Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Drawdowns preceding rallies in the Brownian motion model

We study drawdowns and rallies of Brownian motion. A rally is defined as the difference of the present value of the Brownian motion and its historical minimum, while the drawdown is defined as the difference of the historical maximum and its present value. This paper determines the probability that a drawdown of a units precedes a rally of b units. We apply this result to examine stock market crashes and rallies in the geometric Brownian motion model.     

Forecasting stock market returns over multiple time horizons

In this paper, we seek to demonstrate the predictability of stock market returns and explain the nature of this return predictability. To this end, we introduce investors with different investment horizons into the news-driven, analytic, agent-based market model developed in Gusev et al. [Algo. Finance, 2015, 4, 5–51]. This heterogeneous framework enables us to capture dynamics at multiple timescales, expanding the model’s applications and improving precision. We study the heterogeneous model theoretically and empirically to highlight essential mechanisms underlying certain market behaviours, such as transitions between bull and bear markets and the self-similar behaviour of price changes. Most importantly, we apply this model to show that the stock market is nearly efficient on intraday timescales, adjusting quickly to incoming news, but becomes inefficient on longer timescales, where news may have a long-lasting nonlinear impact on dynamics, attributable to a feedback mechanism acting over these horizons. Then, using the model, we design algorithmic strategies that utilize news flow, quantified and measured, as the only input to trade on market return forecasts over multiple horizons, from days to months. The backtested results suggest that the return is predictable to the extent that successful trading strategies can be constructed to harness this predictability.     

Investment strategies in the long run with proportional transaction costs and a HARA utility function

We consider an agent who invests in a stock and a money market in order to maximize the asymptotic behaviour of expected utility of the portfolio market price in the presence of proportional transaction costs. The assumption that the portfolio market price is a geometric Brownian motion and the restriction to a utility function with hyperbolic absolute risk aversion (HARA) enable us to evaluate interval investment strategies. It is shown that the optimal interval strategy is also optimal among a wide family of strategies and that it is optimal also in a time changed model in the case of logarithmic utility.     

Analytic option pricing and risk measures under a regime-switching generalized hyperbolic model with an application to equity-linked insurance

Option pricing and managing equity linked insurance (ELI) require the proper modeling of stock return dynamics. Due to the long duration nature of equity-linked insurance products, a stock return model must be able to deal simultaneously with the preceding stylized facts and the impact of market structure changes. In response, this article proposes stock return dynamics that combine Lévy processes in a regime-switching framework. We focus on a non-Gaussian, generalized hyperbolic distribution. We use the most popular linked equity of ELIs, the S&P 500 index, as an example. The empirical study verifies that the proposed regime-switching generalized hyperbolic (RSGH) model gives the best fit to data. In investigating the effects of stock return modeling on pricing and risk management for financial contracts, we derive the characteristic function, embedded option price, and risk measure of equity-linked insurance analytically. More importantly, we demonstrate that the regime-switching generalized hyperbolic (RSGH) model is realistic and can meet the stylistic facts of stock returns, which in turn can be employed in option pricing and risk management decisions.     

Minimizing the Probability of Ruin When Consumption is Ratcheted

Abstract

We assume that an agent’s rate of consumption is ratcheted; that is, it forms a nondecreasing process. We assume that the agent invests in a financial market with one riskless and one risky asset, with the latter’s price following geometric Brownian motion as in the Black-Scholes model. Given the rate of consumption, we act as financial advisers and find the optimal investment strategy for the agent who wishes to minimize his probability of ruin. To solve this minimization problem, we use techniques from stochastic optimal control.     

A PDE approach for risk measures for derivatives with regime switching

This paper considers a partial differential equation (PDE) approach to evaluate coherent risk measures for derivative instruments when the dynamics of the risky underlying asset are governed by a Markov-modulated geometric Brownian motion (GBM); that is, the appreciation rate and the volatility of the underlying risky asset switch over time according to the state of a continuous-time hidden Markov chain model which describes the state of an economy. The PDE approach provides market practitioners with a flexible and effective way to evaluate risk measures in the Markov-modulated Black–Scholes model. We shall derive the PDEs satisfied by the risk measures for European-style options, barrier options and American-style options.      

