arXiv subjects

Carol Alexander

Publications and source records attributed to Carol Alexander.

16 recordsLinked to original sources

arXiv2025

Trade Dynamics of the Global Dry Bulk Shipping Network

This study investigates the inherently random structures of dry bulk shipping networks, often likened to a taxi service, and identifies the underlying trade dynamics that contribute to this randomness within individual cargo sub-networks. By analysing micro-level trade flow data from 2015 to 2023, we explore the evolution of dry commodity networks, including grain, coal, and iron ore, and suggest that the Giant Strongly Connected Components exhibit small-world phenomena, indicative of efficient bilateral trade. The significant heterogeneity of in-degree and out-degree within these sub-networks, primarily driven by importing ports, underscores the complexity of their dynamics. Our temporal analysis shows that while the Covid-19 pandemic profoundly impacted the coal network, the Ukraine conflict significantly altered the grain network, resulting in changes in community structures. Notably, grain sub-networks display periodic changes, suggesting distinct life cycles absent in coal and iron ore networks. These findings illustrate that the randomness in dry bulk shipping networks is a reflection of real-world trade dynamics, providing valuable insights for stakeholders in navigating and predicting network behaviours.

q-fin.MF↗

arXiv2022

Inverse and Quanto Inverse Options in a Black-Scholes World

Over 90% of exchange trading on crypto options has always been on the Deribit platform. This centralised crypto exchange only lists inverse products because they do not accept fiat currency. Currently, fiat-based traders can only make deposits in bitcoin, although they can withdraw both bitcoin and ether to their on-chain wallets. Likewise, other major crypto options platforms only list crypto--stablecoin trading pairs in so-called direct options, which are similar to the standard crypto options listed by the CME except the U.S. dollar is replaced by a stablecoin version. Until now a clear mathematical exposition of these products has been lacking. We discuss the sources of market incompleteness in direct and inverse options and compare their pricing and hedging characteristics. Then we discuss the useful applications of currency protected "quanto" direct and inverse options for fiat-based traders and describe their pricing and hedging characteristics, all in the Black-Scholes setting.

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arXiv2022

Net Buying Pressure and the Information in Bitcoin Option Trades

How do supply and demand from informed traders drive market prices of bitcoin options? Deribit options tick-level data supports the limits-to-arbitrage hypothesis about the market maker's supply. The main demand-side effects are that at-the-money option prices are largely driven by volatility traders and out-of-the-money options are simultaneously driven by volatility traders and those with proprietary information about the direction of future bitcoin price movements. The demand-side trading results contrast with prior studies on established options markets in the US and Asia, but we also show that Deribit is rapidly evolving into a more efficient channel for aggregating information from informed traders.

q-fin.GN↗

arXiv2022

Static and Dynamic Models for Multivariate Distribution Forecasts: Proper Scoring Rule Tests of Factor-Quantile vs. Multivariate GARCH Models

A plethora of static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice tends to favour simpler, static models such as historical simulation or its variants whereas most academic research centres on dynamic models in the GARCH family. While numerous studies examine the accuracy of multivariate models for forecasting risk metrics, there is little research on accurately predicting the entire multivariate distribution. Yet this is an essential element of asset pricing or portfolio optimization problems having non-analytic solutions. We approach this highly complex problem using a variety of proper multivariate scoring rules to evaluate over 100,000 forecasts of eight-dimensional multivariate distributions: of exchange rates, interest rates and commodity futures. This way we test the performance of static models, viz. empirical distribution functions and a new factor-quantile model, with commonly used dynamic models in the asymmetric multivariate GARCH class.

