Questions tagged [continuous-time]

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The continuous-time limit of asset price processes where there is more than one asset

I've read Merton's article "On the Mathematics and Economics Assumptions of Continuous-Time Models" (Reprinted in Continuous-time Finance, Chapter 3), where Merton proved that the price of ...
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How to construct continuous futures contracts with multiple maturities

I am trying to replicate the Schwartz-Smith (2000) model and having an issue understanding what the data is and how to generate it. Specifically, the authors use a table of continuous futures with ...
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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) ...
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Relationship of par-curve and zero-curve/spot-curve

I've been trying to bootstrap the zero-curve from a swap curve composed of ESTR OIS swaps. Theory says when the par-curve is upward sloping, the zero-curve will be above the par-curve and vice-versa. ...
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Is Ornstein–Uhlenbeck process the continuous-time correspondence of AR(1) process?

I see the AR(1) process (with $|\alpha| < 1$) can be written in the following way: $$x_{t+1} = \alpha x_t + \epsilon_t$$ $$\Delta x_t = - (1 - \alpha) x_t + \epsilon_t$$ which looks quite like the ...
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Why Girsanov's theorem used here?

It is written in Bjork's ArbitrageTheoryInContinuousTime that ... Assume a martingale measure Q exists. This implies (see the Girsanov theorem) that the price processes have zero drift under $Q$ .....
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What topics come after continuous finance a la Bjork?

Ok so I've understood stochastic calculus and continuous finance. Basically, all of Bjork's "Arbitrage Theory in Continuous Time". What books/topics come next? I was thinking of taking a more ...
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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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which method is the roubust method to estimate the Hurst parameter?

I know there exist lots of method to estimate the Hurst parameter, such as R/S, V/S, GHE, DFA, DMA, Wavelet Spectral Density, Whittle and so on. Can you tell me which one is the best one. Is anyone ...
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Is the 'constant weight in the risky asset' portfolio-strategy self-financing?

My question concerns a topic in quantitative finance that I feel is often brushed under the table: is a given strategy self-financing. We have two assets, one risky and one riskless, defined by the ...
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Why can't/doesn't the Fed adjust the federal funds interest rate continuously?

Maybe the question I'm asking doesn't make sense-- but this is something I've wondered about since I learned about the Fed in high school. The media typically talks about Fed interest rate changes as ...
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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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Bjork exercise 7.6: Claim that depends on $T_1$ and $T_0$

See the solution to Exercise 7.6 here. The solution calculates $E^Q (S(T_1)/S(T_0))$ and then just plugs that into the risk neutral valuation formula. But why? The risk neutral valuation formula ...
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Pricing Secured Barrier Call

A European barrier call with barrier $B = 50$, expiration $T = 31$, and strike $K = 33$ costs $12$. The investor is interested in a product that, unlike this barrier call, offers some protection for ...
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How to construct a continuous price time series out of futures raw data in Excel?

My object of research is corn futures: It is well known that corn futures expire 5 times per year: March, May, July, September and December. Due to their finite life that is limited by their maturity,...
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Figure of Stopping and Continuation Region

I am reading Alternative Characterizations of American Put Options by Carr et al. It is stated there that: Consider an American put option on the stock with strike price $K$ and maturity date $T$. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $x_0=0$. ...
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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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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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