A Revision of the Merton Jump-Diffusion Model: A Simple, Closed-Form Formula

2019 ◽  
Author(s):  
Moawia Alghalith
Keyword(s):  
Closed Form ◽  
Diffusion Model ◽  
Jump Diffusion ◽  
Jump Diffusion Model ◽  
Closed Form Formula

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.

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