# Questions tagged [continuous-time]

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### 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 ...
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### 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 ...
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### 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 ...
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### Non attainable claim - Incomplete market

I am wondering whether there is a standard procedure to find a non attainable (i.e. non replicable) asset in an incomplete market. As an example, let us have the following market ($B = (B^1, B^2, B^3)$...
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### Black Scholes in Practice: Delta Hedging

From the Wikipedia page, we know call option as an example is price through delta hedging. $$\Pi=-V+V_SS$$ and over $[t,t+\triangle t]$ $$\triangle\Pi=-\triangle V+V_S\triangle S$$ My questions ...
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### What's a good book to learn computational finance topics?

I know continuous finance theory roughly equivalent to what's in Bjork's Arbitrage Theory In Continuous Time (most chapters). I'd like to supplement that knowledge with a more hands-on practical ...
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### Value of contingent claim at a given time

Consider a contingent claim whose value at maturity T is given by $\min(S_{T_0}, S_T)$ where $T_0$ is some intermediate time before maturity, $T_0 < T$, and $S_T$ and $S_{T_0}$ are the asset price ...
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### 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 ...
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### Which references would be useful as an introduction to econometrics as it pertains to CONTINUOUS TIME models?

It seems like the problem of trying to estimate model parameters for continuous time models is not commonly covered in standard econometric textbooks, even those focusing on time series. I certainly ...
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### 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 ...
396 views

From Lando (2004)* I am trying to replicate the following figure (Section 2.6 Default Barriers: The Black-Cox Setup): The spreads are computed as follows: $$s(T) = \frac{1}{T}\ln\frac{D}{B_0}-r$$ ...
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### What exactly is the 'continuous asset price model'?

I am reading An Introduction to Financial Option Valuation by Higham. In Chapter 6, the book covers two asset price models, a discrete one and a continuous one. In Section 6.3 (Continuous asset model) ...