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1.
On the theory of option pricing 总被引:11,自引:0,他引:11
A. Bensoussan 《Acta Appl Math》1984,2(2):139-158
The objective of this article is to provide an axiomatic framework in order to define the concept of value function for risky operations for which there is no market. There is a market for assets, whose prices are characterized as stochastic processes. The method consists of constructing a portfolio of these assets which will mimic the risks involved in the operation. We follow the terminology of the theory of options although the set-up goes beyond that particular problem. 相似文献
2.
POUZO Demian 《中国科学A辑(英文版)》2009,52(6):1157-1168
This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert
spaces. The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous, rendering the
problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact
penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results
to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds;
(2) recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical
error in the computation of the operator.
The first anther was supported by US National Science Foundation (Grant No. SES-0631613) and the Cowles Foundation for Research
in Economics 相似文献
3.
In this paper, we study the valuation of Exchange option with credit risk. Since the over-the-counter (OTC) markets have grown rapidly in size, the counterparty default risk is very important and should be considered for the valuation of options. For modeling of credit risk, we use the structural model of Klein [13]. We derive the closed-form pricing formula for the price of the Exchange option with credit risk via the Mellin transform and provide the experiment results to illustrate the important properties of option with numerical graphs. 相似文献
4.
在风险中性假设下,通过建立以外币计价的股票价格服从带跳扩散过程的随机微分方程和外币汇率的随机微分方程,考虑到影响外汇汇率的因素和影响股票价格因素的相关性,得到了与之相关联的几种买入的以本币计价的欧式期权定价公式. 相似文献
5.
David Steinsaltz 《Probability Theory and Related Fields》1997,107(1):99-121
Summary. A self-modifying random walk on is derived from an ordinary random walk on the integers by interpolating a new vertex into each edge as it is crossed. This
process converges almost surely to a random variable which is totally singular with respect to Lebesgue measure, and which
is supported on a subset of having Hausdorff dimension less than , which we calculate by a theorem of Billingsley. By generating function techniques we then calculate the exponential rate
of convergence of the process to its limit point, which may be taken as a bound for the convergence of the measure in the
Wasserstein metric. We describe how the process may viewed as a random walk on the space of monotone piecewise linear functions,
where moves are taken by successive compositions with a randomly chosen such function.
Received: 20 November 1995 / In revised form: 14 May 1996 相似文献
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V. V. Chichagov 《Journal of Mathematical Sciences》1996,81(4):2874-2879
In the present paper, we consider sequential Poisson random walk plans (SPRWPs). In particular, we solve such problems as
the calculation of characteristics of SPRWPs with intensity parameter given, the construction of unbiased estimates of characteristics
of a homogeneous Poisson process observed in the case of a sequential trial plan, the construction of the joint distribution
of Smirnov statistics, and the derivation of an optimal sequential Poisson criterion of given power. Another form of representing
exact formulas for calculating characteristics of SPRWPs was given by A. Dvoretsky, J. Kiefer, and J. Wolfowitz. But they
note no relationship between the SPRWPs and the corresponding sequential criteria; hence those formulas became approximate
but not exact for the sequential criteria.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 186–194, Perm, 1993. 相似文献
10.
A methodology using option pricing to determine a suitable discount rate in environmental management
With the present analysis the authors propose an approach for determining an adequate discount rate in environmental management problems, more specifically radioactive-waste management. It is shown that the classical Black–Scholes pricing formula can be used for determining the adequate present funding to be set-aside for the future. The average funding is equal to the net present value (NPV) of the future costs, including technical-scenario uncertainties. For taking into account the financial uncertainties, the NPV is identified with the strike price of a European put option, and the asset value in the managed fund is identified with the current price. The risk-free rate is the expected return rate of the portfolio. The paper shows that the adequate present funding can be determined for given multi-generational risk levels and an asset allocation by fixing the discount rate and adding a premium to the NPV of future costs. 相似文献
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Sumei Zhang Lihe Wang 《Communications in Nonlinear Science & Numerical Simulation》2013,18(7):1832-1839
This study proposes a pricing model through allowing for stochastic interest rate and stochastic volatility in the double exponential jump-diffusion setting. The characteristic function of the proposed model is then derived. Fast numerical solutions for European call and put options pricing based on characteristic function and fast Fourier transform (FFT) technique are developed. Simulations show that our numerical technique is accurate, fast and easy to implement, the proposed model is suitable for modeling long-time real-market changes. The model and the proposed option pricing method are useful for empirical analysis of asset returns and risk management in firms. 相似文献
14.
