Research articles for the 2020-06-21

A simple model of interbank trading with tiered remuneration
Toshifumi Nakamura

A negative interest rate policy is often accompanied by tiered remuneration, which allows for exemption from negative rates. This study proposes a basic model of interest rates formed in the interbank market with a tiering system. The results predicted by the model largely mirror actual market developments in late 2019, when the European Central Bank introduced, and the Switzerland National Bank modified, the tiering system.

Analytical solution of $k$th price auction
Martin Mihelich,Yan Shu

We provide an exact analytical solution of the Nash equilibrium for the $k$th price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.

Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model
Chinonso Nwankwo,Weizhong Dai,Ruihua Liu

We consider a system of coupled free boundary problems for pricing American put options with regime-switching. To solve this system, we first employ the logarithmic transformation to map the free boundary for each regime to multi-fixed intervals and then eliminate the first-order derivative in the transformed model by taking derivatives to obtain a system of partial differential equations which we call the asset-delta-gamma-speed equations. As such, the fourth-order compact finite difference scheme can be used for solving this system. The influence of other asset, delta, gamma, and speed options in the present regime is estimated based on Hermite interpolations. Finally, the numerical method is tested with several examples. Our results show that the scheme provides an accurate solution that is fast in computation as compared with other existing numerical methods.

Credit migration: Generating generators
Richard J. Martin

Markovian credit migration models are a reasonably standard tool nowadays, but there are fundamental difficulties with calibrating them. We show how these are resolved using a simplified form of matrix generator and explain why risk-neutral calibration cannot be done without volatility information. We also show how to use elementary ideas from differential geometry to make general inferences about calibration stability.

Deep Smoothing of the Implied Volatility Surface
Damien Ackerer,Natasa Tagasovska,Thibault Vatter

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.

Gender Inequality in Research Productivity During the COVID-19 Pandemic
Ruomeng Cui,Hao Ding,Feng Zhu

We study the disproportionate impact of the lockdown as a result of the COVID-19 outbreak on female and male academics' research productivity in social science. We collect data from the largest open-access preprint repository for social science on 41,858 research preprints in 18 disciplines produced by 76,832 authors across 25 countries in a span of two years. We find that during the 10 weeks after the lockdown in the United States, although the total research productivity increased by 35%, female academics' productivity dropped by 13.9% relative to that of male academics. We also show that several disciplines drive such gender inequality. Finally, we find that this intensified productivity gap is more pronounced for academics in top-ranked universities, and the effect exists in six other countries.

Manifold Feature Index: A novel index based on high-dimensional data simplification
Chenkai Xu,Hongwei Lin,Xuansu Fang

In this paper, we propose a novel stock index model, namely the manifold feature(MF) index, to reflect the overall price activity of the entire stock market. Based on the theory of manifold learning, the researched stock dataset is assumed to be a low-dimensional manifold embedded in a higher-dimensional Euclidean space. After data preprocessing, its manifold structure and discrete Laplace-Beltrami operator(LBO) matrix are constructed. We propose a high-dimensional data feature detection method to detect feature points on the eigenvectors of LBO, and the stocks corresponding to these feature points are considered as the constituent stocks of the MF index. Finally, the MF index is generated by a weighted formula using the price and market capitalization of these constituents. The stock market studied in this research is the Shanghai Stock Exchange(SSE). We propose four metrics to compare the MF index series and the SSE index series (SSE 50, SSE 100, SSE 150, SSE 180 and SSE 380). From the perspective of data approximation, the results demonstrate that our indexes are closer to the stock market than the SSE index series. From the perspective of risk premium, MF indexes have higher stability and lower risk.

