scholarly journals A new class of multidimensional Wishart-based hybrid models

2021 ◽  
Author(s):  
Gaetano La Bua ◽  
Daniele Marazzina
Keyword(s):  
Stochastic Volatility ◽  
Hybrid Models ◽  
Pricing Models ◽  
Stochastic Volatility Models ◽  
Market Prices ◽  
New Class ◽  
Volatility Models ◽  
Wishart Processes ◽  
Wishart Process ◽  
Two Hybrid

AbstractIn this article, we present a new class of pricing models that extend the application of Wishart processes to the so-called stochastic local volatility (or hybrid) pricing paradigm. This approach combines the advantages of local and stochastic volatility models. Despite the growing interest on the topic, however, it seems that no particular attention has been paid to the use of multidimensional specifications for the stochastic volatility component. Our work tries to fill the gap: we introduce two hybrid models in which the stochastic volatility dynamics is described by means of a Wishart process. The proposed parametrizations not only preserve the desirable features of existing Wishart-based models but significantly enhance the ability of reproducing market prices of vanilla options.

A comparison of option pricing models

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750024
Author(s):  
Elham Dastranj ◽  
Roghaye Latifi
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Heston Model ◽  
Pricing Models ◽  
Stochastic Volatility Models ◽  
Numerical Examples ◽  
Call Options ◽  
Volatility Models ◽  
Premium Income

Option pricing under two stochastic volatility models, double Heston model and double Heston with three jumps, is done. Firstly, the efficiency of the second model is shown via FFT method, and numerical examples using power call options. Then it is shown that power option yields more premium income under the second model, double Heston with three jumps, than another one.

STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

2020 ◽  
pp. 1-19
Author(s):  
Pengzhan Chen ◽  
Wuyi Ye
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Stochastic Volatility Models ◽  
Period Analysis ◽  
New Class ◽  
Volatility Models ◽  
Volatility Model ◽  
Article Study ◽  
Jump Sizes

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

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