The martingale tag has no wiki summary.
12
votes
5answers
2k views
Is the stock price process a martingale or a Markov process?
Some people claim that the data-generating process for stocks is a "martingale" and that is has the "Markov property".
Are they unrelated? Is it that the Markov property implies some sort of ...
9
votes
4answers
2k views
What is a martingale?
What is a martingale and how it compares with a random walk in the context of the Efficient Market Hypothesis?
6
votes
1answer
406 views
How do equivalent martingale measures arise in pricing?
I'm studying for an exam in financial models and came across this question:
"An agent with $C^2$ strictly increasing concave utility $U$ has wealth $w_0$ at time 0, and wishes to invest his wealth in ...
5
votes
3answers
443 views
How to use Itô's formula to deduce that a stochastic process is a martingale?
I'm working through different books about financial mathematics and solving some problems I get stuck.
Suppose you define an arbitrary stochastic process, for example
$ X_t := W_t^8-8t $ where $ W_t ...
4
votes
1answer
279 views
Change of measure discrete time
Suppose I have a random walk $X_{n+1} = X_n+A_n$ where $A_n$ is an iid sequence, $\mathsf EA_n = A>0$. How to construct a martingale measure for this case?
3
votes
1answer
128 views
Parameter estimation using martingale measures - include real world data?
Please note: I posted this in nuclearphynance first, but didn't get any replies.
For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic ...
2
votes
1answer
123 views
Assumptions based on non-martingale?
Quantitative finance formular are mostly based on martingales, Poisson jump, GBM, CEV, etc..
The logic behind it is that martingale means the future could not be predicted, or, EMH (Efficient-market ...
2
votes
0answers
101 views
Measure change in a bond option problem
This is not a homework or assignment exercise.
I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
