Showing papers in "Quantitative Finance in 2023"
21 citations
TL;DR: In this paper , the authors propose to use weighted variance swaps to hedge permanent losses in Decentralized Finance (CDF) with a weighted variance swap (WV swap).
Abstract: Impermanent Loss in Decentralized Finance can be hedged with weighted variance swaps
4 citations
TL;DR: In this article , it was shown that the implied volatility in the N-component Gaussian mixture model is bounded by the number of crossings of the risk-neutral density with the density of a log-normal distribution with the same mean as the forward price.
Abstract: The number of crossings of the implied volatility function with a fixed level is bounded above by the number of crossings of the risk-neutral density with the density of a log-normal distribution with the same mean as the forward price. It is bounded below by the number of convex payoffs priced equally by the two densities. We discuss the implications of these bounds for the implied volatility in the N-component Gaussian mixture model, with particular attention to the possibility of W-shaped smiles. We show that the implied volatility in this model crosses any level at most times. We show that a bimodal density need not produce a W-shaped smile, and a unimodal density can produce an oscillatory smile. We give monotonicity properties of the implied volatility in Gaussian mixtures under stochastic orderings of the location parameters and volatilities of the mixture components. For some of these results we make use of a novel convexity property of the Black-Scholes price at one strike with respect to the price at another strike. The combined constraints from density crossings and extreme strike asymptotics restrict the allowed shapes of the implied volatility. As an application we discuss a symmetric N = 3 Gaussian mixture model which generates three possible smile shapes: U-shaped, W-shaped and an oscillatory shape with two minima and two maxima.
4 citations
TL;DR: In this paper , the authors developed a data-driven approach for options market making by using a neural network to approximate the market making strategy at each decision time and train them to optimize the expected utility of the market maker.
Abstract: We develop a data-driven approach for options market making. Using stock options data from CBOE, we find that both buy and sell orders exhibit strong self-excitation but insignificant cross-excitation. We show that a Hawkes process with a time-varying baseline intensity and the power law kernel provides a good fit to the data of market order flows for stock options. To solve the optimal market making problem for a single option, we approximate the market making strategy at each decision time by a neural network and train them to optimize the expected utility of the market maker. We study feature selection for the neural networks and compare the out-of-sample performance of the optimal neural network strategy trained from data generated by the Hawkes process and the Poisson process. We find that using the more realistic Hawkes model improves the out-of-sample performance significantly. Furthermore, utilizing the Hawkes process intensity or the expected number of market order arrivals computed under the Hawkes model as an additional input feature can boost the performance. We also show how to solve the market making problem for option portfolios with Greeks and inventory constraints using neural network approximation.
3 citations
TL;DR: In this article , the authors analyse robust dynamic delta hedging of bitcoin options using a set of smile-implied and other smile-adjusted deltas that are either model-free, in the sense that they are the same for every scale-invariant stochastic and/or local volatility model, or they are based on simple regime-dependent parameterisations of local volatility.
Abstract: We analyse robust dynamic delta hedging of bitcoin options using a set of smile-implied and other smile-adjusted deltas that are either model-free, in the sense that they are the same for every scale-invariant stochastic and/or local volatility model, or they are based on simple regime-dependent parameterisations of local volatility. These deltas are popular with option market makers in traditional assets because they are very easy to implement. Previous empirical research on dynamic delta hedging is based solely on equity index options, but analysis of our unique data on hourly historical bitcoin option prices reveals that bitcoin implied volatility curves behave very differently from those of equity index options. For call and put options with a wide range of moneyness and with synthetic constant maturities of 10, 20 and 30 days, we compare the dynamic hedging performance of different smile-adjusted deltas over two one-year periods. We also examine the use of the perpetual contract rather than the standard futures as hedging instrument because the basis risk for the perpetual is very much smaller than it is for calendar futures. Results are presented as testable statistics of hedging error variance ratios. In certain periods the use of smile-implied hedge ratios can significantly out-perform the simple Black–Scholes delta hedge, especially when using the perpetual swap as hedging instrument, where efficiency gains can exceed 30% for out-of-the-money puts, and reach an average of 15% when hedging short-term out-of-the money calls during periods when the implied volatility curve slopes upwards. The advantage of using the perpetual contract is especially evident during 2021, for the longer-term contracts for which the basis is still rather large.
