International Journal of Theoretical and Applied Finance

In this work, we study a dynamic portfolio optimization problem related to pairs trading, which is an investment strategy that matches a long position in one security with a short position in another security with similar characteristics. The relationship between pairs, called a spread, is modeled by a Gaussian mean-reverting process whose drift rate is modulated by an unobservable continuous-time, finite-state Markov chain. Using the classical stochastic filtering theory, we reduce this problem with partial information to an equivalent one with full information and solve it for the logarithmic utility function, where the terminal wealth is penalized by the riskiness of the portfolio according to the realized volatility of the wealth process. We characterize optimal dollar-neutral strategies as well as optimal value functions under full and partial information and show that the certainty equivalence principle holds for the optimal portfolio strategy. Finally, we provide a numerical analysis for a toy example with a two-state Markov chain.

We study a problem of portfolio optimization under a European quantile hedging constraint. More precisely, we consider a class of Markovian optimal stochastic control problems in which two controlled processes must meet a probabilistic shortfall constraint at some terminal date. We denote by $V$ the corresponding value function. Following the arguments introduced in the literature on stochastic target problems, we convert this problem into a state constraint one in which the constraint is defined by means of an auxiliary value function $v$ characterizing the reachable set. This set is therefore not given a priori but is naturally integrated in $v$ solving, in a viscosity sense, a nonlinear parabolic partial differential equation (PDE). Relying on the existing literature, we derive, in the interior of the domain, a Hamilton–Jacobi–Bellman characterization of $V$. However, $v$ involves an additional controlled state variable coming from the diffusion of the probability of reaching the target and belonging to the compact set $[0,1]$. This leads to nontrivial boundaries for $V$ that must be discussed. Our main result is thus the characterization of $V$ at those boundaries. We also provide examples for which comparison results exist for the PDE solved by $V$ on the interior of the domain.

The early exercise premium and the price of an American put option are evaluated by using nonparametric regression on the time to expiration, the moneyness and the volatility of underlying assets. In terms of mean square error (MSE), our nonparametric methods of American put option pricings outperform the existing classical methods for both in-the-sample (1 September 2011–31 January 2012) and out-of-sample (1 September 2012–28 February 2013) testings on the S&P 100 Index (OEX). Our methods have better predictions and more accurate approximations. The Greek letters for both the early exercise premium and the American put option are computed numerically.

We propose an analytical pricing method for stop-loss reinsurance contracts and catastrophe insurance derivatives using a Cox process with jump diffusion Cox–Ingersoll–Ross (CIR) intensity. The expected payoff of these contracts is expressed by the Laplace transform of the integration of the jump diffusion CIR process and the first moment of the aggregate loss. To confirm that the proposed analytical formula provides stable and accurate insurance derivative prices, we simulate them using a full Monte Carlo method compared to those obtained from its theoretical expectation. It shows that it is much faster way to obtain them than the full Monte Carlo method. We also conduct sensitivity analysis by changing the relevant parameters in the loss intensity providing their figures.

Credit valuation adjustment (CVA) pricing models need to be both flexible and tractable. The survival probability has to be known in closed form (for calibration purposes), the model should be able to fit any valid credit default swap (CDS) curve, should lead to large volatilities (in line with CDS options) and finally should be able to feature significant wrong-way risk (WWR) impact. The Cox–Ingersoll–Ross (CIR) model combined with independent positive jumps and deterministic shift (JCIR$++$) is a very good candidate : the variance (and thus covariance with exposure, i.e. WWR) can be increased with the jumps, whereas the calibration constraint is achieved via the shift. In practice however, there is a strong limit on the model parameters that can be chosen, and thus on the resulting WWR impact. This is because only non-negative shifts are allowed for consistency reasons, whereas the upwards jumps of the JCIR$++$ need to be compensated by a downward shift. To limit this problem, we consider the two-side jump model recently introduced by Mendoza-Arriaga and Linetsky, built by time-changing CIR intensities. In a multivariate setup like CVA, time-changing the intensity partly kills the potential correlation with the exposure process and destroys WWR impact. Moreover, it can introduce a forward looking effect that can lead to arbitrage opportunities. In this paper, we use the time-changed CIR process in a way that the above issues are avoided. We show that the resulting process allows to introduce a large WWR effect compared to the JCIR$++$ model. The computation cost of the resulting Monte Carlo framework is reduced by using an adaptive control variate procedure.

This paper provides an investigation of the effects of an investment’s return moments on drawdown-based measures of risk, including Maximum Drawdown (MDD), Conditional Drawdown (CDD), and Conditional Expected Drawdown (CED). Additionally, a new end-of-period drawdown measure is introduced, which incorporates a psychological aspect of risk perception that previous drawdown measures had been unable to capture. While simulation results indicate many similarities in the first and second moments, skewness and kurtosis affect different drawdown measures in radically different ways. Thus, users should assess whether their choice of drawdown measure accurately reflects the kind of risk they want to measure.

We look at the economic significance and at the robustness of the new-generation, tent-shaped return-predicting factors in US Treasuries. We find that, in itself, the precise tent shape is neither robust nor important for predictability. However, we explain why the high number of regressors needed to build a tent factor are required for high predictability, and we provide an economic interpretation for the finding.