Swaps with HTLCs

To achieve interoperability between unconnected ledgers, hash time lock contracts (HTLCs) are commonly used for cross-chain asset exchange. The solution tolerates transaction failure, and can "make the best out of worst'' by allowing transacting agents to at least keep their original assets in case of an abort. Nonetheless, as an undesired outcome, reoccurring transaction failures prompt a critical and analytical examination of the protocol. In this study, we propose a game-theoretic framework to study the strategic behaviors of agents taking part in cross-chain atomic swaps implemented with HTLCs. We study the success rate of the transaction as a function of the exchange rate of the swap, the token price and its volatility, among other variables. We demonstrate that in an attempt to maximize one's own utility as asset price changes, either agent might withdraw from the swap. An extension of our model confirms that collateral deposits can improve the transaction success rate, motivating further research towards collateralization without a trusted third party. A second model variation suggests that a swap is more likely to succeed when agents dynamically adjust the exchange rate in response to price fluctuations.

cs.GT↗

arXiv2020

Deep Smoothing of the Implied Volatility Surface

We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities. Importantly, IVS models need to generate realistic arbitrage-free option prices, meaning that no portfolio can lead to risk-free profits. We propose an approach guaranteeing the absence of arbitrage opportunities by penalizing the loss using soft constraints. Furthermore, our method can be combined with standard IVS models in quantitative finance, thus providing a NN-based correction when such models fail at replicating observed market prices. This lets practitioners use our approach as a plug-in on top of classical methods. Empirical results show that this approach is particularly useful when only sparse or erroneous data are available. We also quantify the uncertainty of the model predictions in regions with few or no observations. We further explore how deeper NNs improve over shallower ones, as well as other properties of the network architecture. We benchmark our method against standard IVS models. By evaluating our method on both training sets, and testing sets, namely, we highlight both their capacity to reproduce observed prices and predict new ones.

q-fin.PR↗

arXiv2019

Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders

We introduce the vine copula autoencoder (VCAE), a flexible generative model for high-dimensional distributions built in a straightforward three-step procedure. First, an autoencoder (AE) compresses the data into a lower dimensional representation. Second, the multivariate distribution of the encoded data is estimated with vine copulas. Third, a generative model is obtained by combining the estimated distribution with the decoder part of the AE. As such, the proposed approach can transform any already trained AE into a flexible generative model at a low computational cost. This is an advantage over existing generative models such as adversarial networks and variational AEs which can be difficult to train and can impose strong assumptions on the latent space. Experiments on MNIST, Street View House Numbers and Large-Scale CelebFaces Attributes datasets show that VCAEs can achieve competitive results to standard baselines.

stat.ML↗

arXiv2019

Linear Credit Risk Models

We introduce a novel class of credit risk models in which the drift of the survival process of a firm is a linear function of the factors. The prices of defaultable bonds and credit default swaps (CDS) are linear-rational in the factors. The price of a CDS option can be uniformly approximated by polynomials in the factors. Multi-name models can produce simultaneous defaults, generate positively as well as negatively correlated default intensities, and accommodate stochastic interest rates. A calibration study illustrates the versatility of these models by fitting CDS spread time series. A numerical analysis validates the efficiency of the option price approximation method.

q-fin.MF↗

arXiv2019

Option Pricing with Orthogonal Polynomial Expansions

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the nested affine cases. We also derive and numerically validate series representations for option Greeks. We depict an extension of our approach to exotic options whose payoffs depend on a finite number of prices.

q-fin.MF↗

arXiv2018

The Jacobi Stochastic Volatility Model

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form coefficients. We derive closed-form series representations for option prices whose discounted payoffs are functions of the asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and can be applied to discretely monitored Asian options. In a numerical analysis we show that option prices can be accurately and efficiently approximated by truncating their series representations.

q-fin.MF↗

arXiv2018

Dependent Defaults and Losses with Factor Copula Models

We present a class of flexible and tractable static factor models for the term structure of joint default probabilities, the factor copula models. These high-dimensional models remain parsimonious with pair-copula constructions, and nest many standard models as special cases. The loss distribution of a portfolio of contingent claims can be exactly and efficiently computed when individual losses are discretely supported on a finite grid. Numerical examples study the key features affecting the loss distribution and multi-name credit derivatives prices. An empirical exercise illustrates the flexibility of our approach by fitting credit index tranche prices.

q-fin.MF↗