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2
votes
2answers
85 views

Markov Pricing kernel

I'm reading about Markov pricing kernels in the lecture notes of a course I'm following, but I have a big doubt on an application of Ito's lemma. The setting is the following: We define the pricing ...
2
votes
3answers
267 views

Why does [dz(t)]^2 converge to dt over infinitesimally short time periods?

I have some trouble understanding a chapter in George Pennacchi textbook "Asset Pricing". Here the author shows that the square of a Wiener Process $[dz(t)]^2$ converges to $dt$ for infinitesimally ...
1
vote
1answer
111 views

Arbitrage Strategy Proof in Bjork

In Tomas Bjork's Arbitrage Theory in Continuous Time (or here), $\exists$ this proposition Proposition 2.9 Suppose that a claim X is reachable with replicating portfolio h. Then any price at t=0 of ...
0
votes
1answer
35 views

GNP/GDP and modelling [closed]

Is GNP a continuous, static or a dynamic model ? What about GDP ? What I do know is that it has yearly discrete values. However, when it is modeled, it becomes a continuous graph. So what exactly is ...
1
vote
1answer
194 views

Examples of non-increasing variance of a time homogeneous Markovian process

This is an edit to the previous question, on stationary process, which was answered by Richard below. Let $x_t$ be a zero mean, time homogeneous Markovian process over time $t$ starting from ...
5
votes
1answer
194 views

From $AR(p)$ to SDE

Let the Vasicek model to be $$\Delta r_{t}=k(\theta - r_{t-1})\Delta t+\sigma\Delta z_{t}$$ Due to the fact that $$\Delta r_{t}=r_{t}-r_{t-1}$$ if you let $\Delta t=1$, it is easy to see by ...
2
votes
3answers
852 views

Analyze raw tick data

I'd like to work with raw tick data and naturally this data is unevenly spaced (for example, a couple of quotes are at the same second etc.) For example ...
8
votes
4answers
479 views

Position management in presence of continuous forecast

Let's say we have an equity liquidity-providing model that was fitted on 1 minute bar periods. The model forecasts the 1-min next period return given the activity of the previous bars. Now, when we ...
7
votes
1answer
3k views

What are the main differences between discrete and continuous time models when modeling asset price dynamics?

My intuition says that both approaches, discrete time models and continuous time models will be models (i.e. approximations) of reality. Therefore it should be possible to develop useful models in ...