Can Negative Interest Rates Really Affect Option Pricing? Empirical Evidence from an Explicitly Solvable Stochastic Volatility Model

We present option pricing under the double stochastic volatility model with stochastic interest rates and double exponential jumps with stochastic intensity in this article. We make two contributions based on the existing literature. First, we add double stochastic volatility to the option pricing model combining stochastic interest rates and jumps with stochastic intensity, and we are the first to fill this gap. Second, the stochastic interest rate process is presented in the Hull–White model. Some authors have concentrated on hybrid models based on various asset classes in recent years. Therefore, we build a multifactor model with the term structure of stochastic interest rates. We also approximated the pricing formula for European call options by applying the COS method and fast Fourier transform (FFT). Numerical results display that FFT and the COS method are much faster than the numerical integration approach used for obtaining the semi-closed form prices. The COS method shows higher accuracy, efficiency, and stability than FFT. Therefore, we use the COS method to investigate the impact of the parameters in the stochastic jump intensity process and the existence of the process on the call option prices. We also use it to examine the impact of the parameters in the interest rate process on the call option prices.

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South Africa’s economic response to monetary policy uncertainty

Journal of Economic Studies ◽

10.1108/jes-07-2015-0131 ◽

2017 ◽

Vol 44 (2) ◽

pp. 282-293 ◽

Cited By ~ 1

Author(s):

Mehmet Balcilar ◽

Rangan Gupta ◽

Charl Jooste

Keyword(s):

Monetary Policy ◽

Interest Rates ◽

Stochastic Volatility ◽

Stochastic Volatility Model ◽

Economic Consequences ◽

Policy Uncertainty ◽

Dsge Model ◽

Content Type ◽

Volatility Model ◽

Central Bankers

Purpose The purpose of this paper is to study the evolution of monetary policy uncertainty and its impact on the South African economy. Design/methodology/approach The authors use a sign restricted SVAR with an endogenous feedback of stochastic volatility to evaluate the sign and size of uncertainty shocks. The authors use a nonlinear DSGE model to gain deeper insights about the transmission mechanism of monetary policy uncertainty. Findings The authors show that monetary policy volatility is high and constant. Both inflation and interest rates decline in response to uncertainty. Output rebounds quickly after a contemporaneous decrease. The DSGE model shows that the size of the uncertainty shock matters – high uncertainty can lead to a severe contraction in output, inflation and interest rates. Research limitations/implications The authors model only a few variables in the SVAR – thus missing perhaps other possible channels of shock transmission. Practical implications There is a lesson for monetary policy: monetary policy uncertainty, in isolation from general macroeconomic uncertainty, often creates unintended adverse consequences and can perpetuate a weak economic environment. The tasks of central bankers are incredibly difficult. Their models project output and inflation with relatively large uncertainty based on many shocks emanating from various sources. It matters how central bankers react to these expectations and how they communicate the underlying risks associated with setting interest rates. Originality/value This is the first study that looks into monetary policy uncertainty into South Africa using a stochastic volatility model and a nonlinear DSGE model. The results should be very useful for the Central Bank as it highlights how uncertainty, that they create, can have adverse economic consequences.

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Option pricing under the fractional stochastic volatility model

ANZIAM Journal ◽

10.21914/anziamj.v63.15204 ◽

2021 ◽

Vol 63 ◽

pp. 123-142

Author(s):

Yuecai Han ◽

Zheng Li ◽

Chunyang Liu

Keyword(s):

Brownian Motion ◽

Option Pricing ◽

Fractional Brownian Motion ◽

Stochastic Volatility ◽

Option Price ◽

Stochastic Volatility Model ◽

Option Prices ◽

European Call Option ◽

Volatility Model ◽

The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

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Partial Derivative Approach for Option Pricing in a Simple Stochastic Volatility Model

SSRN Electronic Journal ◽

10.2139/ssrn.440522 ◽

2003 ◽

Author(s):

Miquel Montero

Keyword(s):

Option Pricing ◽

Stochastic Volatility ◽

Partial Derivative ◽

Stochastic Volatility Model ◽

Volatility Model

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GENERALIZED BN–S STOCHASTIC VOLATILITY MODEL FOR OPTION PRICING

International Journal of Theoretical and Applied Finance ◽

10.1142/s021902491650014x ◽

2016 ◽

Vol 19 (02) ◽

pp. 1650014 ◽

Cited By ~ 16

Author(s):

INDRANIL SENGUPTA

Keyword(s):

Option Pricing ◽

Stochastic Volatility ◽

Gaussian Distribution ◽

Implied Volatility ◽

Stochastic Volatility Model ◽

Inverse Gaussian ◽

Martingale Measures ◽

Structure Preserving ◽

Volatility Model ◽

Equivalent Martingale

In this paper, a class of generalized Barndorff-Nielsen and Shephard (BN–S) models is investigated from the viewpoint of derivative asset analysis. Incompleteness of this type of markets is studied in terms of equivalent martingale measures (EMM). Variance process is studied in details for the case of Inverse-Gaussian distribution. Various structure preserving subclasses of EMMs are derived. The model is then effectively used for pricing European style options and fitting implied volatility smiles.

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