Diversified Portfolios with Jumps in a Benchmark Framework

This paper considers diversified portfolios in a sequence of jump diffusion market models. Conditions for the approximation of the growth optimal portfolio (GOP) by diversified portfolios are provided. Under realistic assumptions, it is shown that diversified portfolios approximate the GOP without requiring any major model specifications. This provides a basis for systematic use of diversified stock indices as proxies for the GOP in derivative pricing, risk management and portfolio optimization. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

A Two-Factor Model for Low Interest Rate Regimes

This paper derives a two-factor model for the term structure of interest rates that segments the yield curve in a natural way. The first factor involves modelling a non-negative short rate process that primarily determines the early part of the yield curve and is obtained as a truncated Gaussian short rate. The second factor mainly influences the later part of the yield curve via the market index. The market index proxies the growth optimal portfolio (GOP) and is modelled as a squared Bessel process of dimension four. Although this setup can be applied to any interest rate environment, this study focuses on the difficult but important case where the short rate stays close to zero for a prolonged period of time. For the proposed model, an equivalent risk neutral martingale measure is neither possible nor required. Hence we use the benchmark approach where the GOP is chosen as numeraire. Fair derivative prices are then calculated via conditional expectations under the real world probability measure. Using this methodology we derive pricing functions for zero coupon bonds and options on zero coupon bonds. The proposed model naturally generates yield curve shapes commonly observed in the market. More importantly, the model replicates the key features of the interest rate cap market for economies with low interest rate regimes. In particular, the implied volatility term structure displays a consistent downward slope from extremely high levels of volatility together with a distinct negative skew. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

A Fair Pricing Approach to Weather Derivatives

This paper proposes a consistent approach to the pricing of weather derivatives. Since weather derivatives are traded in an incomplete market setting, standard hedging based pricing methods cannot be applied. The growth optimal portfolio, which is interpreted as a world stock index, is used as a benchmark or numeraire such that all benchmarked derivative price processes are martingales. No measure transformation is needed for the proposed fair pricing. For weather derivative payoffs that are independent of the value of the growth optimal portfolio, it is shown that the classical actuarial pricing methodology is a particular case of the fair pricing concept. A discrete time model is constructed to approximate historical weather characteristics. The fair prices of some particular weather derivatives are derived using historical and Gaussian residuals. The question of weather risk as diversifiable risk is also discussed. 1991 Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: C16, G10, G13     

Understanding the Implied Volatility Surface for Options on a Diversified Index

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts. Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

From the Minimal Entropy Martingale Measures to the Optimal Strategies for the Exponential Utility Maximization: the Case of Geometric Lévy Processes

In this article, we will consider a multi-dimensional geometric L'evy process as a financial market model. We will first determine the minimal entropy martingale measure (MEMM); we will next derive the optimal strategy for the exponential utility maximization of terminal wealth concretely from the representation of the MEMM. JEL Classification: D46, D52, G12 AMS (2000) Subject Classification: 60G44, 60G51, 60G52,60H20, 60J75, 91B16, 91B28, 94A17     

On the law of one price

We consider the standard discrete-time model of a frictionless financial market and show that the law of one price holds if and only if there exists a martingale density process with strictly positive initial value. In contrast to the classical no-arbitrage criteria, this density process may change its sign. We also give an application to the CAPM.Received: November 2003, Mathematics Subject Classification (2000): 60G44JEL Classification: G13, G11Freddy Delbaen: This research was done during the stay of the author at Université de Franche-Comté.     

¿Han sido el IBEX35 y el IPC definiciones financieramente eficientes del portafolio de mercado?

The present paper questions the financial efficiency of the most used market portfolio proxies in Spain and Mexico (IBEX35 and IPC) in order to determine if these can be considered a proper market portfolio proxy. The paper questions if they can be used as “neutrals”, according to Black & Litterman (1992) proposals in portfolio management. For this purpose, two discrete event simulations that use the Markowtiz-Tobin-Sharpe-Linter model (Markowitz, 1987, p.5) are performed with monthly data of the stock members of these indices in a February 2001 to December 2010 time window. The results are compared by using the Sharpe ratio (Sharpe, 1966) and show that the equilibrium assumptions in the market do not hold, leading to conclude that these market portfolio proxies are inefficient.     

Dynamic portfolio optimization across hidden market regimes

Regime-based asset allocation has been shown to add value over rebalancing to static weights and, in particular, reduce potential drawdowns by reacting to changes in market conditions. The predominant approach in previous studies has been to specify in advance a static decision rule for changing the allocation based on the state of financial markets or the economy. In this article, model predictive control (MPC) is used to dynamically optimize a portfolio based on forecasts of the mean and variance of financial returns from a hidden Markov model with time-varying parameters. There are computational advantages to using MPC when estimates of future returns are updated every time a new observation becomes available, since the optimal control actions are reconsidered anyway. MPC outperforms a static decision rule for changing the allocation and realizes both a higher return and a significantly lower risk than a buy-and-hold investment in various major stock market indices. This is after accounting for transaction costs, with a one-day delay in the implementation of allocation changes, and with zero-interest cash as the only alternative to the stock indices. Imposing a trading penalty that reduces the number of trades is found to increase the robustness of the approach.     