Pricing vulnerable options in a hybrid credit risk model driven by Heston-Nandi GARCH processes
Gechun Liang,Xingchun Wang

This paper proposes a hybrid credit risk model, in closed form, to price vulnerable options with stochastic volatility. The distinctive features of the model are threefold. First, both the underlying and the option issuer's assets follow the Heston-Nandi GARCH model with their conditional variance being readily estimated and implemented solely on the basis of the observable prices in the market. Second, the model incorporates both idiosyncratic and systematic risks into the asset dynamics of the underlying and the option issuer, as well as the intensity process. Finally, the explicit pricing formula of vulnerable options enables us to undertake the comparative statistics analysis.

The Cost of Undisturbed Landscapes
Sebastian Wehrle,Johannes Schmidt,Christian Mikovits

By 2030 Austria aims to meet 100% of its electricity demand from domestic renewable sources, predominantly from wind and solar energy. While wind power reduces CO2 emissions, it is also connected to negative impacts at the local level, such as interference with landscape aesthetics. Nevertheless, wind power comes at lower system integration cost than solar power, so that it effectively reduces system cost. We quantify the opportunity cost of replacing wind turbines with solar power, using the power system model medea. Our findings suggest that these cost of undisturbed landscapes are considerable, particularly when PV is not entirely rolled out as utility scale, open space installations. The opportunity cost is likely high enough to allow for significant compensation of the ones affected by local wind turbine externalities.

Time series copula models using d-vines and v-transforms: an alternative to GARCH modelling
Martin Bladt,Alexander J. McNeil

An approach to modelling volatile financial return series using d-vine copulas combined with uniformity preserving transformations known as v-transforms is proposed. By generalizing the concept of stochastic inversion of v-transforms, models are obtained that can describe both stochastic volatility in the magnitude of price movements and serial correlation in their directions. In combination with parametric marginal distributions it is shown that these models can rival and sometimes outperform well-known models in the extended GARCH family.

Valuing the quality option in agricultural commodity futures: a Monte Carlo simulation based approach
Sanjay Mansabdar,Hussain C Yaganti

Agricultural commodity futures are often settled by delivery. Quality options that allow the futures short to deliver one of several underlying assets are commonly used in such contracts to prevent manipulation. Inclusion of these options reduces the price of the futures contract and leads to degraded contract hedging performance. Valuation of these options is a first step in assessing the impact of the quality options embedded into a futures contract. This paper demonstrates a Monte Carlo simulation based approach to estimate the value of a quality option. In order to improve simulation efficiency, the technique of antithetic variables is used. This approach can help in the assessment of the impact of embedded quality options.

Weak existence and uniqueness for affine stochastic Volterra equations with L1-kernels
Eduardo Abi Jaber

We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is based on approximations using stochastic Volterra equations with $L^2$-kernels combined with a general stability result. Most importantly, we establish weak uniqueness using a duality argument on the Fourier--Laplace transform via a deterministic Riccati--Volterra integral equation. We illustrate the applicability of our results on Hawkes processes and a class of hyper-rough Volterra Heston models with a Hurst index $H \in (-1/2,1/2]$.

Why Stake When You Can Borrow?
Tarun Chitra,Alex Evans

As smart contract platforms autonomously manage billions of dollars of capital, quantifying the portfolio risk that investors engender in these systems is increasingly important. Recent work illustrates that Proof of Stake (PoS) is vulnerable to financial attacks arising from on-chain lending and has worse capital efficiency than Proof of Work (PoW) \cite{fanti_pos_econ}. Numerous methods for improving capital efficiency have been proposed that allow stakers to create fungible derivative claims on their staked assets. In this paper, we construct a unifying model for studying the security risks of these proposals. This model combines birth-death P\'olya processes and risk models adapted from the credit derivatives literature to assess token inequality and return profiles. We find that there is a sharp transition between 'safe' and 'unsafe' derivative usage. Surprisingly, we find that contrary to \cite{fanti2019compounding} there exist conditions where derivatives can \emph{reduce} concentration of wealth in these networks. This model also applies to Decentralized Finance (DeFi) protocols where staked assets are used as insurance. Our theoretical results are validated using agent-based simulation.