International capital asset pricing: Evidence from options

We study the risk dynamics and pricing in international economies through a joint analysis of the time-series returns and option prices on three equity indexes underlying three economies: the S&P 500 Index of the United States, the FTSE 100 Index of the United Kingdom, and the Nikkei-225 Stock Average of Japan. We develop an international capital asset pricing model, under which the return on each equity index is decomposed into two orthogonal jump-diffusion components: a global component and a country-specific component. We apply separate stochastic time changes to the two components so that stochastic volatility can come from both global and country-specific risks. For each economy, we assign separate market prices for the two return risk components and the two volatility risk components. Under this specification, we obtain tractable option pricing solutions. Model estimation reveals several interesting insights. First, global and country-specific return and volatility risks show different dynamics. Global return movements contain a larger discontinuous component, and global return volatility is more persistent than the country-specific counterparts. Second, investors charge positive prices for global return risk and negative prices for volatility risk, suggesting that investors are willing to pay positive premiums to hedge against downside global return movements and upside volatility movements. Third, the three economies contain different risk profiles and also price risks differently. Japan contains the largest idiosyncratic risk component and smallest global risk component. Investors in the Japanese market also price more heavily against future volatility increases than against future market downfalls.     

A duscrete-time model of high-frequency stock returns

A model of intraday financial time series is developed. The model is a dynamic factor model consisting of two equations. First, a rate of return of a ‘stock’ in a single day is assumed to be generated by serveral common factors plus some additive erros (‘intraday equation’). Secondly, the joint distribution of those common factors is assumed to depend on the hidden state of the day, which fluctuates according to a Markov chain (‘day-by-day equation’). Together the equations compose a hidden Markov model.

We investigate properties of the model. Among them is a central limit theorem for cumulative returns, which agrees with the well-known empirical phenomenon in the stock markets that the distributions of longer-horizon returns are closer to the normal. We propose a two-step procedure consisting of the method of principal components and the EM algorithm to estimate the model parameters as well as the unboservable states. In addition, we propose a procedure for predicting intraday returns. Finally, the model is fitted to empirical data, the Standard&Poors 500 Index 5 min return data, to see if the model is capable of describing intraday movements of the index.     

Stock market volatility and equity returns: Evidence from a two-state Markov-switching model with regressors

This paper proposes a two-state Markov-switching model for stock market returns in which the state-dependent expected returns, their variance and associated regime-switching dynamics are allowed to respond to market information. More specifically, we apply this model to examine the explanatory and predictive power of price range and trading volume for return volatility. Our findings indicate that a negative relation between equity market returns and volatility prevails even after having controlled for the time-varying determinants of conditional volatility within each regime. We also find an asymmetry in the effect of price range on intra- and inter-regime return volatility. While price range has a stronger effect in the high volatility state, it appears to significantly affect only the transition probabilities when the stock market is in the low volatility state but not in the high volatility state. Finally, we provide evidence consistent with the ‘rebound’ model of asset returns proposed by Samuelson (1991), suggesting that long-horizon investors are expected to invest more in risky assets than short-horizon investors.     

Volatility transmission in the UK equity market

In this study, the three-factor model of Fama and French and the ‘characteristic model’ of Daniel and Titman are tested using the French Stock Market. Stocks are ranked by size and book to market ratio and then by ex-ante β, HML or SMB loadings. Based on average returns, results reject the factor model with ‘characteristic balanced’ portfolios. In contrast, in time-series regressions, results are consistent with the factor pricing model and inconsistent with the characteristic-based pricing model. Because the value premium is small, conclusions must be interpreted carefully. However, size and market premiums allow more powerful tests of the two models.     

Red chips or H shares: which China-backed securities process information the fastest?

This study examines the information flow between China-backed securities, namely H shares, red chips, Shanghai and Shenzhen listed common shares. We document several findings. We find that an exponential generalized autoregressive conditional heteroscedasticity in mean (EGARCH-M) model appears to describe adequately the return process of the China-backed securities. Our empirical findings show that both H shares and red chips (which are listed in Hong Kong) are more sensitive to ‘good’ news than ‘bad’ news, while stocks listed in the China market are more sensitive to ‘bad’ news than ‘good’ news. Using a multivariate EGARCH-M model, we have found significant return and volatility spillover effects among the China-backed securities. Our study indicates that the red chips appear to spread information to other China-backed markets ‘directly’ or ‘indirectly’. The results imply that the red chip market processes information faster than the other markets.     

Predictability of stock markets with disequilibrium trading

This paper analyses the predictability of a hypothetical market with freely negotiated prices on which exists a censoring of one-period returns which are in excess of an arbitrary level (‘floor’ and ‘ceiling’). It is shown that the expected value of returns (adjusted for drift) conditional on last period information regarding the censoring are equal to zero (and therefore the market is not predictable in mean) if there is no intertemporal spillover on the market. A simple simulation model is proposed and applied for the analysis of the effects of intertemporal and cross-spillovers resulting from quantity constraints. Statistical predictability tests are proposed, based on the corrected Student-t statistic of a regression of returns of some information concerning the previous censoring. An illustrative empirical analysis of six main time series of returns on the Warsaw Stock Exchange confirms their ex-ante, but not ex-post, predictability.     

