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This chapter calibrates the square‐root jump diffusion (SRJD) model to both the VSTOXX futures term structure and for multiple maturities for the VSTOXX options. It uses DX Analytics which provides flexible modeling capabilities for volatility based derivatives based, among other things, on square‐root diffusions and square‐root jump diffusions. The chapter presents calibration results for three different calibration runs. The first run implements a calibration to a single maturity, the second to two maturities simultaneously while the third run does the same for five maturities of the VSTOXX options. The final run shows the effects of not using penalties for deviations from previous optimal parameters which in general would be used to get smoother parameter time series. The highest average mean‐squared error (MSE) value is observed for the calibration case with one maturity only.

In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion to its needs, explore new business, and engage in capital market investments. This is under the assumption that insurance companies’surplus capital adheres to the classical Cramér-Lundberg model. The capital market is made up of risk-free bonds, equities, and derivatives, with pricing dependent on the underlying stock’s basic price and volatility. To obtain the most profitable expressions and functions for the associated investment strategies and time guarantees, we solve a system of expanded Hamilton–Jacobi–Bellman equations. In addition, we delve into scenarios involving optimal investment and reinsurance issues with no derivatives trading. In the end, we present a few numerical instances to display our findings, demonstrating that the efficient frontier in the case of derivative trading surpasses that in scenarios where derivative trading is absent.

AbstractThis paper addresses the problem of delta-hedging in illiquid markets, where transaction costs, limited depth of the limit order book, and market impact of large trades play a significant role. Classical approaches based on the Black–Scholes model assume continuous trading and infinite liquidity, which leads to significant distortions in practice. To overcome these limitations, we propose a reinforcement learning approach with a risk-averse Bellman operator. As a training environment, we employ an agent-based exchange simulator with support for trading the underlying asset and options, which reproduces the market microstructure and limit order book dynamics. A DeepLOB convolutional encoder is used to extract order book features and capture hidden liquidity characteristics. Numerical experiments show that the proposed method produces a realized PnL distribution centered around zero with lighter tails compared to the classical Black–Scholes delta-hedger. Furthermore, the risk aversion parameter enables control over the trade-off between mean profitability and tail risk management. The results demonstrate the efficiency of the approach and its applicability for constructing robust hedging strategies in illiquid markets.

This article analyses the implications of money illusion for investor behaviour and asset prices in a securities market economy with inflationary fluctuations. We provide a belief-based formulation of money illusion which accounts for the systematic mistakes in evaluating real and nominal quantities. The impact of money illusion on security prices and their dynamics is demonstrated to be considerable even though its welfare cost on investors is small in typical environments. A money-illusioned investor's real consumption is shown to generally depend on the price level, and specifically to decrease in the price level. A general-equilibrium analysis in the presence of money illusion generates implications that are consistent with several empirical regularities. In particular, the real bond yields and dividend price ratios are positively related to expected inflation, the real short rate is negatively correlated with realized inflation, and money illusion may induce predictability and excess volatility in stock returns. The basic analysis is generalized to incorporate heterogeneous investors with differing degrees of illusion.

Indexes of commercial property prices face much scarcer transactions data than housing indexes, yet the advent of tradable derivatives on commercial property places a premium on both high frequency and accuracy of such indexes. The dilemma is that with scarce data a low-frequency return index (such as annual) is necessary to accumulate enough sales data in each period. This paper presents an approach to address this problem using a two-stage frequency conversion procedure, by first estimating lower-frequency indexes staggered in time, and then applying a generalized inverse estimator to convert from lower to higher frequency return series. The two-stage procedure can improve the accuracy of high-frequency indexes in scarce data environments. In this paper the method is demonstrated and analyzed by application to empirical commercial property repeat-sales data.

