The purpose of this paper is to explain the reasoning and insight behind the calculation of Indicative Prices for Danish mortgage bonds calculated on NASDAQ on a daily basis.

The paper will be organized as follows: First liquidity in the Danish Mortgage Bond Market will be discussed and the challenges inherent in the market with respect to missing market prices. This will be followed up with a discussion of the principles of Prudent Valuation.

After that there is 2 sections, one that focus on non-callable Danish Mortgage Bonds and one focusing on Fixed Rate callable Mortgage Bonds. Each section, will contain some insight into the calculation and some examples on the calculated indicative prices.

In the last chapter the rating model – which is implemented for the Indicative Prices – will be described. It will all end with a short conclusion.

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This presentation is a follow up on the presentation: “Financial Crisis of 2008”

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The purpose of this paper is to explain the background behind the key-figures for the danish mortgage bonds that are calculated on NASDAQ and at the same time give some insight into the methods employed.

The paper is organized as follows. It starts off with a short history of the Danish Mortgage Credit System.

Next we look at the different kind of Bond-Types, such as: Callable annuity bonds, Non-callable bullet bonds, Floating-to-Fixed, Capped Floaters and Ratchets and Floating-rate bonds. After this we go through the different risk-measures that are being calculated.

The last section is the Technical Section, and it contains the following sub-sections: The stochastic Interest Rate Model, Factors influencing the prepayment behaviour, The debtor distribution, Determining the refinancing-rate, Published prepayments – how are they included in the Prepayment Model?, Delivered or Synthetic cash flow?, The Prepayment Model and The Pricing principle.

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This presentation contains a short introduction to the concepts: Fragility and Anti-Fragility – ideas which original comes from Nassim Taleb 2012 “Antifragil – Things that Gain form Disorder”

The presentation also addresses: Closeout, regulatory issues and payoff risk.

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This paper has two objectives. First we will construct a general model for the variation in the term structure of interest rates, or to put it another way, we will define a general model for the shift function. Secondly, I will specify a VaR model which uses the shift function derived in the first part of the paper as its main building block.

Firstly, using Principal Component Analysis (PCA) we show that it takes a 4 factor model (which, in principle, can very well be considered a 3 factor model due to the limited effect of factor four (4)) to explain the variation in the term structure of interest rates over the period from the beginning of 1990 to mid-1998. These 3 factors can be called a Level factor, a Slope factor and a Curvature factor, where this is in line with what is generally reported in the literature, see among others Litterman and Scheinkmann (1988).

Secondly, we specify a VaR model which relies on the scenario simulation procedure of Jamshidian and Zhu (1997). The general idea behind the scenario simulation procedure is to limit the number of portfolio evaluations by using the factor loadings derived in the first part of paper and then specify particular intervals for the Monte Carlo simulated random numbers and assign appropriate probabilities to these intervals (states).

We find that the scenario simulation procedure is computational efficient, because we with a limited number of states is capable of deriving robust approximations of the probability distribution. We also find that it is very useful for non-linear securities (Danish MBBs), and argue that the method is feasible for large portfolios of highly complex non-linear securities – for example Danish MBBs.

**Keywords:** Multi-factor models, PCA, empirical yield-curve dynamics, APT, VaR, Monte Carlo simulation, scenario simulation, non-linear securities – Danish MBBs

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This presentation discusses counterparty-risk in terms of CVA/DVA. This both from a practical angle and a more pricing theoretical view – with intuition. The presentation, include both the unilateral and the bilateral case.

The presentation also addresses: Closeout, regulatory issues and payoff risk.

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This presentation focuses on a practical example on the modelling of Tail-Risk for Danish Mortgage Bonds during the Financial Crisis of 2008. The message here is: It is worth the effort to try to get better estimates for the Tail-Risk!

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This presentation focus is the discussion of Tail-Risk, and which methods are available.

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This presentation focuses on given an introduction to the modelling of Operationel Risk. Different Risk approaches to Operationel risk are shortly surveyed. Apart from this the presentation includes some selected cases from the financial crisis and what we can learn from these cases.

The presentation also addresses: Closeout, regulatory issues and payoff risk.

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In this paper we first show how to determine the T-forward adjusted risk-measure using the concept of fundamental solution to linear PDE’s. After that, relying on Fourier transformation we derive bond-and bond-option prices for the Extended Vasicek model from Hull and White (1990) and the Quadratic Interest Rate model. With respect to the Quadratic Interest Rate model we succeed in carrying the analysis much further than Jamshidian (1996). A special discrete time model – which in some cases is appropriate for the Quadratic Interest Rate model – is also derived.

The last part of the paper analyse Monte Carlo techniques in connection with spot-rate models with a time-dependent drift. We also introduce a method – using the concept of forward induction – that constrain the Monte Carlo simulated spot-rate process for the matching of the initial yield-curve. For the pricing of path-dependent contingent claim, we deduce that, even though Monte Carlo is the natural method to use, it might not be the most efficient one – at least not when the spot-rate is Markovian.

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