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

Wong, Hoi Ying; Zhao, Jing

doi:10.1002/fut.20452

Cited by 18 publications

(11 citation statements)

References 24 publications

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“…A mean-reverting process is introduced to allow for the common long-term volatility risk in the underlying asset price and counterparty's asset value, which differs from assumption that long-term volatility is constant in Wang et al [13]. This assumption is consistent with the models in Christoffersen et al [21] and Wong and Zhao [22]. The market is fluctuating in reality, and the market factor affects the longterm volatilities of underlying asset price and counterparty's asset value.…”

Section: Introductionmentioning

confidence: 91%

Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility

Yue

Ren

2018

Discrete Dynamics in Nature and Society

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This paper considers the pricing issue of vulnerable European option when the dynamics of the underlying asset value and counterparty’s asset value follow two correlated exponential Lévy processes with stochastic volatility, and the stochastic volatility is divided into the long-term and short-term volatility. A mean-reverting process is introduced to describe the common long-term volatility risk in underlying asset price and counterparty’s asset value. The short-term fluctuation of stochastic volatility is governed by a mean-reverting process. Based on the proposed model, the joint moment generating function of underlying log-asset price and counterparty’s log-asset value is explicitly derived. We derive a closed-form solution for the vulnerable European option price by using the Fourier inversion formula for distribution functions. Finally, numerical simulations are provided to illustrate the effects of stochastic volatility, jump risk, and counterparty credit risk on the vulnerable option price.

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Section: Introductionmentioning

confidence: 91%

Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility

Yue

Ren

2018

Discrete Dynamics in Nature and Society

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“…Our empirical study, however, employs a more advanced approach, the fractional FFT (FRFT), to further speed up the computation. The theoretical grounds for the FRFT can be found in Bailey and Swarztrauber (), and its application in option pricing is detailed in Wong and Zhao ().…”

Section: Option Pricing and The Lévy Beta Calibrationmentioning

confidence: 99%

Lévy betas: Static hedging with index futures

Wong

Cheung

Wong

2011

Journal of Futures Markets

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This study considers calibration to forward-looking betas by extracting information on equity and index options from prices using Lévy models. The resulting calibrated betas are called Lévy betas. The objective of the proposed approach is to capture market expectations for future betas through option prices, as betas estimated from historical data may fail to reflect structural change in the market. By assuming a continuous-time capital asset pricing model (CAPM) with Lévy processes, we derive an analytical solution to index and stock options, thus permitting the betas to be implied from observed option prices. One application of Lévy betas is to construct a static hedging strategy using index futures. Employing Hong Kong equity and index option data from September 16, 2008 to October 15, 2009, we show empirically that the Lévy betas during the sub-prime mortgage crisis period were much more volatile than those during the recovery period. We also find evidence to suggest that the Lévy betas improve static hedging performance 2 Wong, Cheung, and WongJournal of Futures Markets relative to historical betas and the forward-looking betas implied by a stochastic volatility model.

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“…Beyond Lévy processes, Fourier analysis and the FFT method are also applicable to other asset dynamics such as mean-reversion models and stochastic volatility models. See, for example, the works of Wong and Lo (2009) and Wong and Zhao (2010).…”

Section: Introductionmentioning

confidence: 98%