Stock market reaction to policy interventions

ABSTRACT

We analyse stock price reactions to the announcements of monetary and fiscal policy actions in 12 stock exchanges worldwide between 1 June 2007 and 30 June 2012. While past papers have analysed the effect of policy interventions focusing on monetary policy actions (e.g. Ricci 2015), our paper focuses on stock indices either capturing the whole stock market or various industries. By estimating abnormal stock reactions around the announcement date, we show that (1) stock industry indices react to policy interventions in a different manner than the broad stock index does; (2) stock returns react negatively to restriction measures for general and non-banking sector indices; and (3) stock reaction to expansionary measures was stronger at the beginning of the financial crisis.     

The Halloween Effect and Japanese Equity Prices: Myth or Exploitable Anomaly

Bouman and Jacobsen (American Economic Review 92(5), 1618–1635, 2002) examine monthly stock returns for major world stock markets and conclude that returns are significantly lower during the May–October periods versus the November–April periods in 36 of 37 markets examined. They argue that, in general, the Halloween strategy outperforms the buy and hold strategy thereby casting doubt on the validity of the efficient market paradigm. More recently, Maberly and Pierce (Econ Journal Watch 1(1), 29–46, 2004) re-examine the evidence for U.S. equity prices and conclude that Bouman and Jacobsen’s results are not robust to alternative model specifications. Extending prior research, this paper examines the robustness of the Halloween strategy to alternative model specifications for Japanese equity prices. The Halloween effect is concentrated in the period prior to the introduction of Nikkei 225 index futures in September 1986. After the internationalization of Japanese financial markets in the mid-1980s, the Halloween effect disappears.JEL classification: G14, G15     

Interest Rate Risk of European Financial Corporations

We investigate the interest rate exposure of large European financial corporations' equity returns. For the period from January 1982 to March 1995 we estimate multifactor index models to examine the sensitivity of equity returns to market index returns and domestic as well as global interest rate movements. In addition, we specify an APT‐model to test whether an exposure to interest rate movements is rewarded in the cross‐section of expected returns. In the four European markets both domestic and global interest rate shifts constitute driving forces of stock returns beyond the influence of the domestic market indices. However, the exposure to interest rate movements does not seem to be rewarded in the same fashion among the markets.     

‘Slow-burn’ spillover and ‘fast and furious’ contagion: a study of international stock markets

‘Fast and furious’ contagion across capital markets is an important phenomenon in an increasingly integrated financial world. Different from ‘slow-burn’ spillover or interdependence among these markets, ‘fast and furious’ contagion can occur instantly. To investigate this kind of contagion from the US, Japan and Hong Kong to other Asian economies, we design a research strategy to capture fundamental interdependence, or ‘slow-burn’ spillover, among these stock markets as well as short-term departures from this interdependence. Based on these departures, we propose a new contagion measure which reveals how one market responds over time to a shock in another market. We also propose international portfolio analysis for contagion via variance decomposition from the portfolio manager’s perspective. Using this research strategy, we find that the US stock market was cointegrated with the Asian stock markets during four specific periods from 3 July 1997 to 30 April 2014. Beyond this fundamental interdependence, the shocks from both Japan and Hong Kong have significant ‘fast and furious’ contagion effects on other Asian stock markets during the US subprime crisis, but the shocks from the US have no such effects.     

Fundamentalists clashing over the book: a study of order-driven stock markets

Abstract

Agent-based models of market dynamics must strike a compromise between the structural assumptions that represent the trading mechanism and the behavioural assumptions that describe the rules by which traders make their decisions. We present a structurally detailed model of an order-driven stock market and show that a minimal set of behavioural assumptions suffices to generate a leptokurtic distribution of short-term log-returns. This result supports the conjecture that the emergence of some statistical properties of financial time series is due to the microstructure of stock markets.     

Incentives of Stock Option Based Compensation

We introduce explicitly the effort as a choice variable in a continuous time utility maximisation framework of an executive who is partly compensated with stock options. We solve the model in the case where the executive is not allowed to trade in the company’s stock but is able to achieve a partial insurance through trading in a correlated market portfolio. We define the executive’s value of the options through a certainty equivalence approach both in the case of European call options and non-standard capped stock options and study the behaviour of the reservation price as relevant parameters change.JEL Classification: G13, G30, G32, J33, M12     

Asymmetric information and imperfect competition in a continuous time multivariate security model

This paper deals with the problem of price formation in a market with asymmetric information and several risky assets. We then extend the multivariate security model of Caballé and Krishnan (1994) to a continuous time framework, and general utility function. Our model enables us to observe some results which are specific to multi security markets such as Giffen effect. An application of the main result will be the non trivial generalizations of the models of Back (1992) and Cho (1997).Mathematics Subject Classification (1991): 49L10, 60G44, 90A15JEL Classification: G11, G12The author would like to thank his supervisor H. Pham, K. Back and an anonymous referee for useful comments and discussions.     

