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American options on assets with dividends near expiry 总被引:3,自引:0,他引:3
Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate D to the interest rate r . For D > r the put boundary near expiry tends parabolically to the value rK / D where K is the strike price, while for D ≤ r the boundary tends to K in the parabolic-logarithmic form found for the case D =0 by Barles et al. (1995) and by Kuske and Keller (1998) . For the call, these two behaviors are interchanged: parabolic and tending to rK / D for D < r , as was shown by Wilmott, Dewynne, and Howison (1993) , and parabolic-logarithmic and tending to K for D ≥ r . The results are derived twice: once by solving an integral equation, and again by constructing matched asymptotic expansions. 相似文献
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Thomas J. Emmerling 《Mathematical Finance》2012,22(4):645-666
This paper examines the valuation of a generalized American‐style option known as a game‐style call option in an infinite time horizon setting. The specifications of this contract allow the writer to terminate the call option at any point in time for a fixed penalty amount paid directly to the holder. Valuation of a perpetual game‐style put option was addressed by Kyprianou (2004) in a Black‐Scholes setting on a nondividend paying asset. Here, we undertake a similar analysis for the perpetual call option in the presence of dividends and find qualitatively different explicit representations for the value function depending on the relationship between the interest rate and dividend yield. Specifically, we find that the value function is not convex when r > d . Numerical results show the impact this phenomenon has upon the vega of the option. 相似文献
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Marek Rutkowski 《Mathematical Finance》1994,4(4):313-325
The note deals with the pricing of American options related to foreign market equities. the form of the early exercise premium representation of the American option's price in a stochastic interest rate economy is established. Subsequently, the American fixed exchange rate foreign equity option and the American equity-linked foreign exchange option are studied in detail. 相似文献
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Over the last decade, dividends have become a standalone asset class instead of a mere side product of an equity investment. We introduce a framework based on polynomial jump‐diffusions to jointly price the term structures of dividends and interest rates. Prices for dividend futures, bonds, and the dividend paying stock are given in closed form. We present an efficient moment based approximation method for option pricing. In a calibration exercise we show that a parsimonious model specification has a good fit with Euribor interest rate swaps and swaptions, Euro Stoxx 50 Index dividend futures and dividend options, and Euro Stoxx 50 Index options. 相似文献
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M. Motoczyski 《Mathematical Finance》2000,10(2):243-257
One of the well‐known approaches to the problem of option pricing is a minimization of the global risk, considered as the expected quadratic net loss. In the paper, a multidimensional variant of the problem is studied. To obtain the existence of the variance‐optimal hedging strategy in a model without transaction costs, we can apply the result of Monat and Stricker. Another possibility is a generalization of the nondegeneracy condition that appeared in a paper of Schweizer, in which a one‐dimensional problem is solved. The relationship between the two approaches is shown. A more difficult problem is the existence of an optimal solution in the model with transaction costs. A sufficient condition in a multidimensional case is formulated. 相似文献
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高科技企业实行股票期权的探讨 总被引:1,自引:0,他引:1
随着市场经济在我国的不断发展 ,知识和技术已经成为高科技企业竞争的决定性因素。如何充分调动代理人的积极性 ,是理论界和实务界都非常关注的一个问题。必须在充分分析高科技企业实行股票期权的理论基础之上 ,针对目前我国高科技企业在实行股票期权中存在的问题 ,制定出相应的措施。 相似文献
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随着中国利率市场化改革进程的不断推进,中央银行基准利率的调节频率和商业银行存贷款利率的自主调节幅度都在不断扩大,银行的利率风险正在不断增加,因此商业银行迫切要求及时建立完备的利率风险管理体系。然而传统的银行风险管理方法如资产负债缺口管理,久期管理和凸度管理等已经无法适应隐含期权的资产负债的利率风险管理要求。 相似文献
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THE RANGE OF TRADED OPTION PRICES 总被引:1,自引:0,他引:1
Suppose we are given a set of prices of European call options over a finite range of strike prices and exercise times, written on a financial asset with deterministic dividends which is traded in a frictionless market with no interest rate volatility. We ask: when is there an arbitrage opportunity? We give conditions for the prices to be consistent with an arbitrage-free model (in which case the model can be realized on a finite probability space). We also give conditions for there to exist an arbitrage opportunity which can be locked in at time zero. There is also a third boundary case in which prices are recognizably misspecified, but the ability to take advantage of an arbitrage opportunity depends upon knowledge of the null sets of the model. 相似文献
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存款保险的期权定价模型构造及实证研究 总被引:4,自引:0,他引:4
