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1.
Don H. Kim 《Mathematical Finance》2014,24(4):790-820
This paper shows that Singleton and Umantsev's method for swaption pricing in affine models can be simplified and extended to other models. Two alternative methods for approximating the option exercise boundary are introduced: one based on the multivariate Taylor series expansion, and the other based on duration‐matched zero‐coupon bond approximation. Applied to affine models and quadratic‐Gaussian models, these methods are found to give accurate swaption prices. 相似文献
2.
This study uses multiple maturity-independent variables to examine whether the volatility information implied in the term structure of volatility index can improve the prediction of realized volatility. The empirical results for the S&P 500 index show that, in terms of both the in-sample estimation and out-of-sample forecasting, the term structure variables provide substantial incremental contribution to the models with only level variables. Our empirical results are robust to various forms of volatility, alternative ways to develop the term structure variable, the impact of macroeconomic variables, and alternative underlying assets. 相似文献
3.
The Market Model of Interest Rate Dynamics 总被引：14，自引：0，他引：14
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. 相似文献
4.
The Gaussian Affine Term Structure Model (ATSM) introduced by Duffie and Kan is often used in finance to price derivatives written on interest rates or to compute the reserve to hedge a portfolio of credits (CreditVaR), and in macroeconomic applications to study the links between real activity and financial variables. However, a standard three‐factor ATSM, for instance, implies a deterministic affine relationship between any set of four rates, with different times‐to‐maturity, and these relationships are not observed in practice. In this paper, we introduce a new class of affine term structure models, called Bilinear Term Structure Model (BTSM). This extension breaks down the deterministic relationships between rates in structural factor models by introducing lagged factor values, and the linear dependence by considering quadratic effects of the factors. 相似文献
5.
This paper provides a unifying approach for valuing contingent claims on a portfolio of credits, such as collateralized debt obligations (CDOs). We introduce the defaultable (T, x) ‐bonds, which pay one if the aggregated loss process in the underlying pool of the CDO has not exceeded x at maturity T, and zero else. Necessary and sufficient conditions on the stochastic term structure movements for the absence of arbitrage are given. Background market risk as well as feedback contagion effects of the loss process are taken into account. Moreover, we show that any exogenous specification of the volatility and contagion parameters actually yields a unique consistent loss process and thus an arbitrage‐free family of (T, x) ‐bond prices. For the sake of analytical and computational efficiency we then develop a tractable class of doubly stochastic affine term structure models. 相似文献
6.
This paper compares the information extracted from the S&P 500, CBOE VIX, and CBOE SKEW indices for the S&P 500 index option pricing. Based on our empirical analysis, VIX is a very informative index for option prices. Whether adding the SKEW or the VIX term structure can improve the option pricing performance depends on the model we choose. Roughly speaking, the VIX term structure is informative for some models, while the SKEW is very noisy and does not contain much important information for option prices. This paper also extends Zhang et al. (2017, J Futures Markets, 37, 211–237) into three typical affine models. 相似文献
7.
8.
This paper derives domain restrictions on interest rates implied by no‐arbitrage. These restrictions are important for the study of arbitrage opportunities on bond markets, for regulation of these markets, and for econometric modelling. 相似文献
9.
This paper discusses separablc term structure diffusion models in an arbitrage-free environment. Using general consistency results we exploit the interplay between the diffusion coefficients and the functions determining the forward curve. We introduce the particular class of polynomial term structure models. We formulate the appropriate conditions under which the diffusion for a quadratic term structure model is necessarily an Ornstein-Uhlenbeck type process. Finally, we explore the maximal degree problem and show that basically any consistent polynomial term structure model is of degree two or less. 相似文献
10.
Bond Market Structure in the Presence of Marked Point Processes 总被引：11，自引：0，他引：11
We investigate the term structure of zero coupon bonds when interest rates are driven by a general marked point process as well as by a Wiener process. Developing a theory that allows for measure–valued trading portfolios, we study existence and uniqueness of a martingale measure. We also study completeness and its relation to the uniqueness of a martingale measure. For the case of a finite jump spectrum we give a fairly general completeness result and for a Wiener–Poisson model we prove the existence of a time–independent set of basic bonds. We also give sufficient conditions for the existence of an affine term structure. 相似文献
11.
Linear factor models, where the factors are affine processes, play a key role in Finance, since they allow for quasi-closed form expressions of the term structure of risks. We introduce the class of noncausal affine linear factor models by considering factors that are affine in reverse time. These models are especially relevant for pricing sequences of speculative bubbles. We show that they feature nonaffine dynamics in calendar time, while still providing (quasi) closed form term structures and derivative pricing formulas. The framework is illustrated with term structure of interest rates and European call option pricing examples. 相似文献
12.
