An FFT-network for Lévy option pricing

2016

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

x > k

, the Laplace inverse of

{\overset{trueˆ}{f}}_{0}

is just the Black–Scholes formula appearing in .…”

Section: Option Pricingmentioning

confidence: 99%

Option Pricing with Threshold Mean Reversion

Chi

Dong

2016

Self Cite

“…Carr and Madan () demonstrate that a plain vanilla European option can be priced using FFT given the characteristic function of the log‐asset price. Further, Wong and Guan () show that even American exotic options can be priced by FFT.…”

Section: The Modelmentioning

confidence: 99%

Stochastic Skew in the Interest Rate Cap Market

Leung

2013

The term structure of interest rates cannot be used to fully explain and hedge the prices of interest rate derivatives. Unspanned stochastic volatility improves the accuracy of interest rate derivatives valuation but is still inadequate to capture the variation of skews in the implied volatility surface. In this study, we document the stochastic variation of implied volatility skews in the interest rate cap market. To develop a term structure model that is consistent with the empirical phenomena, we incorporate the Wishart process into the standard LIBOR market model, namely, the LIBOR N‐dimensional Wishart (“LNW” for short) market model and derive a closed‐form, accurate, efficient caplet pricing formula. The capacity of the LNW model to capture stochastic skews is examined and compared with that of LIBOR multi‐Heston (“LMH” for short) market model with two and three stochastic volatilities. We find that the LNW model outperforms its LMH counterparts in terms of both in‐sample and out‐of‐sample pricing errors. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1146–1169, 2014

“…To incorporate exotic options, we require a reliable pricing engine for them under the Lévy models. In the case of path‐dependent options, such as barrier, lookback and Asian options, a possible remedy is the FFT network recently developed by Wong and Guan (). A concern with the use of exotic options is their trading liquidity, that is, their market prices may be unable to reflect market information efficiently.…”

Section: Calibrationmentioning

confidence: 99%

Lévy betas: Static hedging with index futures

Cheung

2011

Self Cite

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.