# A Jump Diffusion Model For VIX Volatility Options And Futures

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### Risk, Return, and Ross Recovery

bounded diffusion setting. Since the returns on each asset depend only on expected return and volatility in a dif-fusion setting, the return distribution for each asset is determined. That Ross is moreover able to determine the real-world return distribution in his jump setting is a tes-tament to the power of his restrictions on preferences.

### George Dotsis

4 R&R in Quantitative Finance. Dotsis G. (2019) òBank Capital and the Modigliani Miller Theorem when Loans create Deposits ó. Dotsis, G., (2020) òA New Measure of Option Implied Absolute Deviation

### CURRICULUM VITAE GEORGE J. JIANG - Directory CCB

Extracting Model-Free Volatility from Option Prices: An Examination of the VIX Index, with Yisong Tian, Journal of Derivatives, 2007, Spring, 1-26. Estimating the Latent Variable and Jump Diffusion Models using High-Frequency Data, with Roel Oomen, Journal of Financial Econometrics, 2007 (5), 1-30.

### July 2009 st revision: Sept 2009 General Auto-Regressive

on exotic options is threatened. Therefore the jump-diffusion model survives and quants continue to please their masters by finding evermore rapid ways of finding risk-neutral expectations of option payoffs to facilitate day-1 P&L on exotic options using a model that is silent about hedge slippage and associated risk-capital needs. Heston

### Continuous-time VIX dynamics: On the role of stochastic

study these models is that a stronger dependence of the diffusion. 113. term on the VIX level might decrease the jump intensity of the. 114. models. Extremely high jump intensities may be problematic because. 115. one loses the economic reasoning that jumps cover large, unexpected. 116 -

### Modeling Returns of Stock Indexes through Fractional Brownian

volatility and the correlation between the innovations in asset pricing. Also, Durham and Park (2012) develop a mixed jump-diffusion process on options with volatility of volatility (cf. Ang et al., 2006). An important characteristic of stock markets is the presence of unexpected and sudden jumps. In this regard, Martijn et al. (2015) suggest

### VIX Futures ETNs and Their Derivatives

3 Modeling VXX under Jump Diffusion with Stochastic Long-Term the VXX with the VIX futures and S&P 500 options markets. by including jumps in the volatility

### Model-Free Implied Volatility under Jump-Diffusion Models

Jump-diffusion model; Model-free Implied Volatility; Risk-neutral probability density; Volatility index (VIX) JEL Classifications: C58, C65, G12 1. Introduction. Britten-Jones and Neuberger (2000) proposed a methodology that measures, without the need to specify an option model, the return variability of an underlying asset implied by option

### Model Specification and Risk Premia: Evidence from Futures

Evidence from Futures Options MARK BROADIE, MIKHAIL CHERNOV, and MICHAEL JOHANNES* ABSTRACT This paper examines model specification issues and estimates diffusive and jump risk premia using S&P futures option prices from 1987 to 2003. We first develop a time series test to detect the presence of jumps in volatility, and find strong evidence in

### Calibration and Pricing of CBOE Volatility Index Options

Market-based Pricing and Calibration of VIX Options under Merton s Jump-Di usion Framework by Hede Luquene Gustafsson This thesis examines the performance of Merton s Jump-Di usion model (MJD) in a market based valuation of VIX futures option for three di erent maturities. The rst step was to derive the risk neutral dynamics of the MJD model.

### Modeling VXX under jump di usion with stochastic long-term mean

We develop a model for the VXX, the most actively traded VIX futures exchange- traded note (ETN), using Du e, Pan, and Singleton s (2000) a ne jump di usion, where the volatility process has jumps and a stochastic long-term mean.

### Implementation and Calibration of the Extended Affine Heston

S. Byelkina and A. Levin Implementation and Calibration of Extended Affine Heston Model for Basket Options and Volatility De rivatives. 6th BFS Congress. 6 General Affine Diffusion models A diffusion model considered in this presentation belongs to a broad affine jump-diffusion class of

### Futures Market Volatility: What Has Changed?

Aug 27, 2013 volatility converges to the variation implied by the continuous-time model integrated over the unit of time specified by the econometrician, reflecting both the diffusion component and the jump component of the price process. In contexts such as derivative pricing with jumps, separating the diffusion and jump components of variation is necessary.