stat.ME↗

arXiv2021

Risk-Adjusted Valuation for Real Option Decisions

We model investor heterogeneity using different required returns on an investment and evaluate the impact on the valuation of an investment. By assuming no disagreement on the cash flows, we emphasize how risk preferences in particular, but also the costs of capital, influence a subjective evaluation of the decision to invest now or retain the option to invest in future. We propose a risk-adjusted valuation model to facilitate investors' subjective decision making, in response to the market valuation of an investment opportunity. The investor's subjective assessment arises from their perceived misvaluation of the investment by the market, so projected cash flows are discounted using two different rates representing the investor's and the market's view. This liberates our model from perfect or imperfect hedging assumptions and instead, we are able to illustrate the hedging effect on the real option value when perceptions of risk premia diverge. During crises periods, delaying an investment becomes more valuable as the idiosyncratic risk of future cash flows increases, but the decision-maker may rush to invest too quickly when the risk level is exceptionally high. Our model verifies features established by classical real-option valuation models and provides many new insights about the importance of modelling divergences in decision-makers risk premia, especially during crisis periods. It also has many practical advantages because it requires no more parameter inputs than basic discounted cash flow approaches, such as the marketed asset disclaimer method, but the outputs are much richer. They allow for complex interactions between cost and revenue uncertainties as well as an easy exploration of the effects of hedgeable and un-hedgeable risks on the real option value. Furthermore, we provide fully-adjustable Python code in which all parameter values can be chosen by the user.

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arXiv2021

Targetting Kollo Skewness with Random Orthogonal Matrix Simulation

Modelling multivariate systems is important for many applications in engineering and operational research. The multivariate distributions under scrutiny usually have no analytic or closed form. Therefore their modelling employs a numerical technique, typically multivariate simulations, which can have very high dimensions. Random Orthogonal Matrix (ROM) simulation is a method that has gained some popularity because of the absence of certain simulation errors. Specifically, it exactly matches a target mean, covariance matrix and certain higher moments with every simulation. This paper extends the ROM simulation algorithm presented by Hanke et al. (2017), hereafter referred to as HPSW, which matches the target mean, covariance matrix and Kollo skewness vector exactly. Our first contribution is to establish necessary and sufficient conditions for the HPSW algorithm to work. Our second contribution is to develop a general approach for constructing admissible values in the HPSW. Our third theoretical contribution is to analyse the effect of multivariate sample concatenation on the target Kollo skewness. Finally, we illustrate the extensions we develop here using a simulation study.

stat.CO↗

arXiv2021

Hedging with Bitcoin Futures: The Effect of Liquidation Loss Aversion and Aggressive Trading

We consider the hedging problem where a futures position can be automatically liquidated by the exchange without notice. We derive a semi-closed form for an optimal hedging strategy with dual objectives - to minimise both the variance of the hedged portfolio and the probability of liquidations due to insufficient collateral. The optimal solution depends on the statistical characteristics of the spot and futures extreme returns and parameters that characterise the hedger by loss aversion, choice of leverage and collateral management. An empirical analysis of bitcoin shows that the optimal strategy combines superior hedge effectiveness with a reduction in the probability of liquidation. We compare the performance of seven major direct and inverse hedging instruments traded on five different exchanges, based on minute-level data. We also link this performance to novel speculative trading metrics, which differ markedly between venues.

q-fin.RM↗

arXiv2021

The Role of Binance in Bitcoin Volatility Transmission

We analyse high-frequency realised volatility dynamics and spillovers in the bitcoin market, focusing on two pairs: bitcoin against the US dollar (the main fiat-crypto pair) and trading bitcoin against tether (the main crypto-crypto pair). We find that the tether-margined perpetual contract on Binance is clearly the main source of volatility, continuously transmitting strong flows to all other instruments and receiving only a little volatility. Moreover, we find that (i) during US trading hours, traders pay more attention and are more reactive to prevailing market conditions when updating their expectations and (ii) the crypto market exhibits a higher interconnectedness when traditional Western stock markets are open. Our results highlight that regulators should not only consider spot exchanges offering bitcoin-fiat trading but also the tether-margined derivatives products available on most unregulated exchanges, most importantly Binance.

q-fin.TR↗

arXiv2021

Evaluating the Discrimination Ability of Proper Multivariate Scoring Rules

Proper scoring rules are commonly applied to quantify the accuracy of distribution forecasts. Given an observation they assign a scalar score to each distribution forecast, with the the lowest expected score attributed to the true distribution. The energy and variogram scores are two rules that have recently gained some popularity in multivariate settings because their computation does not require a forecast to have parametric density function and so they are broadly applicable. Here we conduct a simulation study to compare the discrimination ability between the energy score and three variogram scores. Compared with other studies, our simulation design is more realistic because it is supported by a historical data set containing commodity prices, currencies and interest rates, and our data generating processes include a diverse selection of models with different marginal distributions, dependence structure, and calibration windows. This facilitates a comprehensive comparison of the performance of proper scoring rules in different settings. To compare the scores we use three metrics: the mean relative score, error rate and a generalised discrimination heuristic. Overall, we find that the variogram score with parameter p=0.5 outperforms the energy score and the other two variogram scores.

