Stochastic Volatility Model With Correlated Jump Sizes and Independent Arrivals

Abstract

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.

Jump activity analysis of the equity index and the corresponding volatility: Evidence from the Chinese market

“…In other words, the maximum and minimum jump size values are all in period I. This is a very intuitive phenomenon by which dramatic changes occur in the financial crisis (e.g., Chen & Ye, 2020 found that the absolute jump sizes for the 07–09 financial crisis were much larger than those for the other periods, whether the jumps analyzed were in the return or volatility). Third, in terms of the visualization of the frequency of jumps, the 50ETF jump intensity is almost always stationary except for during period I, where it is slightly higher; the iVIX jump intensity in period I much higher than the intensities in other periods.…”

“…Inspired by recent research on jump activity (see Bandi & Renò, 2016; Chen & Ye, 2020; Da Fonseca & Ignatieva, 2019), we assume that the log‐price follows a general affine jump‐diffusion model governed by the following dynamics under an objective measure : where is the discount rate, is the asset risk premium, is a two‐dimensional Wiener process with a correlation coefficient , and is a three‐dimensional Poisson process with intensities (, …”

“…Notably, this model specification that includes both the correlated contemporaneous and independent occurrences of jumps in the asset and volatility covers many popular affine jump‐diffusion models (see Chen & Ye, 2020; Da Fonseca & Ignatieva, 2019). There are two main streams of jump activity modeling: one is the stochastic volatility with contemporaneous jumps model, which considers only contemporaneous jumps (see Duffie et al, 2000; Eraker, 2004), and the other is the stochastic volatility with independent jumps model, which considers only independent jumps (see Eraker et al, 2003).…”

Research on Parameter Estimation and Prediction of Sports Financial Market Volatility Model

“…Instead, it entered a period of high-quality development aimed at maintaining sustained and healthy economic development [8]. To solve the problems of unbalanced, uncoordinated, and insufficient economic development, we must vigorously promote supply-side structural reforms and promote the optimization and upgrading of the industrial structure [9]. Emerging industries can effectively activate the mobility of social resources, accelerate the transformation of old and new power and the agglomeration of innovative elements, and are an important part of achieving highquality economic development [10].…”

Pricing VIX derivatives using a stochastic volatility model with a flexible jump structure

“…Since the time-varying jump intensity is very popular in recent studies, for example, Bates [7] and Aït-Sahalia et al [1] report that more jumps occur during more volatile periods, we consider three cases as follows. (1) We first consider the stochastic volatility model with both CJs and IJs in Bandi and Reno [3] and Chen and Ye [9], that is, is constant for . (2) The jump intensity is a linear function (e.g., [4,10]) of the instantaneous variance, and in this case, we name the model “SVCIJ-I” (note that the SVCIJ model is a special case of the SVCIJ-I model, where the dependent coefficient ).…”