### Subordinated Binomial Option Pricing with Stochastic Arrival

efficacy, we test the extended CCL model against the CCT model using VIX options and futures data as VIX is untraded, in sample and out-of-sample. In the VIX option pricing literature, various stochastic volatility/jump models have been attempted, e.g. applications of Heston s (1993) stochastic volatility model and Merton s jump-diffusion

### HEDGING STRATEGY COMPARISONS OF VOLATILITY INDEX OPTIONS

continuous-time diffusion and the jump diffusion processes to capture the dynamics of volatility indices. They find that the best fit to the data was the model featuring random jumps. Sepp (2008) model the VIX with the dynamics of the variance of the S&P 500 and find that jumps are important in variance. Psychoyios,

### Model Specification and Risk Premia: Evidence from Futures

Evidence from Futures Options MARK BROADIE, MIKHAIL CHERNOV, and MICHAEL JOHANNES∗ ABSTRACT This paper examines model specification issues and estimates diffusive and jump risk premia using S&P futures option prices from 1987 to 2003. We first develop a time series test to detect the presence of jumps in volatility, and find strong evidence in

### The New Market for Volatility Trading

relationship between VIX futures prices and VIX, the term structure of VIX futures prices and the volatility of VIX futures prices. Second, to develop an efficient pricing model for VIX products and to find parameter estimates that best describe the empirical relationships and could be used in pricing VIX futures and options. 2. Data

### Modeling and Forecasting the Volatility of the Nikkei 225

of the volatility indices is the CBOE Volatility Index (VIX). The VIX index is a measure of the market s expectation of the S&P 500 index volatility over the next 30 days implied by the prices of some of the S&P 500 options traded at the CBOE. As mentioned above, the CBOE and its futures exchange (CFE)

### Information about price and volatility jumps inferred from

neutral expectation of future volatility, not an instantaneous volatility measure. The VIX is a biased estimate of the instantaneous volatility. Alternatively, we use the option price to investigate jumps and associated risk premia. And the affine jump-diffusion model and pure jump process in volatility are considered in our simulation.

### DOES THE VIX JUMP? IMPLICATIONS FOR PRICING AND HEDGING

assumption that the volatility jump size is constant rather than being random. Finally, Dotsis et al. (2005) examined the ability of alternative popular continuous-time diffusion and jump diffusion processes to capture the dynamics of eight major European and U.S. volatility indices. They found that the best model in terms of fitting was a mean

### CURRICULUM VITA Date: October 31, 2019

Financial Futures Market, Accepted for publication, The Journal of Futures Markets. Hilliard, Jimmy E and Jitka Hilliard (2019). A Jump-Diffusion Model for Pricing and Hedging with Margined Options: An Application to Crude Oil Contracts, The Journal of Banking and Finance, 98, 137-155. Hilliard, Jimmy E and Haoran Zhang (2018).

### George Dotsis - econ.uoa.gr

Comparison of Continuous Time Models of Implied Volatility Indices , Journal of Banking and Finance, 31, pp. 3584-3603. Dotsis, G., and Markellos, R.N. (2007) The Finite Sample Properties of the GARCH Option Pricing Model , Journal of Futures Markets, 27, pp. 599- 615.

### Study on Effect of Jumping Risk and Volatility Risk on TAIEX

describe the model of implied volatility. Refer to Peña et al.(1999) consider about the implied volatility function of general symmetric and asymmetric, to capture the possible trends of smile curve. Eventually, using HJM model and ad hoc methods to evaluate the Eurodollar futures options;

### Information about price and volatility jumps inferred from

use VIX and S&P 500 futures contracts to test the activity level of returns and the VIX process. They conclude that a jump-diffusion is suitable for the S&P 500 return process, while the VIX index needs a pure-jump process to capture the frequent jumps in VIX. In their research, the VIX index is used as a proxy for volatility level.

