International Journal of Theoretical and Applied Finance

This paper develops a model for the bid and ask prices of a European-type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain. A Girsanov theorem for Markov chains is implemented for the change of coefficients, including the diffusion coefficient which cannot be changed by the usual Girsanov theorem for Brownian motion. The price of a European-type asset is then determined using an Esscher transform and a system of partial differential equations. A dynamic programming principle and a maximum/minimum principle associated with the stochastic control problem are then derived to model bid and ask prices. These prices are not quotes of traders or market makers but represent estimates in our model on which reasonable quantities could be traded.

In this paper, the authors estimate portfolio volatilities and use variance−decomposition techniques and Cholesky factorization to construct a portfolio volatility spillover index. Furthermore, the authors show that spillover risks are persistent and much more common than well-known indicators like the turbulence index and the CBOE VIX index might suggest. Moreover, portfolio volatilities show contributions to and from other portfolio volatilities, which indicate elevated financial market interconnectedness and heightened risk. Foreign exchange contributes strong volatility shocks to other portfolios. More importantly, its contribution has a different magnitude and direction after the Global Financial Crisis (GFC) than before depending on the base currency. To show the causality effects of portfolio volatility spillover the authors apply both econometric models and graph theory, demonstrating that the importance is time varying. This requires monitoring and analysis in decision making regarding portfolio management, portfolio construction, and risk management.

We extend the parametric portfolio policies that exploit firm characteristics to optimize portfolios of stocks and are thus based on asset selection. In addition to this, our extension exploits market indicators for market timing purposes (i.e. optimal allocations between stocks and a risk-free asset). We demonstrate the mechanics of the proposed technique in simulation studies. Specifically, we show that the extended approach is able to produce portfolios based on selection and timing that outperform portfolios that only apply selection, when the applied market indicators have sufficient predictive power. In purely demonstrative empirical applications, we illustrate how investors can use our optimization approach using common market indicators.

In this paper, we study a new class of dynamic risk measures for processes. These new risk measures are derived for the portfolio vectors and adapted to a given filtration. By introducing the notion of discount factor, we deeply analyze the property of cash sub-additivity for these risk measures. Furthermore, by expanding the risk position space, we derive the relationship between these new risk measures and the dynamic convex risk measures introduced by Wei & Hu [(2014) Coherent and convex risk measures for portfolios with applications, Statistics & Probability Letters 90, 114–120]. At last, we establish the representation results for them by making full use of the relationship.

This paper studies the valuation of general contingent claims with short selling bans under the equal-risk pricing (ERP) framework proposed in I. Guo & S.-P. Zhu (2017) [Journal of Economic Dynamics and Control 76, 136–151]. In existing literature, analytical pricing formulae were derived in the special case, where the payoff function is monotonic under risk-neutral measures. In this paper, we establish a unified framework for this new pricing approach so that its range of application can be significantly expanded. The results of I. Guo & S.-P. Zhu (2017) [Journal of Economic Dynamics and Control 76, 136–151] are extended to the case of non-monotonic payoffs (such as a butterfly spread option) under risk-neutral measures. We also provide numerical schemes for computing equal-risk prices under other measures such as the original physical measure. Furthermore, we demonstrate how short selling bans can affect the valuation of contingent claims by comparing equal-risk prices with Black–Scholes prices.

Understanding mortgage prepayment is crucial for any financial institution providing mortgages, and it is important for hedging the risk resulting from such unexpected cash flows. Here, in the setting of a Dutch mortgage provider, we propose to include nonlinear financial instruments in the hedge portfolio when dealing with mortgages with the option to prepay part of the notional early. Based on the assumption that there is a correlation between prepayment and the interest rates in the market, a model is proposed which is based on a specific refinancing incentive. The linear and nonlinear risks are addressed by a set of tradeable instruments in a static hedge strategy. We will show that a stochastic model for the notional of a mortgage unveils nonlinear risk embedded in a prepayment option. Based on a calibration of the refinancing incentive on a data set of more than thirty million observations, a functional form of the prepayments is defined, which accurately reflects the borrowers’ behavior. We compare this functional form with a fully rational model, where the option to prepay is assumed to be exercised rationally.

We consider the worst-case scenario portfolio approach, introduced by Korn & Wilmott (2002), in a multi-asset setting, where asset defaults can occur in addition to asset crashes. In our model, the strictly risk-averse investor does not know which asset is affected by the worst-case scenario. Based on a reformulation of the value function we define the set of minimum constant portfolio processes. We prove the existence of such a process that solves the worst-case crash/ default portfolio problem. In particular, we prove the existence of a portfolio process that is optimal for the investor and at the same time makes him/ her indifferent to the time of occurrence of the worst possible crash or default scenario. The optimal portfolios are derived from solutions of non-linear differential equations. Therefore, we construct an algorithmic framework to analyze selected examples. These examples show the importance of adapting the portfolio process when considering such worst-case scenarios in the investment problem.

We consider indifference pricing of contingent claims consisting of payment flows in a discrete-time model with proportional transaction costs and under exponential disutility. This setting covers utility maximization of terminal wealth as a special case. A dual representation is obtained for the associated disutility minimization problem, together with a dynamic procedure for solving it. This leads to efficient and convergent numerical procedures for indifference pricing, optimal trading strategies and shadow prices that apply to a wide range of payoffs, a large range of time steps and all magnitudes of transaction costs.