Time-Discrete Hedging of Down-and-Out Puts with Overnight Trading Gaps

Hedging down-and-out puts (and up-and-out calls), where the maximum payoff is reached just before a barrier is hit that would render the claim worthless afterwards, is challenging. All hedging methods potentially lead to large errors when the underlying is already close to the barrier and the hedge portfolio can only be adjusted in discrete time intervals. In this paper, we analyze this hedging situation, especially the case of overnight trading gaps. We show how a position in a short-term vanilla call option can be used for efficient hedging. Using a mean-variance hedging approach, we calculate optimal hedge ratios for both the underlying and call options as hedge instruments. We derive semi-analytical formulas for optimal hedge ratios in a Black–Scholes setting for continuous trading (as a benchmark) and in the case of trading gaps. For more complex models, we show in a numerical study that the semi-analytical formulas can be used as a sufficient approximation, even when stochastic volatility and jumps are present.

Change of Persistence in European Electricity Spot Prices

The European Power Exchange has introduced day-ahead auctions and continuous trading spot markets to facilitate the insertion of renewable electricity. These markets are designed to balance excess or lack of power in short time periods, which leads to a large stochastic variability of the electricity prices. Furthermore, the different markets show different stochastic memory in their electricity price time series, which seem to be the cause for the large volatility. In particular, we show the antithetical temporal correlation in the intraday 15 minutes spot markets in comparison to the day-ahead hourly market. We contrast the results from Detrended Fluctuation Analysis (DFA) to a new method based on the Kramers–Moyal equation in scale. For very short term (< 12 hours), all price time series show positive temporal correlations (Hurst exponent H > 0.5) except for the intraday 15 minute market, which shows strong negative correlations (H < 0.5). For longer term periods covering up to two days, all price time series are anti-correlated (H < 0.5).

The Study of a Wealth Distribution Model with a Linear Collision Kernel

The wealth substitution rate, which describes the substitution relationship between agents’ investment in wealth, is introduced into the collision kernel of the Boltzmann equation to study wealth distribution. Using the continuous trading limit, the Fokker–Planck equation is derived and the steady-state solution is obtained. The results show that the inequality of wealth distribution decreases as the wealth substitution rate increases under certain assumptions. The wealth distribution has a bimodal shape if the wealth substitution rate does not equal one.

Intraday analysis of regulation change in microstructure: evidence from an emerging market

PurposeThis study investigates the impact of simultaneously replacing both midday single-price call auction and lunch break with multi-price continuous trading on intraday volatility–volume patterns as well as the intraday volatility–volume nexus.Design/methodology/approachThe analysis utilises 150 m tick-by-tick transaction data related to 333 stocks traded on Borsa Istanbul Equity Market covering a period of 2 months prior to and following the change. In addition to graphic comparisons, the study uses difference in mean tests, panel-fixed generalized least squares (GLS), panel-random GLS and random-effects linear models with AR(1) disturbance regression estimations.FindingsThe results show that intraday volatility and trading volume form an inverse J-shape and are positively correlated. It is observed that the implementation of the regulation change decreased intraday volatility and increased trading volume. Additionally, the results indicate a negative volatility–liquidity and a positive volume–liquidity relationship, supporting the mixture of distribution hypothesis.Research limitations/implicationsEnhanced market efficiency provides greater opportunity for investment and risk management. Investors can benefit from the findings on the intraday volatility–volume nexus, which is an indicator of informed trading, and regulatory authorities can use volume to oversight volatility.Originality/valueThis very rare regulation change of the simultaneous replacement of the lunch break and midday call auction with continuous trading is investigated in the context of intraday volume and volatility. This study also expands upon some important findings on the volume–volatility nexus for the Turkish Stock Market.

Using Statistical Model to Study the Daily Closing Price Index in the Kingdom of Saudi Arabia (KSA)

Classification in statistics is usually used to solve the problems of identifying to which set of categories, such as subpopulations, new observation belongs, based on a training set of data containing information (or instances) whose category membership is known. The article aims to use the Gaussian Mixture Model to model the daily closing price index over the period of 1/1/2013 to 16/8/2020 in the Kingdom of Saudi Arabia. The daily closing price index over the period declined, which might be the effect of corona virus, and the mean of the study period is about 7866.965. The closing price is the last regular deal that took place during the continuous trading period. If there are no transactions on the stock during the day, the closing price is the previous day’s closing price. The closing auction period comes after the continuous trading period (from 3 : 00 PM to 3 : 10 PM), during which investors can enter by buying and selling the stocks at this period. The experimental results show that the best mixture model is E (equal variance) with three components according to the BIC criterion. The expectation-maximization (EM) algorithm converged in 2 repetitions. The data source is from Tadawul KSA.

Stock returns are not always from the same distribution: Evidence from the Great Recession

Portfolio allocation strategies, and notably the mean-variance approach, use past returns to assign optimal weights. Even though both past and expected returns should come from the same distribution, a formal test of whether this holds in practice has not been conducted yet. Thus, the study examines if the daily returns of 242 companies with continuous trading in the S&P index come from the same distribution using the Kolmogorov-Smirnov, Cramér-Von Mises, and Wilcoxon rank-sum tests. The tests suggest that generally stock returns do come from the same distribution. However, the hypothesis is rejected during the Great Recession, with the rejection rate increasing as the forecast horizon increased. The rejection rate, using an array of macroeconomic variables, is found to record high levels of persistence. Although macroeconomic variables were not found to be statistically significant determinants of the rejection rate, market distress has a small but significant effect.

A Stochastic MPC Based Energy Management System for Simultaneous Participation in Continuous and Discrete Prosumer-to-Prosumer Energy Markets

This article studies the exchange of self-produced renewable energy between prosumers (and with pure end consumers), through the discrete trading of energy packages and proposes a framework for optimizing this exchange. In order to mitigate the imbalances derived from discrepancies between production and consumption and their respective forecasts, the simultaneous continuous trading of instantaneous power quotas is proposed, giving rise to a time-ahead market running in parallel with a real-time one. An energy management system (EMS) based on stochastic model predictive control (SMPC) simultaneously determines the optimal bidding strategies for both markets, as well as the optimal utilisation of any energy storage system (ESS). Simulations carried out for a heterogeneous group of agents show that those with SMPC-EMS achieve savings of between 3% and 15% in their energy operation economic result. The proposed structures allows the peer-to-peer (P2P) energy trading between end users without ESS and constitute a viable alternative to avoid deviation penalties in secondary regulation markets.