3 citations
TL;DR: In this article , four distinct clusters of client order flow are identified and their properties analyzed, and the properties of these clusters are compared with those of client flow in other client order flows.
Abstract: Four distinct clusters of client order flow are identified and their properties analyzed
3 citations
TL;DR: In this paper , a risk parity strategy based on portfolio kurtosis as reference measure is introduced, which allocates the asset weights in a portfolio in a way that allows an homogeneous distribution of responsibility for portfolio returns' huge dispersion.
Abstract: In this paper, a risk parity strategy based on portfolio kurtosis as reference measure is introduced. This strategy allocates the asset weights in a portfolio in a manner that allows an homogeneous distribution of responsibility for portfolio returns' huge dispersion, since portfolio kurtosis puts more weight on extreme outcomes than standard deviation does. Therefore, the goal of the strategy is not the minimization of kurtosis, but rather its ‘fair diversification’ among assets. An original closed-form expression for portfolio kurtosis is devised to set up the optimization problem for this type of risk parity strategy. The latter is then compared with the one based on standard deviation by using data from a global equity investment universe and implementing an out-of-sample analysis. The kurtosis-based risk parity strategy has interesting portfolio effects, with lights and shadows. It outperforms the traditional risk parity according to main risk-adjusted performance measures. In terms of asset allocation solutions, it provides more unbalanced and more erratic portfolio weights (albeit without excluding any component) in comparison to those pertaining the traditional risk parity strategy.
3 citations
TL;DR: In this paper, a class of realized semi-parametric conditional autoregressive joint value-at-risk (VaR) and expected shortfall (ES) models is proposed, which implicitly allow the conditional return distribution to change over time via the relationship between VaR and ES.
Abstract: A class of realized semi-parametric conditional autoregressive joint Value-at-Risk (VaR) and Expected Shortfall (ES) models is proposed. This class includes novel specifications that allow separate dynamics for VaR and ES, driven by realized measures of volatility. A measurement equation is included in the model class for risk modeling, meaning it generalizes the parametric Realized-GARCH model into the semi-parametric realm. The proposed models implicitly allow the conditional return distribution to change over time via the relationship between VaR and ES. Employing a quasi-likelihood built on the asymmetric Laplace distribution, a Bayesian Markov Chain Monte Carlo method is used for model estimation, whose finite sample properties are assessed via simulation. In a forecasting study applied to 7 indices and 7 assets, one-day-ahead 1% and 2.5% VaR and ES forecasting results support the proposed model class.
1 citations
TL;DR: In this article , the authors studied the dynamic asset allocation problem faced by an infinitively lived commodity-based sovereign wealth fund under incomplete markets and found that the optimal demand for equity should decrease gradually from 60% to 40% over the next 60 years.
Abstract: This paper studies the dynamic asset allocation problem faced by an infinitively lived commodity-based sovereign wealth fund under incomplete markets. Assuming that the fund receives a non-tradable stream of commodity revenues until a predetermined date, the optimal consumption and investment strategies are state and time-dependent. Using data from the Norwegian Petroleum Fund, we find that the optimal demand for equity should decrease gradually from 60% to 40% over the next 60 years. However, the solution is particularly sensitive to the correlation between oil and stock price changes. We also estimate wealth-equivalent welfare losses, relative to the optimal rule, when following alternative suboptimal investment rules.
1 citations
TL;DR: The authors analyzes the impact of a single round of debt renegotiation on investment and financing decisions, and shows that the renegotiation surplus increases with project risk but decreases with sunk cost.
Abstract: This paper analyzes the impact of a single round of debt renegotiation on investment and financing decisions. We produce an analytical proof for the widely-used assertion that optimal renegotiation time is common default time. We show that debt renegotiation accelerates investment and increases the investment option value by around 15%. Renegotiation surplus increases with project risk but decreases with sunk cost. Investment option value has an inverted U-shaped link with debtholders' bargaining power. If tax rate is moderate, optimal leverage with renegotiation is greater than that without renegotiation but if it is sufficiently high, the opposite holds true.
