Page 49 - CCFA Journal - Sixth Issue

加中金融 Quant Corner 数量分析

5. Conclusions 5. 结论

In this article we used the Stochastic Volatility Inspired (SVI) 本文介绍了随机波动率启发模型 SVI 和构造隐含波动率
model to construct the implied volatility surface: we started by 曲面的方法和数值计算，并举例比较了三种情况下的模
the analytic part of the SVI model and then established the 型计算的结果。我们的结论是 SVI 模型能比较好地拟合
volatility surfaces by the numerical examples. We illustrated
the performance of the algorithm in three cases. The implied 市场观察值。SVI 具有以下的优势：
volatilities from option price and the volatilities generated by 1. SVI 模型可以通过内插值或外延插值来对没有市
SVI model are matched very well. It indicates that SVI model 场报价的新产品定价。
has the following advantages: 1) SVI model can be used to
price new contracts for which there are no quotes on the market 2. SVI 模型得到的隐含波动率是关于执行价格和到
by inter- and extrapolating the parameters in SV model; 2) The 期日的光滑解析函数，所以对各阶导数具有计算
volatility in SVI model is the smooth function of strike and 快速的优点。
maturity with an explicit analytical expression and it will save
computational time for the valuation and derivatives of all
orders. It is easy to implement for practical purposes and SVI 模型在实际程序实现方面也具备简单高效的长处。我
therefore, the SVI model presented in this article are worth 们特此介绍给更多的市场参与者。
recommending to market practitioners.

References
Gatheral, J., Jacquier, A.: Arbitrage-free SVI Volatility Surfaces, Quantitative Finance 14(1), 59-71 (2014).

Heston, S. L.: A closed-form solution for options with stochastic volatility with applications to bonds and currency options, The
Review of Financial Studies 6(2), 327–343 (1993).

Gatheral, J. The Volatility Surface: A Practitioner’s Guide. Wiley Finance, 2006.
Hagan, P.S.,Kumar, D., Lesniewski, A.S.,Woodward, D.E. Managing Smile Risk. Wilmott Magazine, 1:84–108, (2002).

CCFA JOURNAL OF FINANCE February 2022
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