論文

Quasi-Monte Carlo (QMC) methods have been gaining popularity in computational finance as they are competitive alternatives to Monte Carlo methods that can accelerate numerical accuracy. This paper develops a new approach for reducing the effective dimension combined with a randomized QMC method. A distinctive feature of the proposed approach is its sample-based transformation that enables us to choose a flexible manipulation via regression. In the proposed approach, the first step is to perform a regression using the samples to estimate the parameters of the regression model. An optimal transformation is proposed based on the regression result to minimize the effective dimension. An advantage of this approach is that adopting a statistical approach allows greater flexibility in selecting the regression model. In addition to a linear model, this paper proposes a dimension reduction method based on a linear-quadratic model for regression. In numerical experiments, we focus on pricing different types of exotic options to test the effectiveness of the proposed approach. The numerical results show that different regression models are chosen depending on the underlying risk process and the type of derivative securities. In particular, we show several examples where the proposed method works while existing dimension reductions are ineffective.

One of the major limiting factors and criticism about the real options approach is related to issues with estimating the right input values for state variables that are critical to make the right investment decisions under uncertainty. While vast research exists that applies real options valuation to technology investments, scholars often present theoretical findings based on fictional numerical applications neglecting the process of estimating the right input variables for their models. We present a simple framework to obtain these variables for technology investments by analysing publicly available data such as bibliometrics and patents related to any technology and apply it to forecast 3D printing technology diffusion. We base our approach on the Bass model, which is a prominent technique in the area of technology forecasting and show that these methods can help to forecast technology diffusion and obtain the required input parameters for technology investment decisions. We further use our 3D printing example to demonstrate the major differences between the suggested technology diffusion model and a standard Geometric Brownian Motion (GBM) model, as it is often found in Real Options literature. We find that the GBM is often not suitable when analysing technology investments, as it can lead to wrong investment decisions.

Model uncertainty has recently been receiving more attention than risk. This study proposes an effective computational framework to derive optimal strategies for obtaining the upper and lower bounds of Bermudan-style options in the presence of model uncertainty. The optimal hedging strategy under model uncertainty can be formulated as a solution of a minimax problem. We employ approximate dynamic programming and propose an algorithm for effectively solving the minimax problem. This study considers a geometric Brownian motion and an exponential generalized hyperbolic Lévy process as reference models. To take model uncertainty into consideration, we consider a set of equivalent probability measures via an Esscher or a class-preserving transform. Using numerical examples, we discuss the effects of model uncertainty on the size of tracking errors, the hedge portfolio, the possibility of early exercise and positions of options. In addition to investors’ optimal strategies, the study examines Nature’s optimal choice for equivalent probability measures. We find several notable phenomena that occur because of the existence of model uncertainty. We further examine the effects of different types of model uncertainty on option values and optimal hedging strategies.

For a trajectory simulated from s standardized independent normal variates ε = (ε1, . . . , εs )1, the payoff of a European option can be represented as max[g(ε), 0], where the function g(ε) is assumed to be differentiable and it relates to the nature of the derivative securities. In this paper, we develop a new simulation technique by introducing an orthogonal class of transformation to ε so that the function g is instead generated from g(Aε), where A is an s-dimensional orthogonal matrix. The matrix A is optimally determined so that the effective dimension of the underlying function is minimized, thereby enhancing the quasi-Monte Carlo (QMC) method. The proposed simulation approach has the advantage of greater generality and has a wide range of applications as long as the problem of interest can be represented by g(ε). The flexibility of our proposed technique is illustrated by applying it to two high-dimensional applications: Asian basket options and European call options with a stochastic volatility model. We benchmark our proposed method against well-known efficient simulation algorithms that have been advocated in these applications. The numerical results demonstrate that our proposed technique can be an extremely powerful simulation method when combined with QMC.

In this paper, the consider an enhanced quasi-Monte Carlo (QMC) method for pricing derivative securities when the underlying asset price follows an exponential Levy process. In particular, we focus on a special family of the Levy process known as the Meixner process. The enhanced QMC is based ore a generalization of the linear transformation (LT) method of Imai and Tan (2000). The generalized LT method call lie used to simulate general stochastic processes and hence has a wider range of application than the original LT which only applies to the Gaussian process. Using some option examples with dimensions ranging from 4 to 250 as test cases, the numerical results suggest that. the generalized LT-based QMC substantially outperforms the standard applications of quasi-Monte Carlo and Monte Carlo methods.

© 2018 International Association of Engineers. In this paper, we perform an empirical analysis of the dependence structure of international equity and bond markets using the regime-switching copula model. In equity markets, it is observed that negative returns are more strongly dependent than positive returns. This phenomenon is known as asymmetric dependence. The regime-switching copula model, which includes symmetric and asymmetric regimes, is suitable for describing asymmetry. We apply two kinds of flexible multivariate copulas, a skew t copula and a vine copula, to the asymmetric regime to deal with dependencies between two asset classes. In this paper, we analyze three country pairs: the United Kingdom and United States (UK-US), Japan-US, and Italy-US. We find three implications of our empirical analysis. First, highly dependent regimes are different according to the asset pairs. Second, the strength of the asymmetry of each country pair varies, and that of the Japan-US pair is weak. Third, the skew t copula is a better fit to the data, but is not flexible enough to capture extreme dependencies, while the vine copula fits well in spite of having fewer parameters, but cannot express the different extreme dependencies of each asset pair.

条件付き請求権の評価方法を応用し，為替レートの変動に対応して，国の内外に生産拠点を配置するプロジェクトを柔軟性を含めて評価するモデルの構築を提案している．評価技術としては，2項モデルを利用した動的計画法と，各時点における最適生産拠点を決定するための線形計画法が用いられている．

取引コストが存在する場合の満期前行使が可能なアメリカン・オプションの具体的な評価手法を提案している．無裁定条件が成立するオプション価値の上限と下限をそれぞれ数理計画法を用いて定式化している．既存の研究の多くは，最適解や確率測度の存在といった理論分析が中心であるのに対し，本論では，分枝限定法を利用して，非凸計画法を実際に解くアルゴリズムを提案し，具体的にアメリカンオプションの価格幅を導出している．

日本における破産手続きの分析は，多くの場合，法律面や手続き面からの分析が多い．本論文では，破産手続き中の資産売却プロセスをモデル化し，経済的な側面からの分析を行う．次に，このモデルを，実際の破産のケース（クラウンリーシング）に当てはめ，その経済的効率について議論している．

年金商品の一種であるdynamic fund protectionに関する研究論文である．測度変換による新たな解析解導出の方法を提案している．また，原資産がCEV過程の下では解析解が存在しないことから，精度の高い計算結果を得るために，Brownian Bridge法を使ったモンテカルロ法を提案している．また，有限差分法では解けない偏微分方程式の数値解法として，有限要素法の利用を提案している．

リアルオプション分析とゲーム理論との融合研究．柔軟性の罠（不確実性と競合が同時に存在する場合には，場合によって競争上優位に立つ企業がマネジメントの柔軟性を持つが故に，競争上劣位にある企業に競争に敗れる）に注目して分析を行っている．また，本論文での競争優位性が均衡選択理論におけるナッシュ積と密接に関連することを提示している．