1 citations
TL;DR: A new approximate dynamic programming algorithm applied to time series forecasting is described in this article , where the authors apply the algorithm to the forecasting of time series in the context of forecasting time series.
Abstract: A new approximate dynamic programming algorithm applied to time series forecasting
TL;DR: The authors proposed a bottom-up quantitative reverse stress testing framework that identifies forward-looking fragilities tailored to a bank's portfolio, credit and funding strategies, models, and calibration constraints.
Abstract: We propose a bottom-up quantitative reverse stress testing framework that identifies forward-looking fragilities tailored to a bank's portfolio, credit and funding strategies, models, and calibration constraints. Thus, instead of relying on historical events, we run a Monte Carlo simulation, and we mine those future states that contribute the most to a bank's cost of capital expressed in terms of scenario differential. This approach allows identifying both the systemic and idiosyncratic weaknesses of the bank's portfolio, with applications that include solvency risk, extreme events hedging, liquidity risk management, trading and credit limits, model validation and model risk management.
TL;DR: In this paper , the authors model how chatroom traders, forming a coalition via social media platforms, influence the stock price in the presence of large and strategic short sellers, and study the economic consequences of this dynamic game.
Abstract: This paper models how chatroom traders, forming a coalition via social media platforms, influence the stock price in the presence of large and strategic short sellers. The economic consequences of this dynamic game are studied in an equilibrium framework with strategic trading. Various equilibrium phenomena arise, including price bubbles, short squeezes, forced liquidations, and precautionary savings by the large trader. Media groups discipline the large trader's incentive to short sell, but it can either increase or decrease market allocational efficiency. Additionally, it uniformly improves social welfare under the belief-neutral welfare criterion.
TL;DR: In this article , the skew constant-elasticity-of-variance (skew CEV) model is introduced to capture the regulated dynamics of interest rates, and two numerical approaches are proposed: an improved finite difference scheme and a piecewise binomial lattice to evaluate bonds and European/American bond options.
Abstract: Interest rates frequently exhibit regulated or controlled characteristics, for example, the prevailing zero interest rate policy, or the leading role of central banks in short rate markets. In order to capture the regulated dynamics of interest rates, we introduce the skew constant-elasticity-of-variance (skew CEV) model. We then propose two numerical approaches: an improved finite difference scheme and a piecewise binomial lattice to evaluate bonds and European/American bond options. Numerical simulations show that both of these two approaches are efficient and satisfactory, with the finite difference scheme being more superior.
TL;DR: In this article , a coupled GARCH model for the intraday and overnight volatility, using the implied jump magnitude from option markets and the earnings calendar to model anticipated shocks, is introduced.
Abstract: We introduce a coupled GARCH model for the intraday and overnight volatility, using the implied jump magnitude from option markets and the earnings calendar to model anticipated shocks. We estimate the model on DJIA and report on the accuracy of the forecasts.
TL;DR: In this article , a generalization of Markowitz model that incorporates skewness and kurtosis into the classical mean-variance allocation framework is proposed, which provides the closed-form solution of the optimization problem.
Abstract: This paper proposes a generalization of Markowitz model that incorporates skewness and kurtosis into the classical mean–variance allocation framework. The principal appeal of the present approach is that it provides the closed-form solution of the optimization problem. The four moments optimal portfolio is then decomposed into the sum of three portfolios: the mean–variance optimal portfolio plus two self-financing portfolios, respectively, accounting for skewness and kurtosis. Theoretical properties of the optimal solution are discussed together with the economic interpretation. Finally, an empirical exercise on real financial data shows the contribution of the two portfolios accounting for skewness and kurtosis when financial returns depart from Normal distribution.
TL;DR: In this paper , a closed-form solution for a geometric average Asian option was obtained for the case of no jumps and condition on the jump times first and then average over the sequences of jump times.
Abstract: We price Asian options on commodity futures contracts in the presence of stochastic convenience yield, stochastic interest rates and jumps in the commodity spot price. In the case of no jumps, we obtain a closed-form solution for a geometric average Asian option. This analytic result enables us to employ this option as a suitable control variate when pricing the corresponding arithmetic average Asian option. Discussion of further applications and comparative statics are presented. To cover the case with jumps, we condition on the jump times first and then average over the sequences of jump times.
