scholarly journals Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Shican Liu ◽  
Yu Yang ◽  
Hu Zhang ◽  
Yonghong Wu
Keyword(s):  
Closed Form ◽  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Strike Price ◽  
Transform Method ◽  
Variance Swap ◽  
Continuous Sampling ◽  
Jump Diffusion Model ◽  
Pricing Formula

This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock’s dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis.

Option Pricing in a Jump-Diffusion Model with Regime Switching

2009 ◽  
Vol 39 (2) ◽  
pp. 515-539 ◽  
Author(s):  
Fei Lung Yuen ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Mathematical Finance ◽  
Extended Model ◽  
Exotic Options ◽  
Switching Model ◽  
Jump Diffusion Model ◽  
Trinomial Tree ◽  
Tree Method

AbstractNowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

scholarly journals Pricing Participating Products under a Generalized Jump-Diffusion Model

2008 ◽  
Vol 2008 ◽  
pp. 1-30 ◽  
Author(s):  
Tak Kuen Siu ◽  
John W. Lau ◽  
Hailiang Yang
Keyword(s):  
Diffusion Model ◽  
Life Insurance ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Martingale Measure ◽  
Practical Implementation ◽  
Switching Models ◽  
Jump Diffusion Model ◽  
Equivalent Martingale ◽  
Markovian Regime Switching

We propose a model for valuing participating life insurance products under a generalized jump-diffusion model with a Markov-switching compensator. It also nests a number of important and popular models in finance, including the classes of jump-diffusion models and Markovian regime-switching models. The Esscher transform is employed to determine an equivalent martingale measure. Simulation experiments are conducted to illustrate the practical implementation of the model and to highlight some features that can be obtained from our model.

scholarly journals FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS

2012 ◽  
Vol 15 (05) ◽  
pp. 1250037 ◽  
Author(s):  
ALESSANDRO RAMPONI
Keyword(s):  
Fourier Transform ◽  
Regime Switching ◽  
Closed Form Solution ◽  
Jump Diffusion ◽  
Form Solution ◽  
Transform Method ◽  
Finite State ◽  
Jump Diffusion Model ◽  
Log Price ◽  
The Fourier Transform

In this paper we consider a jump-diffusion dynamic whose parameters are driven by a continuous time and stationary Markov Chain on a finite state space as a model for the underlying of European contingent claims. For this class of processes we firstly outline the Fourier transform method both in log-price and log-strike to efficiently calculate the value of various types of options and as a concrete example of application, we present some numerical results within a two-state regime switching version of the Merton jump-diffusion model. Then we develop a closed-form solution to the problem of pricing a Forward Starting Option and use this result to approximate the value of such a derivative in a general stochastic volatility framework.

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