Estimating the Parameters of the Stochastic Volatility Model of the Short-term Interest Rate

2017 ◽  
Vol 19 (6) ◽  
pp. 2921-2932
Author(s):  
Bongju Song
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Short Term ◽  
Volatility Model

PRICING VARIANCE SWAPS UNDER DOUBLE HESTON STOCHASTIC VOLATILITY MODEL WITH STOCHASTIC INTEREST RATE

2021 ◽  
pp. 1-17
Author(s):  
Huojun Wu ◽  
Zhaoli Jia ◽  
Shuquan Yang ◽  
Ce Liu
Keyword(s):  
Interest Rate ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Characteristic Functions ◽  
Stochastic Interest Rate ◽  
Modeling Framework ◽  
Variance Swaps ◽  
Volatility Model ◽  
Stochastic Interest

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations.

scholarly journals An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hao Chang ◽  
Xi-min Rong
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Optimal Investment ◽  
Stochastic Volatility Model ◽  
Power Utility ◽  
Variable Approach ◽  
Volatility Model ◽  
Stochastic Interest ◽  
Hamilton Jacobi Bellman ◽  
Optimal Investment And Consumption

We are concerned with an investment and consumption problem with stochastic interest rate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) model and the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochastic optimal control theory to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility and logarithm utility for our analysis. By using separate variable approach and variable change technique, we obtain the closed-form expressions of the optimal investment and consumption strategy. A numerical example is given to illustrate our results and to analyze the effect of market parameters on the optimal investment and consumption strategies.

scholarly journals Modeling the Effect of Interest Rate Uncertainty on Residents’ Consumption – Based on a DSGE Model Embedded Stochastic Volatility

2018 ◽  
Vol 22 (6) ◽  
pp. 846-852
Author(s):  
Xiaowen Hu ◽  
◽  
Chengchen Hu ◽  
Yiyu Yao
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Negative Impact ◽  
Structural Equations ◽  
Stochastic Volatility Model ◽  
Current Period ◽  
Volatility Model ◽  
Dynamic Stochastic ◽  
The Government ◽  
The Impact

Modeling the effect of uncertainty shock usually employs VAR method. The approach however often leads to the results unstable with different structural equations. Especially it is modeled without a microscopic basis which often implies wrong policy advice. A new method to model the effect of interest rate uncertainty is proposed in this paper that overcomes this limitation. A stochastic volatility model is embedded into a dynamic stochastic general equilibrium framework to study the influence of interest rate uncertainty on the residents’ consumption. Using the third-order perturbation method to identify the impact of interest rate uncertainty on consumption. It is found by simulation that with the interest rate uncertainty increased, the consumption of residents in the current period has obviously decreased due to the preventive saving mechanism. Variance analysis shows that interest rate uncertainty shocks can explain 8% share of consumption volatility. The empirical results are robust when changing the parameter values and the prior distribution of the parameters. The conclusion shows the government should strengthen to guide the public reasonable expectations, to avoid the negative impact of interest rate uncertainty.

scholarly journals Variance and Interest Rate Risk in Unit-Linked Insurance Policies

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 84
Author(s):  
David Baños ◽  
Marc Lagunas-Merino ◽  
Salvador Ortiz-Latorre
Keyword(s):  
Interest Rate ◽  
Interest Rates ◽  
Stochastic Volatility ◽  
Interest Rate Risk ◽  
Stochastic Volatility Model ◽  
Insurance Company ◽  
Insurance Contracts ◽  
Volatility Models ◽  
Volatility Model ◽  
Vasicek Interest Rate Model

One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition, we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model.

INFLATION TARGETING UNDER INFLATION UNCERTAINTY—MULTI-ECONOMY EVIDENCE FROM A STOCHASTIC VOLATILITY MODEL

2020 ◽  
pp. 1-36
Author(s):  
Matthias Hartmann ◽  
Helmut Herwartz ◽  
Maren Ulm
Keyword(s):  
Stochastic Volatility ◽  
Inflation Targeting ◽  
Stochastic Volatility Model ◽  
Target Level ◽  
Short Term ◽  
Inflation Target ◽  
Inflation Uncertainty ◽  
Inflation Rates ◽  
Volatility Model

One of the most important advantages of an inflation target is that it helps to reduce uncertainty about future inflation. However, this confidence may be undermined if actual inflation continuously deviates from the target level. We examine how inflation uncertainty relates to the presence of an inflation target and deviations of inflation from the targeted level. Inflation uncertainty is quantified by means of an unobserved components stochastic volatility model that allows to distinguish between permanent and transitory inflation uncertainty. While long-term inflation appears largely stable in most economies, the short-term inflation uncertainty is found to be time-varying. Most notably, short-term inflation uncertainty is high if inflation rates are below the target level. This is particularly relevant for economies which are currently confronted with the presence of persistently low-inflation rates. Our findings suggest that announcing higher inflation targets as it is currently discussed may be costly in terms of provoking higher inflation uncertainty.

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