New articles on Quantitative Finance


[1] 2107.12439

Proof of non-convergence of the short-maturity expansion for the SABR model

We study the convergence properties of the short maturity expansion of option prices in the uncorrelated log-normal ($\beta=1$) SABR model. In this model the option time-value can be represented as an integral of the form $V(T) = \int_{0}^\infty e^{-\frac{u^2}{2T}} g(u) du$ with $g(u)$ a ``payoff function'' which is given by an integral over the McKean kernel $G(s,t)$. We study the analyticity properties of the function $g(u)$ in the complex $u$-plane and show that it is holomorphic in the strip $|\Im(u) |< \pi$. Using this result we show that the $T$-series expansion of $V(T)$ and implied volatility are asymptotic (non-convergent for any $T>0$). In a certain limit which can be defined either as the large volatility limit $\sigma_0\to \infty$ at fixed $\omega=1$, or the small vol-of-vol limit $\omega\to 0$ limit at fixed $\omega\sigma_0$, the short maturity $T$-expansion for the implied volatility has a finite convergence radius $T_c = \frac{1.32}{\omega\sigma_0}$.


[2] 2107.12447

Bitcoin option pricing: A market attention approach

A model is proposed that models Bitcoin prices by taking into account market attention. Assuming that market attention follows a mean-reverting Cox-Ingersoll-Ross process and allowing it to influence Bitcoin returns (after some delay) leads to a tractable affine model with semi-closed formulae for European put and call prices. A maximum likelihood estimation procedure is proposed for this model. The accuracy of its call and put prices outperforms a number of standard models when tested on real data.


[3] 2107.12462

Robustness and sensitivity analyses for rough Volterra stochastic volatility models

In this paper we perform robustness and sensitivity analysis of several continuous-time rough Volterra stochastic volatility models with respect to the process of market calibration. Robustness is understood in the sense of sensitivity to changes in the option data structure. The latter analyses then should validate the hypothesis on importance of the roughness in the volatility process dynamics. Empirical study is performed on a data set of Apple Inc. equity options traded in four different days in April and May 2015. In particular, the results for RFSV, rBergomi and aRFSV models are provided.


[4] 2107.12516

They Chose to Not Tell You

The world's stock markets display a strikingly suspicious, decades long pattern of overnight and intraday returns that nobody (other than us) has plausibly explained and that nobody (other than us) has clearly and persistently alerted you to. We use correspondence on this topic over the past five years to show that the silence of others on this issue does not arise from their having a good reason to believe this pattern is fine. Separately, and regardless of whether this pattern turns out to be fine, we have documented that people in a position to alert you to the presence of strikingly suspicious return patterns in the world's stock markets that nobody can innocuously explain are aware of this issue, have no good reason to believe it is not a problem, and chose to not tell you.


[5] 2107.12625

Dhaka Water-logging: Causes, Effects and Remedial Policy Options

Water-logging is a major challenge for Dhaka city, the capital of Bangladesh. The rapid, unregulated, and unplanned urbanization, as well as detrimental social, economic, infrastructural, and environmental consequences, not to mention diseases like dengue, challenge the several crash programs combating water-logging in the city. This study provides a brief contextual analysis of the Dhakas topography and natural, as well as storm water drainage systems, before concentrating on the man-made causes and effects of water-logging, ultimately exploring a few remedial measures.


[6] 2107.12702

Income Inequality and Intergenerational Mobility in India

Using three rounds of NSS datasets, the present paper attempts to understand the relationship between income inequality and intergenerational income mobility (IGIM) by segregating generations into social and income classes. The originality of the paper lies in assessing the IGIM using different approaches, which we expect to contribute to the existing literature. We conclude that the country has low-income mobility and high inequality which is no longer associated with a particular social class in India. Also, both may have a negative or positive relationship, hence needs to be studied at a regional level.


[7] 2107.12848

Information Foraging in the Attention Economy

Over the past 200 years, rising rates of information proliferation have created new environments for information competition and, consequently, new selective forces on information evolution. These forces influence the information diet available to consumers, who in turn choose what to consume, creating a feedback process similar to that seen in many ecosystems. As a first step towards understanding this relationship, we apply animal foraging models of diet choice to describe the evolution of long and short form media in response to human preferences for maximising utility rate. The model describes an increase in information rate (i.e., entropy) in response to information proliferation, as well as differences in entropy between short-form and long-form media (such as social media and books, respectively). We find evidence for a steady increase in word entropy in diverse media categories since 1900, as well as an accelerated entropy increase in short-form media. Overall the evidence suggests an increasingly competitive battle for our attention that is having a lasting influence on the evolution of language and communication systems.


[8] 2107.12862

Quasi-sure essential supremum and applications to finance

A notion of essential supremum is developed when the uncertainty is measured by a family of non-dominated and non-compact probability measures. It provides new perspectives on super-replication and allows the Absence of Instantaneous Profit (AIP) to be characterized.


[9] 2107.12872

LOB modeling using Hawkes processes with a state-dependent factor

A point process model for order flows in limit order books is proposed, in which the conditional intensity is the product of a Hawkes component and a state-dependent factor. In the LOB context, state observations may include the observed imbalance or the observed spread. Full technical details for the computationally-efficient estimation of such a process are provided, using either direct likelihood maximization or EM-type estimation. Applications include models for bid and ask market orders, or for upwards and downwards price movements. Empirical results on multiple stocks traded in Euronext Paris underline the benefits of state-dependent formulations for LOB modeling, e.g. in terms of goodness-of-fit to financial data.


[10] 2107.12885

No free lunch for markets with multiple numéraires

We consider a global market constituted by several submarkets, each with its own assets and num\'eraire. We provide theoretical foundations for the existence of equivalent martingale measures and results on superreplication prices which allows to take into account difference of features between submarkets.


[11] 2107.12899

Mortality in Germany during the Covid-19 pandemic

The Covid-19 pandemic still causes severe impacts on society and the economy. This paper studies excess mortality during the pandemic years 2020 and 2021 in Germany empirically with a special focus on the life insurer's perspective. Our conclusions are based on official counts of German governmental offices on the living and deaths of the entire population. Conclusions, relevant for actuaries and specific insurance business lines, including portfolios of pension, life, and health insurance contracts, are provided.


[12] 2107.12484

Constant Function Market Makers: Multi-Asset Trades via Convex Optimization

The rise of Ethereum and other blockchains that support smart contracts has led to the creation of decentralized exchanges (DEXs), such as Uniswap, Balancer, Curve, mStable, and SushiSwap, which enable agents to trade cryptocurrencies without trusting a centralized authority. While traditional exchanges use order books to match and execute trades, DEXs are typically organized as constant function market makers (CFMMs). CFMMs accept and reject proposed trades based on the evaluation of a function that depends on the proposed trade and the current reserves of the DEX. For trades that involve only two assets, CFMMs are easy to understand, via two functions that give the quantity of one asset that must be tendered to receive a given quantity of the other, and vice versa. When more than two assets are being exchanged, it is harder to understand the landscape of possible trades. We observe that various problems of choosing a multi-asset trade can be formulated as convex optimization problems, and can therefore be reliably and efficiently solved.