存款保险定价是存款保险制度建设中的核心内容,保险定价效率直接影响制度的功效。碍于现金流贴现估价模型的局限性,从期权的角度阐述了存款保险与期权的关系,指出存款保险合同实质上就是一份看跌期权,从理论和实证两方面论述了如何运用Black-Schole期权定价模型确定存款保险价格的问题,对实践中存款保险的合理定价和制度建设具有重要的指导意义。 相似文献
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A numéraire is a portfolio that, if prices and dividends are denominated in its units, admits an equivalent martingale measure that transforms all gains processes into martingales. We first supply a necessary and sufficient condition for the generic existence of numéraires in a finite dimensional setting. We then characterize the arbitrage‐free prices and dividends for which the absence of numéraires survives any small perturbation preserving no arbitrage. Finally, we identify the cases when any small, but otherwise arbitrary, perturbation of prices and dividends preserves either the existence of numéraires, or their nonexistence under no arbitrage. 相似文献
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The paper examines equilibrium models based on Epstein–Zin preferences in a framework in which exogenous state variables follow affine jump diffusion processes. A main insight is that the equilibrium asset prices can be computed using a standard machinery of affine asset pricing theory by imposing parametric restrictions on market prices of risk, determined inside the model by preference and model parameters. An appealing characteristic of the general equilibrium setup is that the state variables have an intuitive and testable interpretation as driving the consumption and dividend dynamics. We present a detailed example where large shocks (jumps) in consumption volatility translate into negative jumps in equilibrium prices of the assets as agents demand a higher premium to compensate for higher risks. This endogenous “leverage effect,” which is purely an equilibrium outcome in the economy, leads to significant premiums for out‐of‐the‐money put options. Our model is thus able to produce an equilibrium “volatility smirk,” which realistically mimics that observed for index options. 相似文献
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Daniel Dufresne 《Mathematical Finance》2000,10(4):407-428
This paper has four goals: (a) relate ladder height distributions to option values; (b) show how Laguerre expansions may be used in the computation of densities, distribution functions, and option prices; (c) derive some new results on the integral of geometric Brownian motion over a finite interval; and (d) apply the preceding results to the determination of the distribution of the integral of geometric Brownian motion and the computation of Asian option values. The usual fixed‐strike options on the average are treated, as well as options with payoffs expressed in terms of one over the average of the underlying security, which this author calls “reciprocal Asian options.” In all cases the underlying asset is represented by geometric Brownian motion, the averages are performed continuously, and the options are of European type. 相似文献
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Chenghu Ma 《Mathematical Finance》1998,8(3):249-275
This paper studies the equilibrium characterization of asset pricing in a discrete‐time Lucas exchange economy (Lucas 1978) with the intertemporal recursive utility function of Epstein and Zin (1989). A general formulation of equilibrium asset pricing is presented. It is shown that risk aversion of a certainty equivalent corresponds to risk aversion in the intertemporal asset pricing model. The discrete‐time analogue of Ma's (1993) option pricing formula is derived in an i.i.d. environment, with which we prove an observational nonequivalence theorem in distinguishing the differences of the betweenness recursive utility functions and the expected utility functions. Additionally, when the consumption growth rate follows a first-order Markov process, it is shown that the observational nonequivalence result holds for Kreps–Porteus expected utility. Finally, as by-products, this paper also contains derivations of closed-form formulas for the aggregate equity (with endogenously determined yields), the term structure of interest rates, and European call options on the aggregate equity in a Markov setting. 相似文献
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This paper characterizes the rate of convergence of discrete‐time multinomial option prices. We show that the rate of convergence depends on the smoothness of option payoff functions, and is much lower than commonly believed because option payoff functions are often of all‐or‐nothing type and are not continuously differentiable. To improve the accuracy, we propose two simple methods, an adjustment of the discrete‐time solution prior to maturity and smoothing of the payoff function, which yield solutions that converge to their continuous‐time limit at the maximum possible rate enjoyed by smooth payoff functions. We also propose an intuitive approach that systematically derives multinomial models by matching the moments of a normal distribution. A highly accurate trinomial model also is provided for interest rate derivatives. Numerical examples are carried out to show that the proposed methods yield fast and accurate results. 相似文献