High-Order Methods for Exotic Options and Greeks Under Regime-Switching Jump-Diffusion Models

2020 ◽  
Vol 13 (2) ◽  
pp. 497-515
Author(s):  
global sci
Keyword(s):  
Regime Switching ◽  
Jump Diffusion ◽  
Diffusion Models ◽  
High Order ◽  
Exotic Options ◽  
High Order Methods

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 Exotic Options under a High-Order Markovian Regime Switching Model

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Wai-Ki Ching ◽  
Tak-Kuen Siu ◽  
Li-Min Li
Keyword(s):  
Regime Switching ◽  
Order Effect ◽  
High Order ◽  
Martingale Measure ◽  
Exotic Options ◽  
Lookback Options ◽  
Path Dependent ◽  
Markovian Regime Switching ◽  
The Impact ◽  
Markovian Regime

We consider the pricing of exotic options when the price dynamics of the underlying risky asset are governed by a discrete-time Markovian regime-switching process driven by an observable, high-order Markov model (HOMM). We assume that the market interest rate, the drift, and the volatility of the underlying risky asset's return switch over time according to the states of the HOMM, which are interpreted as the states of an economy. We will then employ the well-known tool in actuarial science, namely, the Esscher transform to determine an equivalent martingale measure for option valuation. Moreover, we will also investigate the impact of the high-order effect of the states of the economy on the prices of some path-dependent exotic options, such as Asian options, lookback options, and barrier options.

scholarly journals Option pricing under regime-switching jump–diffusion models

2014 ◽  
Vol 256 ◽  
pp. 152-167 ◽  
Author(s):  
Massimo Costabile ◽  
Arturo Leccadito ◽  
Ivar Massabó ◽  
Emilio Russo
Keyword(s):  
Option Pricing ◽  
Regime Switching ◽  
Jump Diffusion ◽  
Diffusion Models
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