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JournalISSN: 0960-1627

Mathematical Finance 

Wiley-Blackwell
About: Mathematical Finance is an academic journal published by Wiley-Blackwell. The journal publishes majorly in the area(s): Stochastic volatility & Portfolio. It has an ISSN identifier of 0960-1627. Over the lifetime, 887 publications have been published receiving 72610 citations.


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Journal ArticleDOI
TL;DR: In this paper, the authors present and justify a set of four desirable properties for measures of risk, and call the measures satisfying these properties "coherent", and demonstrate the universality of scenario-based methods for providing coherent measures.
Abstract: 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, and by quantile-based methods. We demonstrate the universality of scenario-based methods for providing coherent measures. We offer suggestions concerning the SEC method. We also suggest a method to repair the failure of subadditivity of quantile-based methods.

8,651 citations

Journal ArticleDOI
TL;DR: In this article, different properties of backward stochastic differential equations and their applications to finance are discussed. But the main focus of this paper is on the theory of contingent claim valuation, especially cases with constraints.
Abstract: We are concerned with different properties of backward stochastic differential equations and their applications to finance. These equations, first introduced by Pardoux and Peng (1990), are useful for the theory of contingent claim valuation, especially cases with constraints and for the theory of recursive utilities, introduced by Duffie and Epstein (1992a, 1992b).

2,332 citations

Journal ArticleDOI
TL;DR: In this article, the authors present 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.
Abstract: 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 sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as well as numerical techniques for calculating the prices of term-structure derivative prices. the case of jump diffusions is also considered.

2,288 citations

Journal ArticleDOI
Jin-Chuan Duan1
TL;DR: In this paper, an option pricing model and its corresponding delta formula were developed in the context of the generalized autoregressive conditional heteroskedastic (GARCH) asset return process.
Abstract: This article develops an option pricing model and its corresponding delta formula in the context of the generalized autoregressive conditional heteroskedastic (GARCH) asset return process. the development utilizes the locally risk-neutral valuation relationship (LRNVR). the LRNVR is shown to hold under certain combinations of preference and distribution assumptions. the GARCH option pricing model is capable of reflecting the changes in the conditional volatility of the underlying asset in a parsimonious manner. Numerical analyses suggest that the GARCH model may be able to explain some well-documented systematic biases associated with the Black-Scholes model.

1,177 citations

Journal ArticleDOI
TL;DR: In this paper, a class of term structure models with volatility of lognormal type is analyzed in the general HJM framework, and a two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.
Abstract: A class of term structure models with volatility of lognormal type is analyzed in the general HJM framework. The corresponding market forward rates do not explode, and are positive and mean reverting. Pricing of caps and floors is consistent with the Black formulas used in the market. Swaptions are priced with closed formulas that reduce (with an extra assumption) to exactly the Black swaption formulas when yield and volatility are flat. A two-factor version of the model is calibrated to the U.K. market price of caps and swaptions and to the historically estimated correlation between the forward rates.

1,113 citations

Performance
Metrics
No. of papers from the Journal in previous years
YearPapers
202342
202237
202153
202045
201935
201837