Option Pricing with Threshold Mean Reversion

Chi, Zeyu; Dong, Fangyuan; Wong, Hoi Ying

doi:10.1002/fut.21795

Cited by 13 publications

(8 citation statements)

References 37 publications

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“…is less than one. The previous literature has also found the same conclusion (Ahmad et al, 2016;Chi et al, 2016;Hart et al, 2015;Mishra, 2017;Tripathy, 2017;Wang et al, 2015). The results of the study also demonstrate that there is a direct relation between stock returns and volatilities of the emerging and developed stock markets.…”

Section: Discussionsupporting

confidence: 76%

“…The theory of mean reversion demonstrates that after touching a certain extreme point, the equity prices return back to their mean prices (Arefin & Ahkam, 2017;Chi, Dong, & Wong, 2016;Lubnau & Todorova, 2015;Ribeiro, Cermeño, & Curto, 2017). The phenomenon is known as the mean reversion if the equity price has a tendency to come back its original long-term average price after some certain time period (Chaves & Viswanathan, 2016;Huang, 2017;Huggins & Schaller, 2013;Trypsteen, 2017).…”

Section: Background Of the Research Studymentioning

confidence: 99%

“…According to previous research studies, the mean reversion process can be segregated into long-term and short-term mean reverting processes. If the return of a stock back into its mean value occurs within a one-month time period then it is known as short-term mean reversion process (Chi et al, 2016;Hart et al, 2015;Ribeiro et al, 2017). The flow of research studies regarding the short-term mean reversion has also been increased due to the access of information on a daily basis regarding the investments.…”

Section: Substantiation From the Literaturementioning

confidence: 99%

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Mean reversion in international markets: evidence from G.A.R.C.H. and half-life volatility models

Ahmed

Vveinhardt

Štreimikienė

et al. 2018

Economic Research-Ekonomska Istraživanja

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The objective of this research is to examine and compare the mean reversion phenomenon in developed and emerging stock markets. An important aim is to measure and compare the speed of mean reversion and half-life of volatility shocks of emerging and developed markets. For this purpose, we have selected five developed and seven emerging markets, and used daily market indices for the period of 1 January 2000 to 30 June 2016. We employed autoregressive conditional heteroskedasticity -Lagrange multiplier (A.R.C.H.-L.M.), generalised autoregressive conditional heteroskedasticity (G.A.R.C.H.) (1, 1), and half-life volatility shock techniques to carry out this research. The results of the study confirmed the mean-reverting process in developed and emerging markets. The South Korean market has the slowest mean reversion, and thus has the highest comparative volatility over a longer period of time. However, the Pakistan stock exchange exhibited the fastest mean reverting process. It is also concluded that the relative volatilities are higher in emerging markets, whereas the comparative volatilities are higher in developed markets. Therefore, it is further concluded that the mean reversion process is much faster in emerging indices except the South Korean and Chinese markets. The study recommends that if investors want higher returns in a shorter period of time then they should invest in emerging markets.

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Section: Discussionsupporting

confidence: 76%

Section: Background Of the Research Studymentioning

confidence: 99%

Section: Substantiation From the Literaturementioning

confidence: 99%

See 1 more Smart Citation

Mean reversion in international markets: evidence from G.A.R.C.H. and half-life volatility models

Ahmed

Vveinhardt

Štreimikienė

et al. 2018

Economic Research-Ekonomska Istraživanja

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“…Further, by showing that the past prices are able to predict the future, indicating the presence of memory pattern, which supported mean reversion. The mean reversion is divided into short term and long term mean reversion (e.g., Chi et al 2016;Hart et al 2015;Lim 2011;etc. ).…”

Section: Literature Reviewmentioning

confidence: 99%

“…According to mean reversion, prices rates after reaching extreme value all return back to their mean values (e.g., Chi et al 2016;Lubnau, Todorova 2015;Henderson 2004;etc.). Thus, a variable is said to be exhibited mean reversion behavior, if it has the tendency to revert back to its long-term average value over the period.…”