A method based on transformations of well-known solutions of term structure equations is presented in order to incorporate Martin Barlow's spot price model for electricity into a model for future prices on electricity. The setting for the evolution of term structures is chosen in the spirit of Da Prato and Zabczyk. 相似文献
13.
本文利用Nelson-Siegel模型,通过实证分析发现:存贷差、狭义货币供应量和保费收入对利率水平有负效应,而工业增加值、企业商品价格指数和上证指数对利率水平有正效应;工业增加值与企业商品价格指数的增加会使利率曲线斜率下降,而狭义货币供应量与保费收入的增加则会使斜率上升。这对预测利率曲线的变化,从而规避由于利率曲线的非平行移动所产生的利率风险有重要的参考意义。 相似文献
14.
Recently, advantages of conformal deformations of the contours of integration in pricing formulas for European options have been demonstrated in the context of wide classes of Lévy models, the Heston model, and other affine models. Similar deformations were used in one‐factor Lévy models to price options with barrier and lookback features and credit default swaps (CDSs). In the present paper, we generalize this approach to models, where the dynamics of the assets is modeled as , where X is a Lévy process, and the interest rate is stochastic. Assuming that X and r are independent, and , the infinitesimal generator of the pricing semigroup in the model for the short rate, satisfies weak regularity conditions, which hold for popular models of the short rate, we develop a variation of the pricing procedure for Lévy models which is almost as fast as in the case of the constant interest rate. Numerical examples show that about 0.15 second suffices to calculate prices of 8 options of same maturity in a two‐factor model with the error tolerance and less; in a three‐factor model, accuracy of order 0.001–0.005 is achieved in about 0.2 second. Similar results are obtained for quanto CDS, where an additional stochastic factor is the exchange rate. We suggest a class of Lévy models with the stochastic interest rate driven by 1–3 factors, which allows for fast calculations. This class can satisfy the current regulatory requirements for banks mandating sufficiently sophisticated credit risk models. 相似文献
15.
We study the term structure of variance (total risk), systematic, and idiosyncratic risk. Consistent with the expectations hypothesis, we find that, for the entire market, the slope of the term structure of variance is mainly informative about the path of future variance. Thus, there is little indication of a time-varying term premium. Turning the focus to individual stocks, we cannot reject the expectations hypothesis for systematic variance, but we strongly reject it for idiosyncratic variance. Our results are robust to jumps and potential statistical biases. 相似文献
16.
本文简要阐述了利率期限结构理论,并分析比较了均衡模型与无套利机会模型、单因子模型和多因子模型的主要特征,最后,利用银行间国债市场1周、2周和4周国债回购利率进行回归得到三个瓦西塞克随机利率期限结构模型,指出了完善中国国债市场的思路。 相似文献
17.
近来财务理论的飞速发展大部分归功于实物期权理论于公司理财中的应用 ,实物期权能发挥如此大的作用一定有它的先进之处。但是由于数学原理的生涩难懂 ,给各界人士理解并探讨期权理论设置了障碍。目前广泛使用的传统公司理财工具 -现金流贴现方法有它的局限性 ,通过对实物期权的历史和原理的阐述 ,加以通俗易懂的例子 ,解释了它在财务理论中的突破性进步。 相似文献
18.
利率期限结构的静态估计是验证动态模型以及进行动态变化分析的基础。本文介绍了三次样条法的基本模型结构,指出了传统三次样条法使用久期倒数作为估计误差权重的逻辑错误,并据此提出了"准久期"加权以及成交量排名加权的概念;通过对比多个样本时间点的估计结果,发现成交量排名加权方法无论在样本内的模型估计还是样本外模型预测方面均优于久期以及准久期倒数加权方法。 相似文献
19.
In this paper we propose semiclosed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed analytic expressions by comparing them with those obtained from benchmark Monte–Carlo simulations. The empirical performance of the two affine GARCH models is tested using different calibration exercises based on historical returns and market quotes on VIX and SPX options. 相似文献
20.
Andrew F. Siegel 《Mathematical Finance》2016,26(4):919-938
To assure price admissibility—that all bond prices, yields, and forward rates remain positive—we show how to control the state variables within the class of arbitrage‐free linear price function models for the evolution of interest rate yield curves over time. Price admissibility is necessary to preclude cash‐and‐carry arbitrage, a market imperfection that can happen even with a risk‐neutral diffusion process and positive bond prices. We assure price admissibility by (i) defining the state variables to be scaled partial sums of weighted coefficients of the exponential terms in the bond pricing function, (ii) identifying a simplex within which these state variables remain price admissible, and (iii) choosing a general functional form for the diffusion that selectively diminishes near the simplex boundary. By assuring that prices, yields, and forward rates remain positive with tractable diffusions for the physical and risk‐neutral measures, an obstacle is removed from the wider acceptance of interest rate methods that are linear in prices. 相似文献