stat.ME↗

arXiv2018

Analytic Moments for GARCH Processes

For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time horizon increases, establishing regularity conditions for the moments of aggregated returns to converge to normal moments. Our empirical study yields excellent approximate predictive distributions from these analytic moments, thus precluding the need for time-consuming simulations.

q-fin.ST↗

arXiv2018

Model Risk in Real Option Valuation

We introduce a general decision tree framework to value an option to invest/divest in a project, focusing on the model risk inherent in the assumptions made by standard real option valuation methods. We examine how real option values depend on the dynamics of project value and investment costs, the frequency of exercise opportunities, the size of the project relative to initial wealth, the investor's risk tolerance (and how it changes with wealth) and several other choices about model structure. For instance, contrary to stylized facts from previous literature, real option values can actually decrease with the volatility of the underlying project value and increase with investment costs.

q-fin.GN↗

arXiv2018

On the Continuous Limit of Weak GARCH

We prove that the symmetric weak GARCH limit is a geometric mean-reverting stochastic volatility process with diffusion determined by kurtosis of physical log returns; this provides an improved fit to implied volatility surfaces. When log returns are normal the limit coincides with Nelson's limit. The limit is unique, unlike strong GARCH limits, because assumptions about convergence of model parameters is unnecessary -- parameter convergence is uniquely determined by time-aggregation of the weak GARCH process.

stat.ME↗

arXiv2017

The Aggregation Property and its Applications to Realised Higher Moments

We develop a general multivariate aggregation property which encompasses the distinct versions of the property that were introduced by Neuberger [2012] and Bondarenko [2014] independently. This way, we classify new types of model-free realised characteristics for which risk premia may be estimated without bias. We focus on the aggregation property for multivariate martingales and log martingales, and then define realised third and fourth moments which allow long-term higher-moment risk premia to be measured, efficiently and without bias, using high-frequency returns.

q-fin.PR↗

arXiv2016

Model-Free Discretisation-Invariant Swap Contracts

Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are initially characterised as solutions to a second-order system of PDEs, then those pay-offs based on martingale and log-martingale processes alone form a vector space. Hence there exist an infinite variety of other variance and higher-moment risk premia that are less prone to bias than standard variance swaps because their option replication portfolios have no discrete-monitoring or jump errors. Their fair values are also independent of the monitoring partition. A sub-class consists of pay-offs with fair values that are further free from numerical integration errors over option strikes. Here exact pricing and hedging is possible via dynamic trading strategies on a few vanilla puts and calls. An S&P 500 empirical study on higher-moment and other DI swaps concludes.

q-fin.MF↗

arXiv2016

Model-Free Discretisation-Invariant Swaps and S&P 500 Higher-Moment Risk Premia

We derive a general multivariate theory for realised characteristics of `model-free discretisation-invariant swaps', so-called because the standard no-arbitrage assumption of martingale forward prices is sufficient to derive fair-value swap rates for such characteristics which have no jump or discretisation errors. This theory underpins specific examples for swaps based on higher moments of a single log return distribution where exact replication is possible via option-implied `fundamental contracts' like the log contact. The common factors determining the S&P 500 risk premia associated with these higher-moment characteristics are investigated empirically at the daily, weekly and monthly frequencies.

q-fin.PR↗

arXiv2016

Tail Risk Premia for Long-Term Equity Investors

We use the P&L on a particular class of swaps, representing variance and higher moments for log returns, as estimators in our empirical study on the S&P500 that investigates the factors determining variance and higher-moment risk premia. This class is the discretisation invariant sub-class of swaps with Neuberger's aggregating characteristics. Besides the market excess return, momentum is the dominant driver for both skewness and kurtosis risk premia, which exhibit a highly significant negative correlation. By contrast, the variance risk premium responds positively to size and negatively to growth, and the correlation between variance and tail risk premia is relatively low compared with previous research, particularly at high sampling frequencies. These findings extend prior research on determinants of these risk premia. Furthermore, our meticulous data-construction methodology avoids unwanted artefacts which distort results.

q-fin.PR↗