Mathematical Finance
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A YIELD‐FACTOR MODEL OF INTEREST RATES
Mathematical Finance - Tập 6 Số 4 - Trang 379-406 - 1996
This paper presents a consistent and arbitrage‐free multifactor model of the
term structure of interest rates in which yields at selected fixed maturities
follow a parametric muitivariate Markov diffusion process with “stochastic
volatility.” the yield of any zero‐coupon bond is taken to be a
maturity‐dependent affine combination of the selected “basis” set of yields. We
provide necessary and suff...
Unspanned stochastic volatility in the multifactor CIR model
Mathematical Finance - Tập 29 Số 3 - Trang 827-836 - 2019
AbstractEmpirical evidence suggests that fixed‐income markets exhibit unspanned
stochastic volatility (USV), that is, that one cannot fully hedge volatility
risk solely using a portfolio of bonds. While Collin‐Dufresne and Goldstein
(2002, Journal of Finance, 57, 1685–1730) showed that no two‐factor
Cox–Ingersoll–Ross (CIR) model can exhibit USV, it has been unknown to date
whether CIR models with...
TRACTABLE ROBUST EXPECTED UTILITY AND RISK MODELS FOR PORTFOLIO OPTIMIZATION
Mathematical Finance - Tập 20 Số 4 - Trang 695-731
Static hedging and pricing of exotic options with payoff frames
Mathematical Finance - Tập 29 Số 2 - Trang 612-658 - 2019
AbstractWe develop a general framework for statically hedging and pricing
European‐style options with nonstandard terminal payoffs, which can be applied
to mixed static–dynamic and semistatic hedges for many path‐dependent exotic
options including variance swaps and barrier options. The goal is achieved by
separating the hedging and pricing problems to obtain replicating strategies.
Once prices ha...
Coherent Measures of Risk
Mathematical Finance - Tập 9 Số 3 - Trang 203-228 - 1999
In this paper we study both market risks and nonmarket risks, without complete
markets assumption, and discuss methods of measurement of these risks. We
present and justify a set of four desirable properties for measures of risk, and
call the measures satisfying these properties “coherent.” We examine the
measures of risk provided and the related actions required by SPAN, by the
SEC/NASD rules, an...
Explicit Representation of the Minimal Variance Portfolio in Markets Driven by Lévy Processes
Mathematical Finance - Tập 13 Số 1 - Trang 55-72 - 2003
In a market driven by a Lévy martingale, we consider a claim ξ. We study the
problem of minimal variance hedging and we give an explicit formula for the
minimal variance portfolio in terms of Malliavin derivatives. We discuss two
types of stochastic (Malliavin) derivatives for ξ: one based on the chaos
expansion in terms of iterated integrals with respect to the power jump
processes and one based ...
BEHAVIORAL PORTFOLIO SELECTION IN CONTINUOUS TIME
Mathematical Finance - Tập 18 Số 3 - Trang 385-426 - 2008
This paper formulates and studies a general continuous‐time behavioral portfolio
selection model under Kahneman and Tversky's (cumulative) prospect theory,
featuring S‐shaped utility (value) functions and probability distortions. Unlike
the conventional expected utility maximization model, such a behavioral model
could be easily mis‐formulated (a.k.a. ill‐posed) if its different components do
not ...
OPTIMAL INSURANCE DESIGN UNDER RANK‐DEPENDENT EXPECTED UTILITY
Mathematical Finance - Tập 25 Số 1 - Trang 154-186 - 2015
We consider an optimal insurance design problem for an individual whose
preferences are dictated by the rank‐dependent expected utility (RDEU) theory
with a concave utility function and an inverse‐S shaped probability distortion
function. This type of RDEU is known to describe human behavior better than the
classical expected utility. By applying the technique of quantile formulation,
we solve the...
Return Dynamics when Persistence is Unobservable
Mathematical Finance - Tập 11 Số 4 - Trang 415-445 - 2001
This paper proposes a new theory of the sources of time‐varying second (and
higher) moments in financial time series. The key idea is that fully rational
agents must infer the stochastic degree of persistence of fundamental shocks.
Endogenous changes in their uncertainty determine the evolution of conditional
moments of returns. The model accounts for the principal observed features of
volatility ...
A DIFFUSION MODEL FOR ELECTRICITY PRICES
Mathematical Finance - Tập 12 Số 4 - Trang 287-298 - 2002
Starting from a simple supply/demand model for electricity, we obtain a
diffusion (i.e., jumpless) model for spot prices which can exhibit price spikes.
We estimate the parameters in the model using historical data from the Alberta
and California markets. and compare this model with some others used for spot
prices.
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