5
votes
Accepted
markov property for stochastic differential equation
Here, we assume that
\begin{align*}
g(t, x) = \mathbb{E}\left(h(X_T) \mid X_t = x \right).
\end{align*}
Note that, by Shiryaev, $g(t, x)$
is a Borel measurable function such that, for any Borel ...
- 21.3k
3
votes
Accepted
Use of markov process in option pricing
The Markov property dictates that the future states of a stochastic process only depend on its current state, not any previous states. In a discrete setting, this can be written as:
$$\mathbb{P}(X_{n+...
- 6,515
3
votes
Prove that $E[g(X_T)|\mathscr F_t] = E[g(X_T)|X_t]$
This is a corollary of Feynman-Kac theorem. For self-containedness,
I re-produce the proof as follows.
Assume that there exists a $C^{1,2}$-function $F=F(t,x)$ defined
on $[0,T]\times\mathbb{R}$ that ...
3
votes
Accepted
When predicting Forex price using HMM what, typically, are the states and what are the observations?
Your decision. You can define the states to be "positive return" or "negative return". So if the return is negative, then its state would be that "negative return".
Or, you could even model them ...
- 46
2
votes
Accepted
Non-recombining lattice in non-markovian models
I think I might have found the solution to my own question. The Markov property as stated above has no direct relation with the recombination of the approximating lattice. However, if we consider the &...
2
votes
Accepted
Markov switching regime for stock returns
Two things to note:
First you are assuming that stock returns follow some type of AR(1) which I do not think is a reasonable model;
Casting consideration (1) aside, you can estimate what you want by ...
- 8,621
2
votes
Accepted
Continuous-time two-state Markov process
This is a continuous-time Markov chain with rate matrix
$$Q=\begin{pmatrix}
-\mu_H & \mu_H\\
\mu_L & -\mu_L
\end{pmatrix}.$$
The transition matrix associated with going from time $t$ to time $...
- 237
1
vote
How can I 'quantize' a time-series in 'groups' exhibiting similar patterns?
Regime detection with hidden Markov model:
http://scikit-learn.sourceforge.net/stable/modules/hmm.html
- 194
1
vote
Accepted
Why does the Weak Form of Market Efficiency and Markov Property hold?
The weak form of the efficient market hypothesis (EMH) just says that the market is efficient to all prior information contained within price. By definition, the weak form of EMH obeys the Markov ...
- 3,025
1
vote
Why Markov Functional Models (Hunt 2000) are not yet so popular?
The Markov-functional model is widely used by dealers around the Street in particular for Bermudan swaptions. So we cannot say it is not popular. Of course, there has been some criticisms since its ...
- 49
1
vote
Why Markov Functional Models (Hunt 2000) are not yet so popular?
In context of Bermudan Options, I believe that since the model determines everything exogenously, calibrating to swaptions may give you cases where the implied forward rate is negatively correlated to ...
- 2,561
Only top scored, non community-wiki answers of a minimum length are eligible