Optimal dealer's pricing strategy under regime switching economy

The research examines the optimal behaviour of a single dealer who is faced with a stochastic demand and supply to trade. Their market activities are depicted as the stochastic generation of market orders according to a Markovian Regime Switching Poisson process. The intensities of Bid and Ask orders are assumed to be dependent on the state of the economy and the objective is to effectively describe the temporal microstructure, or moment-to-moment trading activities in asset markets. Using stochastic dynamic programming, we derive the optimal bid and ask prices that maximize the dealer's expected utility of terminal wealth as a function of the state in which they find themself. The relationship of the bid and ask prices to inventory of the dealer, instantaneous variance of return, stochastic arrival of transactions and other variables is examined. Finally, we solve the optimization problem numerically, using a Finite Element Method.2 page(s

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.1 page(s

Analysis of pricing financial derivatives under regime-switching economy

Theoretical thesis.Bibliography: pages103-113.1. Introduction -- 2. A regime-switching binomial model for pricing and risk management of European options -- 3. Ruin contingent life annuities under regime-switching variance gamma process -- 4. Pricing participating products under a generalized and regime-switching jump-diffusion model -- 5. Summary and conclusion.In this thesis we argue that regime-switching models can significantly improve the pricing models for financial derivatives. We use three examples to analyse the valuation of derivative contracts under the Markovian regime-switching framework, namely, 1) a European call option, 2) a Ruin Contingent Life Annuity, and 3) a participating product. Such a regime-switching framework unveils a potent class of models. Throughout the modulation of the model parameters by a Markov chain, they can simultaneously explain the asymmetic leptokurtic features of the returns' distribution, as well as the volatility smile and the volatility clustering effect. The intuition behind regime-switching models is to capture the appealing idea that the macro-economy is subjected to regular, yet unpredictable in time, states, which in turn affects the prices of financial securities.The market considered in this thesis is incomplete in general due to additional sources of uncertainty, particularly the regime-switching risk. Under these market conditions, a perfectly replicating trading strategy does not exist and there is more than one equivalent martingale measure. As a result, a perfect hedge for derivative contracts is impossible and the holder of the financial derivative needs to impose some testable restrictions to price the residual risk. In this study, we argue that a condition that minimizes the elative entropy between the risk-neutral and the historical probability measures is very suitable. Such condition, determines a price for the derivative contract that maximizes an exponential utility function for the holder. For doing so, we either use the Minimum Entropy Martingale Measure or Esscher Transform to choose the equivalent martingale measure.Due to the complexity of the pricing models, stemmed from either the modeling assumptions or the path-dependency of the payoff of the derivatives products, there is no known analytical solution to our problems. We employ different numerical methods in each chapter, depending on the respective modeling framework, to approximate the solutions. We also examine numerically the performance of simple hedging strategies 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.Mode of access: World wide web1 online resource (x, 113 pages

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.10 page(s

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

Purpose: We price regime switching risk, when pricing contingent claims in discrete time nance. In addition, we analyse the risk of market incompleteness under Markovian regime switching framework. Originality: This is the first paper in the literature that prices regime switching risk, when pricing contingent claims in discrete time finance. Abstract: We discuss the pricing and risk management problems of standard European-style options in a Markovian regime-switching CRR binomial model. The market in the model is incomplete, so the no-arbitrage condition is not enough to x a unique pricing kernel, hence, a unique option price. Using the minimal entropy martingale measure, we determine a pricing kernel and derive the corresponding delta hedging strategy. We examine numerically the performance of the 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 will also be discussed. Design/methodology/approach: Using the minimal entropy martingale measure, we determine a pricing kernel and derive the corresponding delta hedging strategy. We examine numerically the performance of the hedging strategy by investigating the terminal distribution of hedging errors and the associated risk measures such as Value at Risk and Expected Shortfall.2 page(s

Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model

In this paper we propose a maximum entropy estimator for the asymptotic distribution of the hedging error for options. Perfect replication of financial derivatives is not possible, due to market incompleteness and discrete-time hedging. We derive the asymptotic hedging error for options under a generalised jump-diffusion model with kernel bias, which nests a number of very important processes in finance. We then obtain an estimation for the distribution of hedging error by maximising Shannon’s entropy subject to a set of moment constraints, which in turn yields the value-at-risk and expected shortfall of the hedging error. The significance of this approach lies in the fact that the maximum entropy estimator allows us to obtain a consistent estimate of the asymptotic distribution of hedging error, despite the non-normality of the underlying distribution of returns

Risk measures and behaviors for bonds under stochastic interest rate models

This paper develops a model for measuring the risk inherent from trading a bond position under some important stochastic interest rate models. We employ the value at risk (VaR) and expected shortfall (ES) as proxies for the extreme risk inherent from trading a bond position. In particular, we concern ourselves with the average tail behavior of the real-world profit/loss distribution for a bond position. We investigate the risk behaviors of a bond position under some stochastic interest rate models including the Merton model, the Vasicek model, and the Cox-Ingersoll-Ross (CIR) model.14 page(s