Variance swaps under Lévy process with stochastic volatility and stochastic interest rate in incomplete markets

Yang, Ben-zhang; Yue, Jia; Huang, Nan-jing

doi:10.48550/arxiv.1712.10105

Cited by 2 publications

(3 citation statements)

References 27 publications

(64 reference statements)

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“…Equilibrium asset pricing is always an important and ongoing topic for any financial market, and it has been extensively studied by a number of authors [9,11,18,28,31]. It also can be used to deal with insider trading problem and the history can be dated back to 1985, when Kyle [22] developed a model, in which a large trader is assumed to possess long-lived private information about the value of a stock that will be revealed at some known date and optimally trades continuously into the stock to maximize his/her expected profits, while risk-neutral market makers try to infer the information possessed by the insider from the aggregate order flow.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

Yang

Huang

2020

Appl Math Optim

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In this paper, the Kyle model of insider trading is extended by characterizing the trading volume with long memory and allowing the noise trading volatility to follow a general stochastic process. Under this newly revised model, the equilibrium conditions are determined, with which the optimal insider trading strategy, price impact and price volatility are obtained explicitly. The volatility of the price volatility appears excessive, which is a result of the fact that a more aggressive trading strategy is chosen by the insider when uninformed volume is higher. The optimal trading strategy turns out to possess the property of long memory, and the price impact is also affected by the fractional noise. constant since new private information is introduced every period caused by the deterministic changes in the noise trading volatility. Stochastic variation was also introduced in the noise trading volume by Foster and Viswanathan [15], and this model was then empirically tested to show the joint behavior of the price volatility, volume, and price impact. However, a noticeable shortcoming of these extensions is the assumption that the information is short-lived, which is not realistic. Later on, deterministic noise trading volatility was directly incorporated into the Kyle model so that intra-day patterns of liquidity trading can be successfully captured [4]. Such an assumption on the noise trading volatility is still not appropriate since it gives rise to the deterministic price impact and further leads to the situation where expected execution costs of liquidity traders do not depend on the timing of their trading. A more recent extension to the Kyle model was proposed by Collin-Dufresne and Fos [11], who considered stochastic noise trading volatility, and showed that this is the only guarantee that insider's liquidity timing option can generate a stochastic price volatility as well as a nonzero correlation among the price volatility, market depth, and uninformed trading volume.Despite all the advantages of the model proposed in [11], it has not taken into consideration that the volatility is characterized by long memory, which is a consensus among financial econometricians. In particular, Bollerslev and Jubinski [7] presented the evidence of long memory in the volatility and investigated the extent to which the volume and volatility share common long-run dependencies. In line with this, they also proposed that the mixture-of-distributions hypotheses (MDH) might be better viewed as long-run proposition, after observing that occasional structural breaks can give rise to long-range dependence [17]. This implies long-range dependence could be induced under the MDH by occasional changes in the mean and/or volatility of the intra-day volumes and returns, which are generated due to the reaction traders make to information events. Furthermore, fractionally-integrated models were shown to provide a useful description of volatility dynamics in the presence of structural breaks because they effectively allow the unconditional ...

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Section: Introductionmentioning

confidence: 99%

Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

Yang

Huang

2020

Appl Math Optim

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“…Zhu and Lian [29] solved the discretely sampled variance swaps pricing formula under Heston's stochastic volatility model using a partial differential equation approach. Recently, Yang et al [25] focus on the pricing of the variance swaps in the financial market where the stochastic interest rate and the volatility of the stock are driven by the Cox-Ingersoll-Ross model and Heston model with simultaneous Lévy jumps, respectively. However, to our best knowledge, there are only a few researchers to consider the pricing of volatility swaps in the literature.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, we derive the discrete and continuous sampled volatility swap pricing formulas by employing transform techniques and show the relationship between two pricing formulas. The contributions of this paper can be summarized as follows: (i) proposes stochastic volatility with jumps and stochastic intensity model at the first time; (ii) derives the joint moment generating function of this model by using the affine structure method introduced by Duffie[16] and the results presented in Yang et al[25]; (iii) gives the pricing formula for discrete and continuous samples, respectively; (iv) shows the impacts of jumps and stochastic intensity on the fair strike price of volatility swaps.…”

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confidence: 99%

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

Yang

Jia

Wang

et al. 2019

Applied Mathematics and Computation

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In this paper, a pricing formula for volatility swaps is delivered when the underlying asset follows the stochastic volatility model with jumps and stochastic intensity. By using Feynman-Kac theorem, a partial integral differential equation is obtained to derive the joint moment generating function of the previous model. Moreover, discrete and continuous sampled volatility swap pricing formulas are given by employing transform techniques and the relationship between two pricing formulas is discussed. Finally, some numerical simulations are reported to support the results presented in this paper.

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Variance swaps under Lévy process with stochastic volatility and stochastic interest rate in incomplete markets

Cited by 2 publications

References 27 publications

Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

Equilibrium Price and Optimal Insider Trading Strategy Under Stochastic Liquidity with Long Memory

Volatility swaps valuation under stochastic volatility with jumps and stochastic intensity

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