### A Jump Diffusion Model for VIX Volatility Options and Futures

A Jump Diffusion Model for VIX Volatility Options and Futures Dimitris Psychoyiosa, George Dotsisb, Raphael N. Markellosc Abstract Implied volatility indices are becoming increasingly popular as a measure of market uncertainty and as a vehicle for developing derivative instruments to hedge against unexpected changes in volatility.

### 0(1/$2&))( /3(45#(6%15#7#&( 37$%$1#()/17#4'

Volatility Model: Pricing of Vanilla Options and Econometric Estimation De Marco, Stefano Asymptotics and calibration for American options Deelstra, Griselda The Role of the Dependence between Mortality and Interest Rates when pricing Guaranteed Annuity Options 2:50-3:15 Utility Selection Wong, Kwok Chuen -Risk Portfolio of stochastic

### Pricing VIX Futures on Affine Stochastic Volatility Models

VIX futures on 26 March 2004 and VIX options on 24 February 2006. These will be the first of an entire family of volatility products traded in exchanges. Since the underlying VIX, or equivalently the model-free implied volatility of SPX options, is not tradable, it is impossible to use the no-arbitrage relationship to derive the fair

### Option Volatility And Pricing Advanced Trading Strategies And

May 25, 2021 Europe at the Options Industry Council Trading VIX Derivatives will be a comprehensive book covering all aspects of the Chicago Board Options Exchange stock market volatility index. The book will explain the mechanics and strategies associated with trading VIX options, futures, exchange trading notes and options on exchange traded notes. Known as

### Willow tree algorithms for pricing VIX derivatives under jump

price formulas for VIX futures and option under the pure di usion 3/2-model. Based on the 4/2 stochastic volatility model proposed by Grasselli (2017), Lin et al. (2017) derive integral price formulas for VIX derivatives under the 4/2 stochastic volatility plus jump model. Later, Lin et al.

### Introduction - CAIA

launched Volatility Index (VIX) futures and options in 2004 and 2006, respectively. The VIX in its current form, according to the CBOE, measures the level of expected volatility of the S&P 500 Index over the next 30 days that is implied in the bid/ask quotations of SPX options. Literature Review Comparing Rising & Falling Volatility

### ModelingVIXFuturesandPricingVIX Options in the Jump Di usion

VIX futures is derived by developing a term-structure model for VIX futures. We analyze the VIX futures by the Merton Jump Diﬀusion model and allow for stochastic interest rates in the model. The per-formance of the model is investigated based on the daily VIX futures prices from the Chicago Board Option Exchange (CBOE) data. Also, the model

### VOLATILITY COMPONENTS THE TERM STRUCTURE DYNAMICS OF UTURES

Second, we propose a new pricing framework for VIX futures. Empirically, the difﬁculty with VIX futures is the nonlinear pricing relation with underlying state variables. Many a study has been devoted to ﬁnd a tractable pricing formula for VIX futures. For example, Carr and Wu (2003) and Dupire (2006) use model-free

### Estimating the Leverage Parameter of Continuous-time

implied volatility calculation step is conveniently done by exchanges and other institutions. On the heels of the success of VIX, the universe of model-free implied volatility indices, as well as exchange-traded options and futures on these volatility indices, has been expanding rapidly in recent years.

### Valuation of Volatility Derivatives

Merton jump-diffusion model (constant volatility lognormal plus independent jumps). AVG (Asymmetric variance gamma) CGMY (More complicated version of AVG) NIG (Normal inverse Gaussian) List does not include time-changed models such as VG-CIR

### Essays on Volatility Derivatives and Portfolio Optimization

ity (SV) model and the Bates and Scott stochastic volatility with jumps (SVJ) model. We provide formulas to price VIX futures under the SV and SVJ models. We discuss the properties of these models in fitting VIX futures prices using market VIX futures data and SPX options data. We empirically investigate profit and loss of strategies which

### Chrilly Donninger Chief Scientist, Sibyl-Project Sibyl

(Graphic-1 and 5), the mean-reversion level exp(μ)is about 5 points higher than for the VIX (Graphic-2 and 6). The jump model has also for the VSTOXX a large positive bias, the diffusion-only model a small negative one. The jump-model predicts the direction in 54% of the cases right, the diffusion-only model in 62.2%.