| 1. |
- Aurell, Erik, et al.
(författare)
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Growth optimal investment and pricing of derivatives
- 2000
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Ingår i: Physica A. - 0378-4371 .- 1873-2119. ; 280:04-mar, s. 505-521
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Tidskriftsartikel (refereegranskat)abstract
- We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. tinder the assumptions of no trading costs, and no restrictions on lending, we find an appropriate equivalent martingale measure that prices the underlying and the derivative security. We compare our result with other alternative pricing procedures in the literature, and discuss the limits of validity of the lognormal approximation. We also generalize the pricing method to a market with correlated stocks. The expected estimation error of the optimal investment fraction is derived in a closed form, and its validity is checked with a small-scale empirical test.
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| 2. |
- Hult, Henrik, 1975-, et al.
(författare)
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Convex Optimization
- 2012
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Ingår i: Springer Series in Operations Research and Financial Engineering. - New York, NY : Springer Nature. ; , s. 33-38
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Bokkapitel (refereegranskat)abstract
- Many of the investment and hedging problems we will encounter can be formulated as a minimization of a function over a set determined by the investor’s risk and budget constraints and other restrictions on the type of positions that the investor can take. Such problems become particularly tractable if both the function to be minimized and the set over which the minimization is done are convex. The minimization problem is in this case called a convex optimization problem. This chapter presents basic results for solving convex optimization problems that will be applied in subsequent chapters.
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| 3. |
- Hult, Henrik, 1975-, et al.
(författare)
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Empirical Methods
- 2012
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Ingår i: Risk and Portfolio Analysis. - New York, NY : Springer Nature. ; , s. 197-229
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Bokkapitel (refereegranskat)abstract
- In this chapter we consider a modeling approach that uses a set of historical data, such as bond prices, share prices, claim sizes, or exchange rates, to model the value at a future time T > 0 of portfolios whose values depend on a given set of assets and possibly also liabilities. Here we want the data to speak for themselves in the sense that the model for the future values should only be based on information available in the given historical data samples. The assumption we make is therefore that the information in the samples is representative of future values and that no additional probability beliefs of the modeler are relevant.
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| 4. |
- Hult, Henrik, 1975-, et al.
(författare)
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Multivariate Models
- 2012
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Ingår i: Risk and Portfolio Analysis. - New York, NY : Springer Nature. ; , s. 273-330
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Bokkapitel (refereegranskat)abstract
- In this chapter, we consider multivariate models for the joint distribution of several risk factors such as returns or log returns for different assets, zero rate changes for different maturity times, changes in implied volatility, and losses due to defaults on risky loans. Our aim is to specify a good model for the future value g(X) of a portfolio, where the function g is known and its argument X is a random vector of, for instance, log returns and zero rate changes over a given future time period. Since the function g is known, what remains is to make a good choice of probability distribution for random vector X.
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| 5. |
- Hult, Henrik, 1975-, et al.
(författare)
-
Parametric Models and Their Tails
- 2012
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Ingår i: Springer Series in Operations Research and Financial Engineering. - New York, NY : Springer Nature. ; , s. 231-271
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Bokkapitel (refereegranskat)abstract
- In this chapter we consider approaches to selecting a parametric family of distributions for a random variable and approaches to estimating the parameters. We also present techniques for analyzing the tails of the chosen probability distribution and the effect of the tails on the estimation of risk measures. Finally, we consider a semiparametric approach to the estimation of tail probabilities. It provides an alternative to relying on a full parametric model in order to produce estimates of tail probabilities beyond the range of the sample data.
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| 6. |
- Hult, Henrik, 1975-, et al.
(författare)
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Quadratic Hedging Principles
- 2012
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Ingår i: Risk and Portfolio Analysis. - New York, NY : Springer Nature. ; , s. 39-83
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Bokkapitel (refereegranskat)abstract
- Fix a future time T and let L be the value of a liability at that time. One example of L is the portfolio value of derivative instruments issued by a bank. Another example is the value of future claims from insurance products sold by an insurance company. Typically the holder of the liability does not want to speculate on a favorable outcome of this random variable. The ideal approach to managing the risk of an unfavorable outcome of L would be to purchase a portfolio whose value A (A for assets) at the future time T exactly matches that of the liability. In that case, A = L, and the risk of an unfavorable outcome of L is removed completely by purchasing the asset portfolio. The problem with this approach is that it is not always possible to find a portfolio of assets whose future value corresponds exactly to that of the liability; one example is when the liability is made up of insurance claims.
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| 7. |
- Hult, Henrik, 1975-, et al.
(författare)
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Quadratic Investment Principles
- 2012
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Ingår i: Risk and Portfolio Analysis. - New York, NY : Springer Nature. ; , s. 85-126
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Bokkapitel (refereegranskat)abstract
- In this chapter, we present investment principles solely based on means and variances of asset returns and budget restrictions. To begin with, we only consider risky assets in the sense that the variances of the returns are strictly positive. We will then consider the more interesting situation where we also have the possibility to invest (or deposit) money in a risk-free asset.
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| 8. |
- Hult, Henrik, 1975-, et al.
(författare)
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Risk Measurement Principles
- 2012
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Ingår i: Risk and Portfolio Analysis. - New York, NY : Springer Nature. ; , s. 159-194
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Bokkapitel (refereegranskat)abstract
- In this chapter, we take a close look at the principles of risk measurement. We argue that it is natural to quantify the riskiness of a position in monetary units so that the measurement of the risk of a position can be interpreted as the size of buffer capital that should be added to the position to provide a sufficient protection against undesirable outcomes. In the investment problems in Chap. 4, variance was used to quantify the riskiness of a portfolio. However, variance, being just the expected squared deviation from the mean value, does not differentiate between good positive deviations and bad negative deviations and cannot easily be translated into meaningful monetary values unless the future value we consider is close to normally distributed. The risk premium considered in Chap. 5 is more natural than the variance as a summary of the riskiness and potential reward of a position. However, the risk premium is difficult to use effectively to control the risk taking of a financial institution or to determine whether the aggregate position of a company or business unit is acceptable from a risk perspective. In this chapter, we will present measures of risk, including the widely used value-at-risk and expected shortfall, analyze their properties, and evaluate their performance in a large number of examples.
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| 9. |
- Hult, Henrik, 1975-, et al.
(författare)
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Utility-Based Investment Principles
- 2012
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Ingår i: Risk and Portfolio Analysis. - New York, NY : Springer Nature. ; , s. 127-157
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Bokkapitel (refereegranskat)abstract
- In the previous chapter we measured the quality of an investment in terms of the expected value E[V1] and the variance Var(V1) of the future portfolio value V1 and determined portfolio weights (subject to constraints) that maximize a suitable trade-off$$\mathrm{E}[{V }_{1}] - c\mathrm{Var}({V }_{1})/(2{V }_{0})$$ between a large expected value and a small variance. Attractive features of this approach are that the probability distribution of V1 does not have to be specified in detail and that explicit expressions for the optimal portfolio weights are found that have intuitive interpretations. We saw that this approach makes perfect sense if we consider portfolio values V1 that can be expressed as linear combinations of asset returns whose joint distribution is a multivariate normal distribution. However, unless there are good reasons to assume a multivariate normal distribution (or, more generally, as will be made clear in Chap. 9, an elliptical distribution), solutions provided by the quadratic investment principles can be rather misleading. Here we want to allow for a probability distribution of any kind, and this calls for more general investment principles that are not only based on the variance and expected value of V1.
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