Exact and approximate solutions for options with time-dependent stochastic volatility

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• 作者：Joanna Goard ; ^{joanna@uow.edu.au" class="auth_mail}
• 关键词：Stochastic volatility ; Volatility model ; Option pricing
• 刊名：Applied Mathematical Modelling
• 出版年：1 June 2014
• 年：2014
• 卷：38
• 期：11-12
• 页码：2771-2780
• 全文大小：519 K

文摘

In this paper it is shown how symmetry methods can be used to find exact solutions for European option pricing under a time-dependent 3/2-stochastic volatility model d="mmlsi9" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0307904X13007415&_mathId=si9.gif&_user=111111111&_pii=S0307904X13007415&_rdoc=1&_issn=0307904X&md5=2d34131ab364cfce5405e91687c52bc0">JSB inlineImage" height="22" width="215" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0307904X13007415-si9.gif">dden">de">$\mathit{<font\; color="red">d</font>v}=\mathit{kv}(A(t)-v)\mathit{<font\; color="red">d</font>t}+{\mathit{bv}}^{\frac{3}{2}}\mathit{<font\; color="red">d</font>Z}$. This model with d="mmlsi10" class="mathmlsrc">data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0307904X13007415&_mathId=si10.gif&_user=111111111&_pii=S0307904X13007415&_rdoc=1&_issn=0307904X&md5=15157759beedd70b38c649b8817e2e5e" title="Click to view the MathML source">A(t)dden">de">$A(t)$ constant has been proven by many authors to outperform the Heston model in its ability to capture the behaviour of volatility and fit option prices. Further, singular perturbation techniques are used to derive a simple analytic approximation suitable for pricing options with short tenor, a common feature of most options traded in the market.