Dupire's equation for bubbles
Dupire's equation for bubbles
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杜皮尔气泡方程
DOI：
10.1142/s0219024912500410
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发表时间：
2012
影响因子：
0.5
通讯作者：
J. Tysk
中科院分区：
文献类型：
--
作者：
Erik Ekström;J. Tysk
我们研究了带有气泡的局部波动率模型的Dupire方程，即贴现的标的资产遵循严格的局部鞅的模型。如果期权价格由风险中性估值给出，则贴现期权价格过程是一个真正的鞅，并且我们证明了看涨期权的Dupire方程与通常的方程相比包含额外的条款。然而，看跌期权的Dupire方程采用的是通常的形式。此外，Dupire方程解的唯一性在一般情况下是丧失的，我们展示了如何从所有可能的解中挑选出期权价格。本文还研究了衍生品折现价格过程仅为局部鞅的模型的Dupire方程。
We study Dupire's equation for local volatility models with bubbles, i.e. for models in which the discounted underlying asset follows a strict local martingale. If option prices are given by risk-neutral valuation, then the discounted option price process is a true martingale, and we show that the Dupire equation for call options contains extra terms compared to the usual equation. However, the Dupire equation for put options takes the usual form. Moreover, uniqueness of solutions to the Dupire equation is lost in general, and we show how to single out the option price among all possible solutions. The Dupire equation for models in which the discounted derivative price process is merely a local martingale is also studied.