Section: Introductionmentioning

confidence: 99%

Speed of Mean Reversion: An Empirical Analysis of Kse, Lse and Ise Indices

Palwasha

Ahmad

Ahmed

et al. 2018

Technological and Economic Development of Economy

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Abstract. The purpose of this study is to determine the presence of mean reversion in the stock markets indices of Pakistan, moreover, to measure, and compare the speed of mean reversion of the stock markets indices across Pakistan. In order to carry out the research study, the daily data of three stock indices of Pakistan such as: KSE-100, LSE-25 and ISE-10 are collected from 2003 to 2014. After the application of tests such as ARCH and GARCH, it was found that returns series of KSE-100, LSE-25 and ISE-10 indices exhibit mean reversion, indicating that the returns revert back to their historical value after reaching an extreme value. Further, the mean reversion rate shows that KSE-100 index has the slowest mean reversion, however, the ISE-10 index has the fastest mean reversion among the three indices. Therefore, the results of the study concluded that KSE-100 index, due to the slowest mean reversion rate has higher volatility over a longer period of time. On the contrary, since, ISE-10 index has exhibited the fastest mean reversion with the lowest volatility as compared to others. But due to fast mean reversion rate, it will help investors to gain profits over a shorter period of time. Thus, it can be recommended that the investor willing to bear the risk of time and looking for long-term investment should invest in KSE-100 index. However, investors looking for higher profits in a shorter period can invest in the ISE-10 index but with higher risk-returns trade-off.

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Variance swaps under the threshold Ornstein–Uhlenbeck model

Dong

Wong

2017

Appl Stoch Models Bus & Ind

Self Cite

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Variance swap is a typical financial tool for managing volatility risk. In this paper, we evaluate different types of variance swaps under a threshold Ornstein-Uhlenbeck model, which exhibits both mean reversion and regime switching features in the underlying asset price. We derive the analytical solution for the joint moment generating function of log-asset prices at two distinct time points. This enables us to price various types of variance swaps analytically.regime-switching is originated by Hamilton ([10]). Although there are many possible models for regime-switching, the self-exciting threshold autoregressive (SETAR) model proposed by Tong ([11]) admits a tractable likelihood function for parameter estimation and is a popular regime-switching model alternative to the one used in Kim et al. ([3]). Tsay ([12]) points out that the SETAR model can capture jump phenomena observed in practice because of discontinuity at the threshold. Therefore, it can be efficiently estimated and empirically tested with real data. We offer empirical evidence for the SETAR model with historical crude-oil spot price.By considering the diffusion limit of the SETAR model, we propose a threshold Ornstein-Uhlenbeck (TOU) process {X t } t≥0 and derive the corresponding analytical formulas for various variance swaps. To this end, we have to examine the joint distribution of X T 1 and X T 2 at two fixed time points. To characterize the distributional property, we derive the joint moment-generating function (MGF) [e 1 X T 1 + 2 X T 2 |X t = x] in two steps. We find the closed-form expression for[e X T |X t = x] in the first step and apply it to the joint MGF in the second step. A PDE framework similar to Wong and Zhao ([13]) is applied to obtain the solution. Consequently, the analytical solution of the MGF brings us the pricing formulas of variance swaps in terms of Laplace inversion. We implement the solution using numerical methods proposed by Abate and Valkó ([14], [15]).The remainder of the paper is organized as follows. Section 2 introduces TOU model with empirical support. Section 3 states the two-step method for deriving the analytical solution of the joint MGF. Section 4 is the application of the joint MGF in variance swaps pricing. Section 5 numerically examines the accuracy of the closed-form solution of MGF and variance swaps price derived under TOU model. Section 6 concludes. The preliminaryTo formulate our problem in a PDE framework under a n-regime TOU model, we introduce Lemma 2.1 in the succeeding text, which is useful in many circumstances in this paper.With the conditions in (27) and (28) and the derivative property of Kummer's function M (a, b, z) and U(a, b, z), we deduce a linear equation system (17) for solving the coefficients c 21 and c 22 .

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Option Pricing with Threshold Mean Reversion

Cited by 13 publications

References 37 publications

Mean reversion in international markets: evidence from G.A.R.C.H. and half-life volatility models

Mean reversion in international markets: evidence from G.A.R.C.H. and half-life volatility models

Speed of Mean Reversion: An Empirical Analysis of Kse, Lse and Ise Indices

Variance swaps under the threshold Ornstein–Uhlenbeck model

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