Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market

Nikos K. Nomikos; Orestes A. Soldatos

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Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market

机译：跳跃扩散模型的模型隐含波动性分析：来自Nordpool市场的经验证据

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In this paper we examine the importance of mean reversion and spikes in the stochastic behaviour of the underlying asset when pricing options on power. We propose a model that is flexible in its formulation and captures the stylized features of power prices in a parsimonious way. The main feature of the model is that it incorporates two different speeds of mean reversion to capture the differences in price behaviour between normal and spiky periods. We derive semi-closed form solutions for European option prices using transform analysis and then examine the properties of the implied volatilities that the model generates. We find that the presence of jumps generates prominent volatility skews which depend on the sign of the mean jump size. We also show that mean reversion reduces the volatility smile as time to maturity increases. In addition, mean reversion induces volatility skews particularly for ITM options, even in the absence of jumps. Finally, jump size volatility and jump intensity mainly affect the kurtosis and thus the curvature of the smile with the former having a more important role in making the volatility smile more pronounced and thus increasing the kurtosis of the underlying price distribution.

机译：在本文中，我们研究了在对期权定价时标的资产均值回归和峰值对随机行为的重要性。我们提出了一个模型，该模型具有灵活的表达方式，并以简约的方式体现了电价的典型特征。该模型的主要特点是它结合了两种不同的均值回复速度，以捕获正常和尖峰期之间的价格行为差异。我们使用转换分析得出欧洲期权价格的半封闭式解决方案，然后检查模型生成的隐含波动率的属性。我们发现跳跃的存在会产生明显的波动偏斜，这取决于平均跳跃大小的符号。我们还表明，随着到期时间的增加，均值回归会减少波动性微笑。此外，即使没有跳跃，均值回归也会引起波动偏斜，特别是对于ITM期权而言。最后，跳跃大小的波动性和跳跃强度主要影响峰度，因此，微笑的曲率具有更大的作用，前者在使波动性微笑更加明显并因此增加基础价格分布的峰度方面具有更重要的作用。

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来源
《Energy economics》 |2010年第2期|302-312|共11页
作者
Nikos K. Nomikos; Orestes A. Soldatos;
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作者单位

Faculty of Finance, Cass Business School, London EC1Y 8TZ, UK;

Research, Total Gas & Power Ltd, London E14 5BF, UK;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
affine jump diffusion models; implied volatility; volatility skew; electricity derivatives; risk management;

机译：仿射跳跃扩散模型;隐含波动率;波动率偏斜;电力衍生品;风险管理;

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1. On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility [J] . Elisa Alòs, Jorge A. León, Josep Vives Finance and Stochastics . 2007,第4期

机译：具有随机波动率的跳跃扩散模型隐含波动率的短时行为
2. Jump activity analysis for affine jump-diffusion models: Evidence from the commodity market [J] . Da Fonseca Jose, Ignatieva Katja Journal of banking & finance . 2019,第FEBa期

机译：仿射跳跃扩散模型的跳跃活动分析：来自商品市场的证据
3. Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms [J] . Li T. Ray, Rodrigo Marianito R. European Journal of Applied Mathematics . 2017,第5期

机译：使用MELLIN变换的跳跃扩散模型中的期权定价和隐含波动的替代结果
4. Computation of time-dependent implied volatility from point observations for European options under jump-diffusion models [C] . Slavi G. Georgiev, Lubin G. Vulkov International Conference on Application of Mathematics in Engineering and Economics . 2019

机译：在跳跃扩散模型下对欧洲选项的点观察计算时间依赖性隐含波动的计算
5. Mathematical modeling and analysis of options with jump -diffusion volatility [D] . Andreevska, Irena 2008

机译：具有跳扩散波动率的期权的数学建模和分析
6. The benefit of modeling jumps in realized volatility for risk prediction: Evidence from Chinese mainland stocks [O] . Yin Liao -1

机译：建模的好处是可以预测风险的实际波动率：来自中国大陆股票的证据
7. We analyze, in this paper, a DSGE New Keynesian model with indi- visible labor where firms may belong to two different final goods producing sectors one where wages and employment are determined in competitive labor markets and the orther where wages and employment are the result of a contractual process between unions and firms. Bargaining between firms and monopoly unions implies real wage rigidity in the model and, in turn, an endogenous trade-off between output stabilization and infla- tion stabilization. We show that the negative effect of a productivity shock on inflation and the positive effect of a cost-push shock is crucially determined by the proportion of firms that belong to the competitive sec- tor. The larger is this number, the smaller are these effects. We derive a welfare based objective function as a second order Taylor approxima- tion of the expected utility of the economy's representative agent and we analyze optimal monetary policy. We show that the larger is the num- ber of firms that belong to the competitive sector, the smaller should be the response of the nominal interest rate to exogenous productivity and cost-push shocks. If we consider, however, an instrument rule where the interest rate must react to inflationary expectations, the rule is not af- fected by the structure of the labor market. The results of the model are consistent with a well known empirical regularity in macroeconomics, i.e. that employment volatility is larger than real wage volatility. [O] . Lorenza Rossi, Fabrizio Mattesini 100

机译：在本文中，我们分析了DsGE新凯恩斯主义模型，该模型具有明显的劳动力，其中企业可能属于两个不同的最终产品生产部门，其中工资和就业是在竞争性劳动力市场中确定的，而工资和就业是由工资和就业导致的。工会和公司之间的合同过程。企业和垄断联盟之间的讨价还价意味着模型中的实际工资刚性，反过来，产出稳定和通货膨胀稳定之间的内生权衡。我们表明，生产率冲击对通货膨胀的负面影响以及成本推动冲击的积极影响，主要取决于属于竞争部门的企业比例。这个数字越大，这些效果越小。我们得出一个基于福利的目标函数作为经济代理人的预期效用的二阶泰勒近似，我们分析最优货币政策。我们表明，属于竞争性行业的企业数量越大，名义利率对外生生产率和成本推动冲击的反应就越小。但是，如果我们考虑利率必须对通胀预期作出反应的工具规则，则该规则不受劳动力市场结构的影响。该模型的结果与宏观经济学中众所周知的经验规律一致，即就业波动率大于实际工资波动率。

Analysis of model implied volatility for jump diffusion models: Empirical evidence from the Nordpool market

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