Pricing of index options under a minimal market model with log-normal scaling

Abstract

This paper describes a two-factor model for a diversified market index using the growth optimal portfolio with a stochastic and possibly correlated intrinsic timescale. The index is modelled using a time transformed squared Bessel process with a log-normal scaling factor for the time transformation. A consistent pricing and hedging framework is established by using the benchmark approach. Here the numeraire is taken to be the growth optimal portfolio. Benchmarked traded prices appear as conditional expectations of future benchmarked prices under the real world probability measure. The proposed minimal market model with log-normal scaling produces the type of implied volatility term structures for European call and put options typically observed in real markets. In addition, the prices of binary options and their deviations from corresponding Black–Scholes prices are examined.     

Financial Crisis and Intertemporal Linkages Across the ASEAN-5 Stock Markets

The stock indices of five ASEAN countries, namely, Singapore, Malaysia, Indonesia, Thailand and the Philippines have experienced a structural change after mid-1997 due to the Asian financial crisis, and another shift slightly more than a year later when the markets rebounded. Contemporaneous correlation in stock returns is the strongest and Indonesia leads the movements of the other indices during the crisis. The relative influence of foreign shocks is much more felt during the crisis, as seen in the stronger and longer horizon of responses of all the markets. The stock indices are cointegrated before, but not during the crisis. Price feedbacks between the larger markets of Singapore, Malaysia and Indonesia that existed before the crisis disappear once the crisis is over. Short-run linkages of Malaysia with the other markets have weakened after the crisis. With an increase in the degree of exogeneity of its stock market, contemporaneous co-movements with the other markets have reduced and the causal relationships no longer exist.JEL Classification: G15, F30An earlier draft of this paper was presented at the 11th Annual Conference on Pacific Basin Finance, Economics & Accounting held in Taipei. This paper benefited from the discussions at the conference. We are grateful to two anonymous referees for helpful comments and suggestions which led to further improvement of the paper.     

Forecasting Surrender Rates Using Elliptical Copulas and Financial Variables

A multistage stochastic model to forecast surrender rates for life insurance and pension plans is proposed. Surrender rates are forecasted by means of Monte Carlo simulation after a sequence of GLM, ARMA-GARCH, and copula fitting is executed. The model is illustrated by applying it to age-specific time series of surrender rates derived from pension plans with annuity payments of a Brazilian insurer. In the GLM process, the only macroeconomic variable used as an explanatory variable is the Brazilian real short-term interest rate. The advantage of such a variable is that we can take future market expectation through the current term structure of interest rates. The GLM residuals of each age/gender group are then modeled by ARMA-GARCH processes to generate i.i.d. residuals. The dependence among these residuals is then modeled by multivariate Gaussian and Student's t copulas. To produce a conditional forecast on a stock market index, in our application we used the residuals of an ARMA-GARCH model fitted to the Brazilian stock market index (Ibovespa) returns, which generates one of the marginal distributions used in the dependence modeling through copulas. This strategy is adopted to explain the high and uncommon surrender rates observed during the recent economic crisis. After applying known simulation methods for elliptical copulas, we proceeded backwards to obtain the forecasted distributions of surrender rates by application, in the sequel, of ARMA-GARCH and GLM models. Additionally, our approach produced an algorithm able to simulate multivariate elliptical copulas conditioned on a marginal distribution. Using this algorithm, surrender rates can be simulated conditioned on stock index residuals (in our case, the residuals of the Ibovespa returns), which allows insurers and pension funds to simulate future surrender rates assuming a financial stress scenario with no need to predict the stock market index.     

Asymptotic arbitrage and numéraire portfolios in large financial markets

This paper deals with the notion of a large financial market and the concepts of asymptotic arbitrage and strong asymptotic arbitrage (both of the first kind) introduced in Probab. Theory Appl. 39, 222–229 (1994) and in Finance Stoch. 2, 143–172 (1998). We show that the arbitrage properties of a large market are completely determined by the asymptotic behavior of the sequence of the numéraire portfolios related to small markets. The obtained criteria can be expressed in terms of contiguity, entire separation, and Hellinger integrals, provided that these notions are extended to sub-probability measures. As examples, we consider market models on finite probability spaces, semimartingale models, and diffusion models. We also examine a discrete-time infinite horizon market model with one log-normal stock. This work was supported by Southern Federal University, grant No. 26 “Mathematical Finance” and by RFBR, grant 07-01-00520.