Lookback options and dynamic fund protection under multiscale stochastic volatility

Self Cite

Mean reversion and regime switching are well‐known features of commodity prices. Recent empirical research additionally documents the time variation of the mean reversion rate and volatility. This paper considers the option pricing framework for an underlying commodity price with mean reversion rate and volatility change according to a self‐exciting regime switching model. We offer empirical evidence for the proposed model and derive analytic pricing formulas for the European and barrier options. Numerical examples demonstrate the application and the ability of the proposed model in capturing volatility smile and regime‐switching in the mean reversion rate, simultaneously. © 2016 Wiley Periodicals, Inc. Jrl Fut Mark 37:107–131, 2017

Section: Lookback Optionsmentioning

confidence: 99%

Option Pricing with Threshold Mean Reversion

Chi

Dong

Wong

2016

Self Cite

“…The Greek correction term is a combination of the gamma, delta-gamma, vega, and delta-vega of the option. The model developed by Fouque et al (2003) has been applied to defaultable bonds (Fouque, Sircar, & Solna, 2006), lookback options (Wong and Chan, 2007), default correlation (Fouque, Wignall, & Zhou, 2008) and turbo warrants (Wong and Chan, 2008). Despite the fact that the model of Fouque et al (2003) does not take into account the mean reversion on the asset value process, it relies heavily on the assumption that the mean reversion rates of the two SV driving factors are close to zero and infinity, respectively, in order to derive asymptotic solutions.…”

Section: Introductionmentioning

confidence: 99%

Currency option pricing: Mean reversion and multi‐scale stochastic volatility

Wong

Zhao

2010

Self Cite

This paper investigates the valuation of currency options when the underlying currency follows a mean-reverting lognormal process with multi-scale stochastic volatility. A closed-form solution is derived for the characteristic function of the log-asset price. European options are then valued by means of the Fourier inversion formula. The proposed model enables us to calibrate simultaneously to the observed currency futures and the implied volatility surface of the currency options within a unified framework. The fractional fast Fourier transform (FFT) is adopted to implement the Fourier inversion, thus ensuring that the grid spacing restriction of the standard FFT can be relaxed, which results in a more efficient computation. Using Monte Carlo simulation as a benchmark, our numerical examples show that the derived option pricing formula is accurate and efficient for practical use.

“…Journal of Futures Markets DOI: 10.1002/fut we consider two classes of models: the multiscale stochastic volatility models (Fouque & Han, 2004;Fouque et al, 2000;Fouque, Papanicolaou, Sircar, & Solna, 2003;Gatheral, 2006;Lewis, 2000;Wong & Chan, 2007) and the jump models (Cont & Tankov, 2004;Schoutens, 2003). Usually the first type of model is used to price financial derivatives having medium or long residual lives.…”

Section: Introductionmentioning

confidence: 99%

“…Fouque and Han (2004) extend the technique introduced in Fouque and Han (2003) to approximate the prices of Asian options under the multiscale stochastic volatility model proposed in . More recently Wong and Chan (2007) proposed a multiscale stochastic volatility model and used it to price a long-term financial product called dynamic fund protection. In their model framework they give a series expansion for the price of lookback options.…”

Section: Introductionmentioning

confidence: 99%

An explicitly solvable multi‐scale stochastic volatility model: Option pricing and calibration problems

Fatone¹,

Mariani²,

Recchioni³

et al. 2009

We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic Option Pricing and Calibration Problems 863Journal of Futures Markets DOI: 10.1002/fut differential equations. The two stochastic variances vary on two distinct time scales and can be regarded as auxiliary variables introduced to model the dynamics of the asset price. Under some assumptions, the transition probability density function of the stochastic process solution of the model is represented as a onedimensional integral of an explicitly known integrand. In this sense the model is explicitly solvable. We consider the risk-neutral measure associated with the proposed multiscale stochastic volatility model and derive formulae to price European vanilla options (call and put) in the multiscale stochastic volatility model considered. We use the thus-obtained option price formulae to study the calibration problem, that is to study the values of the model parameters, the correlation coefficients of the Wiener processes defining the model, and the initial stochastic variances implied by the "observed" option prices using both synthetic and real data. In the analysis of real data, we use the S&P 500 index and to the prices of the corresponding options in the year 2005. The web site http://www.econ.univpm.it/recchioni/finance/w7 contains some auxiliary material including some animations that helps the understanding of this article. A more general reference to the work of the authors and their coauthors in mathematical finance is the web site