TL;DR: In this paper , space scaling and time changing self-decomposable laws at unit time are used to synthesize risk neutral variance term structures, where space scaling contributes towards front end options while time changing works on the back end.
Abstract: Risk neutral variance term structures are characterized by their time elasticities. They are synthesized by space scaling and time changing self-decomposable laws at unit time. Monotone concave or convex time elasticities are modeled using exponential functions while gamma functions permit changes in curvature. Results for both cases as time changes are followed by those with simultaneous space-scaling and time-changing. Space scaling contributes towards front end options while time changing works on the back end. Splitting the space scaling and time changing for the positive and negative moves delivers models with rising absolute skewness and kurtosis. The space scaled and time changed densities are those of additive processes. The space scaled process scales a solution to a time varying OU equation driven by a time changed Lévy process taken at log time. The mean reversion rates for the OU process are the variance time elasticities. The two processes are termed the space scaled and time change components and their relative contributions, space to time are determined to be twice the ratio of their variance elasticities. In particular, the space scaling elasticity synthesizes the effects of perpetual motion as captured by mean reversion in the underlying OU equation.
TL;DR: In this paper , the authors consider the problem of optimal dynamic trading in the presence of predictable returns and proportional transaction costs for an investor choosing among multiple assets and provide exact trading rules for N-assets that follow an MA(1) process.
Abstract: We consider the problem of optimal dynamic trading in the presence of predictable returns and proportional transaction costs for an investor choosing among multiple assets. The value of each security equals the expected value of holding the asset plus the value of all options to trade. We provide exact trading rules for N-assets that follow an MA(1) process. Simulations demonstrate the impact of transaction costs, volatility, and predictability on optimal trading behavior. The optimal trading rule can substantially increase performance if transaction costs vary among assets.
TL;DR: In this paper , the authors develop ML models that solve the problems associated with risk premia forecasting by separating risk prediction into two independent tasks, a time series model and a cross-sectional model, and using neural networks with skip connections.
Abstract: The measurement of financial risk premia, the amount that a risky asset will outperform a risk-free one, is an important problem in asset pricing. The noisiness and non-stationarity of asset returns makes the estimation of risk premia using machine learning (ML) techniques challenging. In this work, we develop ML models that solve the problems associated with risk premia forecasting by separating risk premia prediction into two independent tasks, a time series model and a cross-sectional model, and using neural networks with skip connections to enable their deep neural network training. These models are tested robustly with different metrics, and we observe that our models outperform several existing standard ML models. A known issue with ML models is their ‘black box’ nature, i.e. their opaqueness to interpretability. We interpret these deep neural networks using local approximation-based techniques that provide explanations for our model's predictions.
TL;DR: In this paper , a generative model based on recurrent neural networks for the complete dynamics of a limit order book is developed by decomposing the probability of each transition into a product of conditional probabilities of order type, price level, order size and time delay.
Abstract: In this work, a generative model based on recurrent neural networks for the complete dynamics of a limit order book is developed. The model captures the dynamics of the limit order book by decomposing the probability of each transition into a product of conditional probabilities of order type, price level, order size and time delay. Each such conditional probability is modelled by a recurrent neural network. Several evaluation metrics for generative models related to trading execution are introduced. Using these metrics, it is demonstrated that the generative model can be successfully trained to fit both synthetic and real data from the Nasdaq Stockholm exchange.
TL;DR: In this paper , the authors study and classify optimal martingales in the dual formulation of optimal stopping problems and obtain the dual upper bound for the optimal stopping problem with low variance.
Abstract: In this article we study and classify optimal martingales in the dual formulation of optimal stopping problems. In this respect we distinguish between weakly optimal and surely optimal martingales. It is shown that the family of weakly optimal and surely optimal martingales may be quite large. On the other hand it is shown that the surely optimal Doob-martingale, that is, the martingale part of the Snell envelope, is in a certain sense robust under a particular random perturbation. This new insight leads to a novel randomized dual martingale minimization algorithm that doesn't require nested simulation. As a main feature, in a possibly large family of optimal martingales the algorithm may efficiently select a martingale that is as close as possible to the Doob martingale. As a result, one obtains the dual upper bound for the optimal stopping problem with low variance.
