We discuss a simple, exactly solvable model of stochastic stock dynamics that incorporates regime switching between healthy and distressed regimes. Using this model, which is analytically tractable, we discuss a way of extracting expected returns for stocks from realized CDS spreads, essentially, the CDS market sentiment about future stock returns. This alpha/signal could be useful in a cross-sectional (statistical arbitrage) context for equities trading.

In this paper we consider two problems on optimal implementation delay of taxation with trade-off for spectrally negative L\'{e}vy insurance risk processes. In the first case, we assume that an insurance company starts to pay tax when its surplus reaches a certain level $b$ and at the termination time of the business there is a terminal value incurred to the company. The total expected discounted value of tax payments plus the terminal value is maximized to obtain the optimal implementation level $b^*$. In the second case, the company still pays tax subject to an implementation level $a$ but with capital injections to prevent bankruptcy. The total expected discounted value of tax payments minus the capital injection costs is maximized to obtain the optimal implementation level $a^*$. Numerical examples are also given to illustrate the main results in this paper.

This paper presents the solution to a European option pricing problem by considering a regime-switching jump diffusion model of the underlying financial asset price dynamics. The regimes are assumed to be the results of an observed pure jump process, driving the values of interest rate and volatility coefficient. The pure jump process is assumed to be a semi-Markov process on finite state space. This consideration helps to incorporate a specific type of memory influence in the asset price. Under this model assumption, the locally risk minimizing price of the European type path-independent options is found. The F\"{o}llmer-Schweizer decomposition is adopted to show that the option price satisfies an evolution problem, as a function of time, stock price, market regime, and the stagnancy period. To be more precise, the evolution problem involves a linear, parabolic, degenerate and non-local system of integro-partial differential equations. We have established existence and uniqueness of classical solution to the evolution problem in an appropriate class.

This paper investigates the hedging performance of pegged foreign exchange market in a regime switching (RS) model introduced in a recent paper by Drapeau, Wang and Wang (2019). We compare two prices, an exact solution and first order approximation and provide the bounds for the error. We provide exact RS delta, approximated RS delta as well as mean variance hedging strategies for this specific model and compare their performance. To improve the efficiency of the pricing and calibration procedure, the Fourier approach of this regime-switching model is developed in our work. It turns out that: 1 -- the calibration of the volatility surface with this regime switching model outperforms on real data the classical SABR model; 2 -- the Fourier approach is significantly faster than the direct approach; 3 -- in terms of hedging, the approximated RS delta hedge is a viable alternative to the exact RS delta hedge while significantly faster.