This exercise deals with obtaining martingales. Suppose X t is a geometric process with drift ? and
Question:
This exercise deals with obtaining martingales. Suppose Xt is a geometric process with drift ? and diffusion parameter ?.
(a) When would the e-rt Xt be a martingale? That is, when would the following equality hold.
(b) More precisely, remember from the previous derivation that
Or, again,
Which selection of ? would make e?rt?Xt a martingale? Would
? = r
work?
(c) How about
? = r + ?2?
(d) now try:
? = r ? ? ?2.
Note that each one of these selections defines a different distribution for the e?rt Xt.
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...
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Related Book For 
An Introduction to the Mathematics of financial Derivatives
ISBN: 978-0123846822
2nd Edition
Authors: Salih N. Neftci
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