Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering

Anatoliy Swishchuk; Raimondo Manca

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Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering

机译：金融工程中局部半马尔可夫波动率的方差和波动率互换的建模和定价

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We consider a semi-Markov modulated security market consisting of a riskless asset or bond with constant interest rate and risky asset or stock, whose dynamics follow gemoetric Brownian motion with volatility that depends on semi-Markov process. Two cases for semi-Markov volatilities are studied: local current and local semi-Markov volatilities. Using the martingale characterization of semi-Markov processes, we find the minimal martingale measure for this incomplete market. Then we model and price variance and volatility swaps for local semi-Markov stochastic volatilities.

机译：我们考虑由一个具有不变利率的无风险资产或债券以及具有风险资产或股票的半马尔可夫调制证券市场，其动态遵循伴随半马尔可夫过程的波动的布朗运动。研究了半马尔可夫波动率的两种情况：局部电流和局部半马尔可夫波动率。使用半马尔可夫过程的ting表征，我们找到了这个不完整市场的最小mar度量。然后，我们对局部半马尔可夫随机波动率建模并对其价格差异和波动率互换进行建模。

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来源
《Mathematical Problems in Engineering》 |2010年第3期|p.333-349|共17页
作者
Anatoliy Swishchuk; Raimondo Manca;
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作者单位

Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary,AB, Canada TIN 1N4;

Department of Mathematics, University of Rome "La Sapienza", Via del Castro, Laurenziano 9,00161 Rome, Italy;

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1. Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering [J] . AnatoliySwishchuk, RaimondoManca Mathematical Problems in Engineering: Theory, Methods and Applications . 2010,第5期

机译：金融工程中局部半马尔可夫波动率的方差和波动率互换的建模和定价
2. Pricing variance and volatility swaps in a stochastic volatility model with regime switching: Discrete observations case [J] . Elliott R.J., Lian G.-H. Quantitative finance . 2013,第5期

机译：具有政权切换的随机波动率模型中的定价方差和波动率互换：离散观测案例
3. Variance swaps, volatility swaps, hedging and bounds under multi-factor Heston stochastic volatility model [J] . Issaka Aziz Stochastic Analysis and Applications . 2020,第5期

机译：在多因素髋关节随机波动率模型下的差异递送，挥动递送，对冲和界限
4. Pricing Variance Swaps with Stochastic Volatility [C] . Song-Ping Zhu, Guang-Hua Lian World Congress on Engineering . 2009

机译：定价方差随随机波动率递送
5. Exact simulation of financial models with stochastic volatility and jumps, and lattice methods for corporate debt pricing. [D] . Kaya, Ozgur. 2005

机译：具有随机波动性和跳跃性的财务模型的精确模拟，以及用于公司债务定价的格方法。
6. How Volatilities Nonlocal in Time Affect the Price Dynamics in Complex Financial Systems [O] . Lei Tan, Bo Zheng, Jun-Jie Chen, -1

机译：时间上非本地波动率如何影响复杂金融系统中的价格动态
7. Modeling and Pricing of Covariance and Correlation Swaps for Financial Markets with Semi-Markov Volatilities [O] . Giovanni Salvi, Anatoliy V. Swishchuk 2014

机译：具有半马尔可夫波动率的金融市场协方差和相关互换的建模与定价

Modeling and Pricing of Variance and Volatility Swaps for Local Semi-Markov Volatilities in Financial Engineering

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