Rossella Agliardi 《Mathematical Methods in the Applied Sciences》2012,35(11):1256-1268
This work illustrates how several new pricing expressions for exotic options can be derived within a Lévy framework by employing a unique pricing expression. To the purpose, a unifying formula is obtained by solving some nested Cauchy problem for pseudodifferential equations generalizing Black–Scholes PDE. The main result extends (Agliardi R. The quintessential option pricing formula under Lévy processes. Applied Mathematics Letters 2009; 22:1626‐1631) and is a powerful tool for generating new valuation expressions. Several examples of pricing formulas under the Lévy processes are provided to illustrate the flexibility of the method. Some of them are new in the financial literature. Finally, many existing pricing formulas of the traditional Gaussian model are easily obtained as a by‐product. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
Assessing the markets perception of future interest and inflation rate volatility is of crucial importance to assess the evolution of expectations in an inflation targeting framework. This article aims to evaluate the information content of implied volatilities extracted from a Brazilian interest-rate call option. We compared the predictive performance of three different approaches: one using the traditional [Black F. The pricing of commodity contracts. J Financ Econ 1976;3:167–79] method, another one using the extended-Vasicek model, and in the third approach, we use a GARCH(2, 1) model. The empirical evidence was more favorable to the extended-Vasicek method. Moreover, extended-Vasicek’s implied volatilities could predict around 33% (adjusted R2) of the variations in realized volatility. Further research could test for the predictive content of long memory options such as those suggested in Wang et al. [Wang X-T, Qiu W-Y, Ren F-Y. Option pricing of fractional version of the Black–Scholes model with Hurst exponent H being in . Chaos, Solitons & Fractals 2001;12:599–608; Wang X-T, Ren F-Y, Liang X-Q. A fractional version of the Merton model. Chaos, Solitons & Fractals 2003;15:455–63]. 相似文献
16.
A random walk with a branching system in random environments 总被引:1,自引:0,他引:1
We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on Z with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system. 相似文献
17.
A BLACK-SCHOLES FORMULA FOR OPTION PRICING WITH DIVIDENDS 总被引:2,自引:0,他引:2
XuWENSHENG WUZHEN 《高校应用数学学报(英文版)》1996,11(2):159-164
Abstract. We obtain a Black-Scholes formula for the arbitrage-free pricing of Eu-ropean Call options with constant coefficients when the underlylng stock generatesdividends. To hedge the Call option, we will always borrow money from bank. We seethe influence of the dividend term on the option pricing via the comparison theoremof BSDE(backward stochastic di~erential equation [5], [7]). We also consider the option pricing problem in terms of the borrowing rate R whichis not equal to the interest rate r. The corresponding Black-Sdxoles formula is given.We notice that it is in fact the borrowing rate that plays the role in the pricing formula. 相似文献
18.
We consider a boundary value problem for a nonlinear differential equation which arises in an option pricing model with transaction costs. We apply the method of upper and lower solutions in order to obtain solutions for the stationary problem. Moreover, we give conditions for the existence of solutions of the general evolution equation. 相似文献
19.
一类具有随机利率的跳扩散模型的期权定价 总被引:4,自引:0,他引:4
假定股票价格的跳过程为比Po isson过程更一般的跳过程一类特殊的更新过程,在风险中性的假设下,推导出了具有随机利率的跳扩散模型的欧式期权定价公式.从而推广了文[3]的结果. 相似文献
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A.Q.M. Khaliq B.A. Wade M. Yousuf J. Vigo‐Aguiar 《Numerical Methods for Partial Differential Equations》2007,23(5):1249-1276
A new family of numerical schemes for inhomogeneous parabolic partial differential equations is developed utilizing diagonal Padé schemes combined with positivity–preserving Padé schemes as damping devices. We also develop a split version of the algorithm using partial fraction decomposition to address difficulties with accuracy and computational efficiency in solving and to implement the algorithms in parallel. Numerical experiments are presented for several inhomogeneous parabolic problems, including pricing of financial options with nonsmooth payoffs.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 相似文献