The aim of this paper is to investigate the impact of fi nancial transaction taxes (FTTs) on the stability of fi nancial markets. This paper presents an agent-based fi nancial market model and simulations in which agents follow technical and fundamental trading rules to determine their speculative investment positions. The model developed by Westerhoff (2009) was chosen for implementation and was extended by FTT and arising transaction costs. Because FTTs may be defi ned in various ways, this paper defi nes assets as tax objects. The model includes direct interactions between speculators, which may lead them to decide to change their trading behavior and addresses a technical and a fundamental strategy of market participants. The results suggest that the modifi ed model has a tendency to stabilize itself in the long term if fundamental trading rules outweigh the technical trading method. This model could be used when bubbles and crashes occur in fi nancial markets. Asset prices would be stabilized because their value targets near the fundamental value and volatility would also be minimized. Setting FTTs at a low rate for market stabilization is important. If FTTs and consequent transaction costs are too high, then the fi nancial system will destabilize and prices will grow without limit. The model described in this paper explores dependence market stability to the extent of FTTs. However, the model should not be interpreted as a model only for the introduction of FTT, but as a general model of transaction costs’ infl uence on the fi nancial market.

Purpose – The purpose of this paper is to provide market risk calculation for an equity-based trading portfolio. Instead of relying on the purely stochastic internal model method which banks currently apply in line with the Basel regulatory requirements, the author also propose including alternative price mechanisms from the financial literature in the regulatory framework. Design/methodology/approach – For this purpose, a financial market model with heterogeneous agents is developed, capturing the realistic feature that parts of the investors do not follow the assumption of no arbitrage, but are motivated by behavioral heuristics instead. Findings – Although both the standard stochastic and the behavioral model are restricted to a calibration including the last 250 trading days, the latter is able to capitalize possible turbulence on financial markets and likewise the well-known phenomenon of excess volatility – even if the last 250 days reflect a non-turbulent market. Practical implications – Thus, including agent-based models in the regulatory framework could create better capital requirements with respect to their level and counter-cyclicality. Originality/value – This in turn could reduce the extent to which bubbles arise, since market participants would have to anticipate comprehensively the costs of such bubbles bursting. Furthermore, a key ratio is deduced from the agent-based construction to lower the influence of speculative derivatives.

Purpose – This paper aims to analyze the statistical characteristics of changes in property forward prices. As highlighted in a survey conducted at the MIT Center for Real Estate in 2006, the relatively weak understanding in their prices is one of the most important barriers in their use. In this context, the analysis of the forward price term structure is essential. Do the short- and long-term forward prices behave similarly? Do property derivatives behave like other derivative assets or other related assets? This study also investigates the lead–lag relationship between spot and forward returns for different maturities. Design/methodology/approach – Using four years and nine months of data on the UK Investment Property Databank (IPD), all property total return swaps are examined. We strip the swaps into their forwards and study their statistical characteristics (the first four moments and their autocorrelation levels). The relationships among the forward contracts, the underlying asset (IPD index and IPD unsmoothed) and other assets (risk-free rate, listed real estate) are explored. Using the Yiu et al. (2005) methodology, the lead–lag relationship between the spot and the forwards is assessed. Findings – The index appears to be significantly less volatile and less efficient, in terms of correlation than its own derivative contracts. Moreover, changes in forward prices are leading indicators of the IPD index. Their risks tend to converge with the implied volatility of the REIT’s operating asset but without being affected by the general stock market risks. Regarding the forward price–discovery function, investors should collect information not only from the spot market but also, maybe primarily, from the derivative market. Originality/value – In this paper, we use a never-exploited database that is relative to the quotes of the UK IPD swaps. It is the first attempt to analyze the statistical characteristics of their changes. Our results show that these prices are clearly superior to the spot series, in terms of risks but without behaving affected by the tyranny of the past values. These findings may conduct to consider new methods to unsmooth current real estate indices. Characterized by a strong sensitivity to the changes in the information set, property derivative-based indicators should lead to increased efficiency in the spot market.

In this chapter we explore the various derivative contracts that could be traded to hedge portfolio‐level asymmetric dependence (AD). Hedging AD directly involves trading multi‐underlying derivative products with exposure to implied correlation skew. We review the various strategies that practitioners use in order to trade implied correlation. We subsequently propose a long–short equity derivative strategy involving corridor variance swaps that provides exposure to aggregate implied AD consistent with the adjusted J statistic. This strategy provides a more direct hedge against the drivers of AD, in contrast to the current practice of simply hedging the effects of AD with volatility derivatives.