Analytical pricing of vulnerable options under a generalized jump-diffusion model

In this paper we propose a model to price European vulnerable options. We formulate their credit risk in a reduced form model and the dynamics of the spot price in a completely random generalized jump-diffusion model, which nests a number of important models in finance. We obtain a closed-form price for the vulnerable option by (1) determining an equivalent martingale measure, using the Esscher transform and (2) manipulating the pay-off structure of the option four further times, by using the Esscher-Girsanov transform

Optimal Bid-Ask Spread in Limit-Order Books under Regime Switching Framework

This paper advocates a regime-switching model to capture the risk of structural changes in the economy, when determining the optimal bid-ask spread in limit order books. In our model, the market-maker faces an inventory risk due to the diffusive nature of the stocks' mid-price and a transactions risk due to a Poisson arrival of market "buy" and "sell" orders. We propose that the intensity of the orders depend on the state of the economy, and in the event of a structural change, market makers will face different intensity of order flows, reflecting the new market conditions. In our model, the dealer is a wealth maximizing agent who dynamically manages his portfolio. We employ Hamilton-Jacobi-Bellman equation for the dynamic programming problem, and we solve the problem numerically using the Galerkin method

Pricing and managing risks of European-style options in a Markovian regime-switching binomial model

We discuss the pricing and risk management problems of standard European-style options in a Markovian regime-switching binomial model. Due to the presence of an additional source of uncertainty described by a Markov chain, the market is incomplete, so the no-arbitrage condition is not sufficient to fix a unique pricing kernel, hence, a unique option price. Using the minimal entropy martingale measure, we determine a pricing kernel. We examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as Value at Risk and Expected Shortfall. The impacts of the frequency of re-balancing the hedging portfolio and the transition probabilities of the modulating Markov chain on the quality of hedging are also discussed

Pricing and managing risks of ruin contingent life annuities under regime switching variance gamma process

We propose a model for valuing ruin contingent life annuities under the regime-switching variance gamma process. The Esscher transform is employed to determine the equivalent martingale measure. The PIDE approach is adopted for the pricing formulation. Due to the path dependency of the payoff of the insurance product and the non-existence of a closed-form solution for the PIDE, the finite difference method is utilized to numerically calculate the value of the product. To highlight some practical features of the product, we present a numerical example. Finally, we examine numerically the performance of a simple hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as the value at risk and the expected shortfall. The impacts of the frequency of re-balancing the hedging portfolio on the quality of hedging are also discussed

Pricing equity linked annuities under regime switching generalized gamma process

We propose a model for valuing equity linked annuity (ELA) products under a generalized gamma model with a Markov-switching compensator. We suppose that the market interest rate and all the parameters of the underlying reference portfolio switch over time according to the state of an economy, which is modelled by a continuous-time Markov chain. The model considered here can provide market practitioners with flexibility in modelling the dynamics of the reference portfolio. We price the ELA by pricing its embedded options, for which we employ the regime-switching version of Esscher transform to determine the pricing kernel. A system of coupled partial-differential-integral equations satisfied by the embedded option prices is derived. Simulation results of the model have been presented and discussed

Pricing participating products with Markov-modulated jump--diffusion process: An efficient numerical PIDE approach

We propose a model for the valuation of participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. The Esscher transform is employed to determine an equivalent martingale measure in the incomplete market. The results are further manipulated through the utilization of the change of numeraire technique to reduce the dimensions of the pricing formulation. This paper is the first that extends the technique for a generalized jump-diffusion process with a Markov-switching kernel-biased completely random measure, which nests a number of important and popular models in finance. A numerical analysis is conducted to illustrate the practical implications

Dynamic correlation of stock and bond returns in Asian markets with determinants of macroeconomic conditions and market risk

This paper examines the dynamic correlation between stock and bond returns for five advanced Asian markets. Test Statistics suggest that co-movements of stock-bond returns are time-varying over the last 15 years in most of the countries in our sample. The stock-bond correlations are positively correlated with Consumer Price Index (CPI) and Gross Domestic Product (GDP) expectations respectively. The results show that during a period of high stock market volatility measured by the respective implied volatilities and conditional variances, there is a divergence between the stock and bond prices movement. We also found that in advanced Asian economies, there is a significant positive correlation between stock-bond returns and bond market risk as measured by the conditional variance of bond returns

Optimal overbooking strategies in the airlines using dynamic programming approach in continuous time

We propose a novel approach to solve the long-standing challenge of airline overbooking management. We solve the problem using dynamic programming with an industrial setting characterised as near-to-perfect competition where airlines strategically overbook their flights to control their market shares instead of a more conventional setting with a revenue maximisation. The theorised optimisation problem is constructed using a terminal utility criterion and with the application of the Hamilton-Jacobi-Bellman equation. The analysis expands on four most commonly applicable overbooking strategies, and the results provide guidance on how airlines can choose a strategy to pursue an optimisation solution best suited to them

Forecasting spikes in electricity return innovations

This paper evaluates the accuracy of several hundred one-day-ahead value at risk (VaR) forecasts for predicting Australian electricity returns. We propose a class of observation-driven time series models referred to as asymmetric exponential generalised autoregressive score (AEGAS) models. The mechanism to update the parameters over time is provided by the scaled score of the likelihood function in the AEGAS model. Based on this new approach, the results provide a unified and consistent framework for introducing time-varying parameters in a wide class of non-linear models. The Australian energy markets is known as one of the most volatile and, when compared to some well-known models in the recent literature as benchmarks the fitting and forecasting results demonstrate the superior performance and considerable flexibility of proposed model for electricity markets

A non-parametric estimation for implied volatility

We provide a non-parametric method for stochastic volatility modelling. Our method allows the implied volatility to be governed by a general Levy-driven Ornstein{Uhlenbeck process, the density function of which is hidden to market participants. Using discrete-time observation we estimate the density function of the stochastic volatility process via developing a cumulant M-estimator for the Levy measure. In contrast to other non-parametric estimators (such as kernel estimators), our estimator is guaranteed to be of the correct type. We implement this method with the aid of a support-reduction algorithm, which is an ecient iterative unconstrained optimisation method. For the empirical analysis, we use discretely observed data from two implied volatility indices, VIX and VDAX. We also present an out-of-sample test to compare the performance of our method with other parametric models