Questions tagged [continuous-time]

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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-Cox yield spreads

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 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 ...
Maeu's user avatar
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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,...
LuLuLu's user avatar
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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 ...
user86422's user avatar
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Comparative statics on $c/r$ using fundamental asset pricing equation

Consider the fundamental asset pricing equation for a perpetual coupon bond: $$rP = c + \mu P' + \sigma^2/2 P''$$ with standard boundary conditions $P(\bar x) = \bar x$ and $\underset{x\rightarrow \...
Luca Gi's user avatar
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Is there a closed form solution to the following system of SDEs?

Suppose we have the system \begin{align} dr_t=\alpha_r(x_t-r_t)dt+\sigma_rdW_t^r\\ dx_t=\alpha_x(\bar{x}-x_t)dt+\sigma_xdW_t^x\\ \end{align} As this system is affine, I believe there should be an easy ...
Carl's user avatar
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Derive Q-dynamics of $\ln S_t$ having multiplicative error structure

From Kwon, T. Y. (2012). Three essays on credit risk models and their bayesian estimation (Doctoral dissertation): Assume the following log equity price model: $$\ln S_t = g_S(V_t,t,\Theta_V) + Z_T$$...
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A hitting time of an open set for a càdlàg process is a stopping time

In Protter Stochastic Integration and Differential Equations, Springer (2003), the following definition is given: Definition. Let $X$ be a stochastic process and let $\Delta$ be a Borel set in $\...
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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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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) ...
herbhofsterd's user avatar
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Stock price modelling under binomial tree model?

In binomial tree model, the stock price is modelled in the form of $S_{k\delta}=S_{(k-1)\delta}\exp(\mu\delta+\sigma\sqrt\delta Z_k)$, where $\delta$ is time invertal between two observations $S_{k\...
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Cost of carry proof

I'm currently review Arbitrage Pricing in Continuous time by Bjork and am stuck on this concept: Honestly I'm not too sure where to start as this chapter makes no mention of the Cost of Carry formula ...
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Can Merton's continuous-time portfolio model be reformulated without a utility function?

Under the standard Merton optimization problem the agent maximizes expected utility $$J(\pi,c) =\mathbb{E}\Big[\int_0^TU(c_tX_t) dt + U(X_T)\Big],$$ where the dynamics of wealth of the agent satisfy $...
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