203 research outputs found
CAPM, rewards, and empirical asset pricing with coherent risk
The paper has 2 main goals: 1. We propose a variant of the CAPM based on
coherent risk. 2. In addition to the real-world measure and the risk-neutral
measure, we propose the third one: the extreme measure. The introduction of
this measure provides a powerful tool for investigating the relation between
the first two measures. In particular, this gives us - a new way of measuring
reward; - a new approach to the empirical asset pricing
Pricing and hedging in incomplete markets with coherent risk
We propose a pricing technique based on coherent risk measures, which enables
one to get finer price intervals than in the No Good Deals pricing. The main
idea consists in splitting a liability into several parts and selling these
parts to different agents. The technique is closely connected with the
convolution of coherent risk measures and equilibrium considerations.
Furthermore, we propose a way to apply the above technique to the coherent
estimation of the Greeks
Coherent measurement of factor risks
We propose a new procedure for the risk measurement of large portfolios. It
employs the following objects as the building blocks: - coherent risk measures
introduced by Artzner, Delbaen, Eber, and Heath; - factor risk measures
introduced in this paper, which assess the risks driven by particular factors
like the price of oil, S&P500 index, or the credit spread; - risk contributions
and factor risk contributions, which provide a coherent alternative to the
sensitivity coefficients.
We also propose two particular classes of coherent risk measures called Alpha
V@R and Beta V@R, for which all the objects described above admit an extremely
simple empirical estimation procedure. This procedure uses no model assumptions
on the structure of the price evolution.
Moreover, we consider the problem of the risk management on a firm's level.
It is shown that if the risk limits are imposed on the risk contributions of
the desks to the overall risk of the firm (rather than on their outstanding
risks) and the desks are allowed to trade these limits within a firm, then the
desks automatically find the globally optimal portfolio
Selfdecomposability of Weak Variance Generalised Gamma Convolutions
Weak variance generalised gamma convolution processes are multivariate
Brownian motions weakly subordinated by multivariate Thorin subordinators.
Within this class, we extend a result from strong to weak subordination that a
driftless Brownian motion gives rise to a self-decomposable process. Under
moment conditions on the underlying Thorin measure, we show that this condition
is also necessary. We apply our results to some prominent processes such as the
weak variance alpha-gamma process, and illustrate the necessity of our moment
conditions in some cases
Stochastic Volatility for Levy Processes.
Three processes reflecting persistence of volatility are initially formulated by evaluating three Lévy processes at a time change given by the integral of a mean-reverting square root process. The model for the mean-reverting time change is then generalized to include non-Gaussian models that are solutions to Ornstein-Uhlenbeck equations driven by one-sided discontinuous Lévy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general mean-corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean-corrected exponential model is not a martingale in the filtration in which it is originally defined. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered filtrations consistent with the one-dimensional marginal distributions of the level of the process at each future date.Risque de marché; Gestion du risque; Volatilité (finances); Risk management; Volatility (finance); Stochastic processes; Processus stochastiques; Finances; Modèles mathématiques;
From Local Volatility to Local Levy Models.
We define the class of local LĂ©vy processes. These are LĂ©vy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded option prices of all strikes and maturities. The local LĂ©vy processes generalize the class of local volatility models. Closed forms for local speed functions for a variety of cases are also presented. Numerical methods for recovery are also described.Levy processes; Derivatives securities; Random walks (mathematics); Volatility (finance); Options (finance);
Calibration for Weak Variance-Alpha-Gamma Processes
The weak variance-alpha-gamma process is a multivariate LĂ©vy process constructed by weakly subordinating Brownian motion, possibly with correlated components with an alpha-gamma subordinator. It generalises the variance-alpha-gamma process of Semeraro constructed by traditional subordination. We compare three calibration methods for the weak variance-alpha-gamma process, method of moments, maximum likelihood estimation (MLE) and digital moment estimation (DME). We derive a condition for Fourier invertibility needed to apply MLE and show in our simulations that MLE produces a better fit when this condition holds, while DME produces a better fit when it is violated. We also find that the weak variance-alpha-gamma process exhibits a wider range of dependence and produces a significantly better fit than the variance-alpha-gamma process on a S&P500-FTSE100 data set, and that DME produces the best fit in this situation.B. Buchmann's research was supported by ARC grant DP160104737. K. Lu's research was supported by an Australian Government Research Training Program Scholarship
- …