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5

I could be wrong, but this question seems to be about taking one set of cash flows and representing it using a set of derivatives. There are an almost unlimited number of applications for this kind of approach. There is an entire field of study dedicated to it: financial engineering. A good textbook on the subject is "Principles of Financial ...


3

If you allow $X_t$ to be two dimensional then a model with a stock price $X_t^1$ and its variance process $X_t^2$ (stochastic volatility) would fit your definition. In such cases to my knowledge we often don't have a closed form of the density of $X_T^1$ but in some cases we have a closed form of the Laplace transform. An example is the Heston model.


3

In my estimation, you are best-served by creating these sheets from scratch. There are a number of reasons for this: You will thoroughly understand the underlying machinations of each calculation You can customize to your specific needs, and so on... If you are looking for some decent introductory texts, I have benefited from Moyer Excel Templates. More ...


3

I don't know what $\mu$ stands for in the model so let me just recall the standard Black-Scholes formalism. It's likely that everything can be extended with minor modifications to the model you're interested in. The price of the vanilla call option with a strike $K$ is equal to the expectation of the discounted pay-off $$C_K=\mathbb E(e^{-rT}(S_T-K)_+),$$ ...


2

I would create separate estimates for volume and choice of debt instrument. There are tools to estimate these simultaneously but I do not see a compelling advantage here. I assume the volume is conditional on the choice of debt issuance so you might start by predicting choice of debt issuance and use this as an input to the volume model. The volume model ...


2

@amber - As a general hint: try to solve a small-scale case first. Pick a two- or better three-asset $(\mu,\Sigma)$ and construct the objectives. Construct the "skewness tensor" (it's not a matrix, you can think of it like a "cube" or something - consult this book on how you can actually represent it as a matrix, or Fabozzi et al's textbook for an ...


2

Saying that you can't analyze something as is does not make it garbage. You can't eat flour "as-is", but that doesn't mean you throw it out. In order to use "standard" analysis tools, you must first transform the series into something compatible. Some examples of such a transformation include k-th order differences or a log transformation. These ...


2

Bond Price Dynamics I do not know the source of the bond dynamics you show above but seeing how we are dealing with an affine model there is a very elegant way to derive those. Due to the model being affine the bond price is given by $$P(t,T)=A(t,T)e^{-r(t)B(t,T)}$$ you can find the exact formulas for $A(t,T)$ and $B(t,T)$ in this document (or just read ...


1

Net Debt = Total Debt - Cash You can also see from the graph, that Net Debt is always below Total Debt. Cash (and liquid marketable securities) is deducted from Debt, because it could be in theory directly used to repay the debt, hence only "Net Debt" is important; think a company with 1mio Debt and 1mio Cash, one would not say it was in debt because it ...


1

Any of a wide variety of local vol models, where (from your equation) $b(\cdot,\cdot)$ is some fitted surface, are unlikely to have closed-form solutions for the terminal distribution. Indeed it's well-known that these models tend to have very unusual forward term structures of volatility. As a specific example, take $b(\cdot,\cdot)$ to be an approximation ...


1

There is a lot of ways to understand why stationarity allows to apply usual time series analysis. Here is one more. Very often, the theoretical justification of what you do in time series need to be able to identify the mean formula and the expectation: $$\frac{1}{N}\sum_{n=1}^N X_n \underset{N\rightarrow +\infty}{\longrightarrow} \mathbb{E} X, $$ where the ...


1

You can check the wikipedia page to find out "the the basic model assumptions" for the a stationary random process, and I assume "the correct reasoning on relationships" are the model that describe a random process. But intuitively speaking, if the data are sampled from a stationary random process, then you can predict the future by deductively extrapolate ...


1

I'm not aware of any exercises. You do not mention whether you tried Google. A good set of spreadsheets is on the Home Page for Aswath Damodaran. You could convert it into "exercises" by first working through them yourself and then comparing to Damodaran's solution (or whether it gives the same results).


1

It seems that you speak about a "quote tax". In Europe some markets now ask for fees for orders even if they are not executed if you exceed an order to trade ratio to prevent them from cpu-harrassing flows. Let s wait and see what will append. The effect should be similar to the One of a tax. The real question is: how can you make the difference between an ...



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