基于傅里叶级数展开式的有效期权定价方法

A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L~vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.     

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.     

Sharp distribution free lower bounds for spread options and the corresponding optimal subreplicating portfolios

We derive in closed form distribution free lower bounds and optimal subreplicating strategies for spread options in a one-period static arbitrage setting. In the case of a continuum of strikes, we complement the optimal lower bound for spread options obtained in [Rapuch, G., Roncalli, T., 2002. Pricing multiasset options and credit derivatives with copula, Credit Lyonnais, Working Papers] by describing its corresponding subreplicating strategy. This result is explored numerically in a Black-Scholes and in a CEV setting. In the case of discrete strikes, we solve in closed form the optimization problem in which, for each asset S₁ and S₂, forward prices and the price of one option are used as constraints on the marginal distributions of each asset. We provide a partial solution in the case where the marginal distributions are constrained by two strikes per asset. Numerical results on real NYMEX (New York Mercantile Exchange) crack spread option data show that the one discrete lower bound can be far and also very close to the traded price. In addition, the one strike closed form solution is very close to the two strike.     

Explicit portfolio for unit-linked life insurance contracts with surrender option

Introducing a surrender option in unit-linked life insurance contracts leads to a dependence between the surrender time and the financial market. [J. Barbarin, Risk minimizing strategies for life insurance contracts with surrender option, Tech. rep., University of Louvain-La-Neuve, 2007] used a lot of concepts from credit risk to describe the surrender time in order to hedge such types of contracts. The basic assumption made by Barbarin is that the surrender time is not a stopping time with respect to the financial market.The goal of this article is to make the hedging strategies more explicit by introducing concrete processes for the risky asset and by restricting the hazard process to an absolutely continuous process.First, we assume that the risky asset follows a geometric Brownian motion. This extends the theory of [T. Møller, Risk-minimizing hedging strategies for insurance payment processes, Finance and Stochastics 5 (2001) 419–446], in that the random times of payment are not independent of the financial market. Second, the risky asset follows a Lévy process.For both cases, we assume the payment process contains a continuous payment stream until surrender or maturity and a payment at surrender or at maturity, whichever comes first.     

Superconvergence estimates of finite element methods for American options

In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. 39 (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and interpolation postprocessing analysis technique, we present sharp L ²-, L ^∞-norm error estimates and an H ¹-norm superconvergence estimate for this finite element method. As a by-product, the global superconvergence result can be used to generate an efficient a posteriori error estimator. This work was supported in part by the National Natural Science Foundation of China (10471103 and 10771158), the National Basic Research Program (2007CB814906), Social Science Foundation of the Ministry of Education of China (Numerical Methods for Convertible Bonds, 06JA630047), Tianjin Natural Science Foundation (07JCY-BJC14300), and Tianjin University of Finance and Economics.     

Reflected BSDE Driven by a Lévy Process

In this paper, we study the reflected solution of one-dimensional backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. We prove the existence and uniqueness of the solution using a penalization method combined with Snell envelope theory.      

A general framework for pricing Asian options under stochastic volatility on parallel architectures

In this paper, we present a transform-based algorithm for pricing discretely monitored arithmetic Asian options with remarkable accuracy in a general stochastic volatility framework, including affine models and time-changed Lévy processes. The accuracy is justified both theoretically and experimentally. In addition, to speed up the valuation process, we employ high-performance computing technologies. More specifically, we develop a parallel option pricing system that can be easily reproduced on parallel computers, also realized as a cluster of personal computers. Numerical results showing the accuracy, speed and efficiency of the procedure are reported in the paper.     

银行项目信贷风险决策分析

利用实物期权的方法对银行项目信贷的期权特性进行了讨论,对项目的收益与风险进行了更为准确的数理分析.为使结论更加准确可靠,并对具体的实例进行了剖析,说明了衍生产品在银行的项目信贷过程中也可以很好地理论指导实践,使银行能够更好地对贷前风险进行有效控制.     

波动率服从有限的马尔可夫过程的期权定价

通过对服从有限马儿可夫过程的标的资产价格波动率进行分析,得出了在未来时刻波动的预测模型,并给出了相应的期权定价方法。     

Modeling investment behavior under price cap regulation

Motivated by the frequently observed criticism of the regulatory practice arising from companies in the industries concerned, we investigate the impact of regulation on investment behavior. Therefore, we model the investment timing and volume of a firm acting in a regulated market. When capping prices, the regulatory authority imposes a price ceiling on market prices. Accordingly, we use a real option approach where the price cap that limits possible future firm values enters the firm’s portfolio in form of a short call option position. By comparing this framework to a competitive benchmark model, we derive an optimal price setting rule for regulators. Moreover, it can be shown how deviations from this optimum affect the investment behavior of firms.