TL;DR: In this article , two risk-neutral measures circumventing the undesirable path dependence feature are proposed, based on the extended Girsanov principle and the Esscher transform, and they also show that such pricing approaches are feasible, and provide numerical implementation schemes.
Abstract: An important challenge regarding the pricing of derivatives is related to the latent nature of volatility. Most studies disregard the uncertain nature of volatility when pricing options; the few authors who account for it typically consider the risk-neutral posterior distribution of the latent volatility. As the latter distribution differs from its physical measure counterpart, this leads to at least two issues: (1) it generates some unwanted path dependence and (2) it oftentimes requires to simultaneously track the physical and risk-neutral distributions of the latent volatility. This article presents pricing approaches purging such a path-dependence issue. This is achieved by modifying conventional pricing approaches (e.g. the Girsanov transform) to formally recognize the uncertainty about the latent volatility during the pricing procedure. The two proposed risk-neutral measures circumventing the aforementioned undesired path-dependence feature are based on the extended Girsanov principle and the Esscher transform. We also show that such pricing approaches are feasible, and we provide numerical implementation schemes.
TL;DR: In this paper , the forecasting accuracy of simple parametric RiskMetrics type volatility and covariance models, with a focus on ad hoc parameter choice instead of a data-intensive calibration procedure, was evaluated.
Abstract: A plethora of academic papers on generalized autoregressive conditional heteroscedasticity (GARCH) models for bitcoin and other cryptocurrencies have been published in academic journals. Yet few, if indeed any, of these are employed by practitioners. Previous academic studies produce results that are fragmented, confusing and conflicting, so there is no commercial incentive to drive an expensive implementation of complex multivariate GARCH models, which anyway would commonly require more data for calibration than are available in the history of most cryptocurrencies, at least at the daily frequency. Consequently, this paper assesses the forecasting accuracy of simple parametric RiskMetrics type volatility and covariance models, with a focus on ad hoc parameter choice instead of a data-intensive calibration procedure. We provide extensive backtests of hourly and daily Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts that are regarded as best practice in the industry and commonly used for regulatory approval. Our results demonstrate that much simpler models in the exponentially weighted moving average (EWMA) class are just as accurate as GARCH models for VaR and ES forecasting, provided they capture an asymmetric volatility response and a heavy-tailed returns distribution. Moreover, on ranking each model's variance and covariance forecasts using average scores generated from proper univariate and multivariate scoring rules, there is no evidence of superior performance of variance and covariance forecasts generated by GARCH models, using either daily or hourly data.
TL;DR: In this paper , the authors consider two extensions of the traditional approach: first, different dependence structures are modelled by different copulae, such as the Gaussian, Student-t, Normal Inverse Gaussian and Archimedean Copulae; second, different risk measures such as value-at-risk, expected shortfall and spectral risk measures are employed to find the optimal hedge ratio.
Abstract: The introduction of derivatives on Bitcoin enables investors to hedge risk exposures in cryptocurrencies. Because of volatility swings and jumps in cryptocurrency prices, the traditional variance-based approach to obtain hedge ratios may not be suitable for hedgers. In this work, we consider two extensions of the traditional approach: first, different dependence structures are modelled by different copulae, such as the Gaussian, Student-t, Normal Inverse Gaussian and Archimedean copulae; second, different risk measures, such as value-at-risk, expected shortfall and spectral risk measures are employed to find the optimal hedge ratio. Extensive out-of-sample tests using the data from the time period December 2017 until May 2021 give insights in the practice of hedging various cryptos and crypto indices, including Bitcoin, Ethereum, Cardano, the CRIX index and a number of crypto-portfolios. Evidence shows that BTC futures can effectively hedge BTC and BTC-involved indices. This promising result is consistent across different risk measures and copulae except for the Frank copula. On the other hand, we observe complex and diverse dependence structures between non-BTC-related cryptocurrencies and the BTC futures. As a consequence, the hedge performance of non-BTC-related cryptocurrencies is mixed and even suitable for some assets.