High-Order Expansion Based Saddlepoint Approximation Errors of the Heston Stochastic Volatility Model

2021 ◽  
Author(s):  
Jannick Garde Schreiner
Keyword(s):  
Stochastic Volatility ◽  
Saddlepoint Approximation ◽  
High Order ◽  
Stochastic Volatility Model ◽  
Order Expansion ◽  
Volatility Model ◽  
Approximation Errors ◽  
High Order Expansion

Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method

2016 ◽  
Vol 03 (04) ◽  
pp. 1650030
Author(s):  
Mengzhe Zhang ◽  
Leunglung Chan
Keyword(s):  
Stochastic Volatility ◽  
Approximation Method ◽  
Regime Switching ◽  
Saddlepoint Approximation ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Chain Process ◽  
Volatility Model ◽  
Highly Nonlinear ◽  
The Given

Pricing a volatility swap is a highly nonlinear problem. Explicit solutions of the prices of volatility swaps are notoriously difficult to find. In this paper, we consider a saddlepoint approximation method for the valuation of a volatility swap under the Heston’s stochastic volatility model with regime switching. All the values of key parameters in our model are supposed to depend on the states of a continuous time observable Markov chain process. We present a closed-form exact cumulant generating functions (CGFs) of the continuous realized variance. Additionally, an approximated CGF is given. Then we approximate the volatility swaps by the saddlepoint approximation formula which derived from the Fourier inversion representation. The numerical results suggest that the alternative saddlepoint approximation method (ASAP) and the approximated ASAP method could both produce fairly accurate results for the given range of maturities.

A non-Gaussian stochastic volatility model

1998 ◽  
Vol 2 (2) ◽  
pp. 33-47 ◽  
Author(s):  
Yuichi Nagahara ◽  
Genshiro Kitagawa
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Volatility Model ◽  
Non Gaussian
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