Strict Local Martingales, Bubbles, and No Early Exercise

نویسنده

  • Soumik Pal
چکیده

We show pathological behavior of asset price processes modeled by continuous strict local martingales under a risk-neutral measure. The inspiration comes from recent results on financial bubbles. We analyze, in particular, the effect of the strict nature of the local martingale on the usual formula for the price of a European call option, especially a strong anomaly when call prices decay monotonically with maturity. A complete and detailed analysis for the archetypical strict local martingale, the reciprocal of a three dimensional Bessel process, has been provided. Our main tool is based on a general h-transform technique (due to Delbaen and Schachermayer) to generate positive strict local martingales. This gives the basis for a statistical test to verify a suspected bubble is indeed one (or not).

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Analysis of continuous strict local martingales via h-transforms

We study strict local martingales via h-transforms, a method which first appeared in Delbaen-Schachermayer [7]. Although nonnegative local martingales are supermartingales, we identify a class of convex functions which when applied to such local martingales produce submartingales. We extend part of this analysis to conformal local martingales in dimensions three and higher. An interesting conne...

متن کامل

Strict Local Martingales With Jumps

A strict local martingale is a local martingale which is not a martingale. There are few explicit examples of “naturally occurring” strict local martingales with jumps available in the literature. The purpose of this paper is to provide such examples, and to illustrate how they might arise via filtration shrinkage, a phenomenon we would contend is common in applications such as filtering, contr...

متن کامل

No Arbitrage Conditions For Simple Trading Strategies

Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the c...

متن کامل

No Arbitrage Conditions for Simple Trading Strategies Erhan Bayraktar and Hasanjan Sayit

Strict local martingales may admit arbitrage opportunities with respect to the class of simple trading strategies. (Since there is no possibility of using doubling strategies in this framework, the losses are not assumed to be bounded from below.) We show that for a class of non-negative strict local martingales, the strong Markov property implies the no arbitrage property with respect to the c...

متن کامل

A Visual Criterion for Identifying Itô Diffusions as Martingales or Strict Local Martingales

It is often important, in applications of stochastic calculus to financial modelling, to know whether a given local martingale is a martingale or a strict local martingale. We address this problem in the context of a time-homogenous diffusion process with a finite lower boundary, presented as the solution of a driftless stochastic differential equation. Our main theorem demonstrates that the qu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007