A new closed-form formula for pricing European options under a skew Brownian motion

In this paper, we present a new pricing formula based on a modified Black–Scholes (B-S) model with the standard Brownian motion being replaced by a particular process constructed with a special type of skew Brownian motions. Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options.” The European Journal of Finance 13 (6): 523–544] have worked on this model, the results they obtained are incorrect. In this paper, not only do we identify precisely where the errors in Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options”. The European Journal of Finance 13 (6): 523–544] are, we also present a new closed-form pricing formula based on a newly proposed equivalent martingale measure, called ‘endogenous risk neutral measure’, by which only endogenous risks should and can be fully hedged. The newly derived option pricing formula takes the B-S formula as a special case and it does not induce any significant additional burden in terms of numerically computing option values, compared with the effort involved in computing the B-S formula.     

Second order approximations for limit order books

In this paper, we derive a second order approximation for an infinite-dimensional limit order book model, in which the dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator (e.g. the volume standing at the top of the book). We study the fluctuations of the price and volume process relative to their first order approximation given in ODE–PDE form under two different scaling regimes. In the first case, we suppose that price changes are really rare, yielding a constant first order approximation for the price. This leads to a measure-valued SDE driven by an infinite-dimensional Brownian motion in the second order approximation of the volume process. In the second case, we use a slower rescaling rate, which leads to a non-degenerate first order approximation and gives a PDE with random coefficients in the second order approximation for the volume process. Our results can be used to derive confidence intervals for models of optimal portfolio liquidation under market impact.     

Deviations from Fundamentals in US and EU Stock Markets: A Comparative Analysis

Abstract

A ‘two-stage growth’ discounted cash flow (DCF) model is built to test whether changes in the underlying market fundamentals help to explain movements in stock prices. Empirical results on two samples of US and EU stocks show that the ‘fundamental’ earning price ratio (E/P) explains a significant share of cross-sectional variation of the observed E/P, this impact being stronger in the US market. It is also found that: (i) the fundamental component of the E/P has superior explanatory power than simpler measures of expected earnings growth; (ii) ‘non-fundamental’ components, interpreted as signals reducing asymmetric information (such as firm size, the number of forecasts and the chartist momentum), mitigate the role of the fundamentals; (iii) current deviations from the fundamentals are affected by ex post adjustment of publicly available information in the EU sample. It is argued that differences in regulatory environments and in the composition of investors between the US and EU financial systems may help to explain these comparative findings. Results appear consistent with the ‘market integrity hypothesis’ postulating that reliance on publicly observable fundamentals is higher when insider trading is lower.     

Corporate social responsibility reports: topic analysis and big data approach

ABSTRACT

This paper performs topic modeling using all publicly available CSR (Corporate Social Responsibility) reports for all constituent firms of the major stock market indices of 15 industrialized countries included in MSCI Europe for the sample period from 1999 to 2016. Our text mining results and LDA analyses indicate that ‘employees safety’, ‘employees training support’, ‘carbon emission’, ‘human right’, ‘efficient power’, and ‘healthcare medicines’ are the common topics reported by publicly listed companies in Europe and the UK. There is a clear sector bias with industrial firms emphasizing ‘employee safety’, Utilities concentrating on ‘efficient power’ while consumer discretionary and consumer staples highlighting ‘food waste’ and ‘food packaging.’ To produce these results, we used a battery of python code to organize the hundreds of reports downloaded from Bloomberg and the internet, the latest R-algorithm to estimate LDA (Latent Dirichlet Allocation) model and the LDAvis interactive tool to visualize and refine the LDA model.     

Log-normal continuous cascade model of asset returns: aggregation properties and estimation

Multifractal models and random cascades have been successfully used to model asset returns. In particular, the log-normal continuous cascade is a parsimonious model that has proven to reproduce most observed stylized facts. In this paper, several statistical issues related to this model are studied. We first present a quick, but extensive, review of its main properties and show that most of these properties can be studied analytically. We then develop an approximation theory in the limit of small intermittency λ²???1, i.e. when the degree of multifractality is small. This allows us to prove that the probability distributions associated with these processes possess some very simple aggregation properties across time scales. Such a control of the process properties at different time scales allows us to address the problem of parameter estimation. We show that one has to distinguish two different asymptotic regimes: the first, referred to as the ‘low-frequency asymptotics’, corresponds to taking a sample whose overall size increases, whereas the second, referred to as the ‘high-frequency asymptotics’, corresponds to sampling the process at an increasing sampling rate. The first case leads to convergent estimators, whereas in the high-frequency asymptotics, the situation is much more intricate: only the intermittency coefficient λ² can be estimated using a consistent estimator. However, we show that, in practical situations, one can detect the nature of the asymptotic regime (low frequency versus high frequency) and consequently decide whether the estimations of the other parameters are reliable or not. We apply our results to equity market (individual stocks and indices) daily return series and illustrate a possible application to the prediction of volatility and conditional value at risk.