Papers - Imai, Junichi

Dimension reduction for Quasi-Monte Carlo methods via quadratic regression

Imai J., Tan K.S.

Mathematics and Computers in Simulation 227   371 - 390 2025.01

ISSN  03784754

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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.

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A Numerical Method for Hedging Bermudan Options under Model Uncertainty

Junichi Imai

第53回 2020年度夏季JAFEE大会 (JAFEE)  24 ( 2 ) 893 - 916 2022.06

ISSN  13875841

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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.

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Assessing Capital Investment Strategy with Convex Adjustment Cost under Ambiguity.

Junichi Imai; Motoh Tsujimura

International Journal of Real Options & Strategy 9   11 - 39 2022

Joint Work, Lead author, Accepted

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Estimating Parameters for Technology Investments: An Application to 3D Printing

Robin Schneider, Hitoshi Hirakawa, Noboru Hosoda, Rong Jin, Junichi Imai

Journal of the Operations Research Society of Japan 64 ( 3 ) 129 - 157 2021

Research paper (scientific journal), Last author, Accepted

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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.

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User-based Valuation of Digital Subscription Business Models

Robin Schneider, Junichi Imai

International Journal of Real Options and Strategy 8   1 - 26 2020.12

Research paper (scientific journal), Joint Work, Accepted,  ISSN  2186-4667

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マーク付き多次元Hawkes過程を用いた高頻度注文板データの分析

佐藤,正崇, 今井,潤一

ジャフィー・ジャーナル 18   63 - 88 2020

Research paper (scientific journal), Joint Work, Accepted

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Valuing Investments in Digital Transformation of Business Models

Robin Schneider, Junichi Imai

International Journal of Real Options and Strategy 7   1 - 26 2019

Research paper (scientific journal), Joint Work, Accepted

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An empirical analysis of the dependence structure of international equity and bond markets using regime-switching copula model

Otani Y., Imai J.

IAENG International Journal of Applied Mathematics (IAENG International Journal of Applied Mathematics)  48 ( 2 ) 191 - 205 2018.05

Research paper (scientific journal), Joint Work, Accepted,  ISSN  19929978

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© 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 e

A Study on a Membrane Ceilings Business under Ambiguity

Yuta Fukui, Junichi Imai

International Journal of Real Options and Strategy 6   13 - 44 2018

Research paper (scientific journal), Joint Work, Accepted

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リアルオプションアプローチによる平均回帰過程の下での投資タイミングの分析

Fukui Yuta, IMAI Junichi

リアルオプション研究 7 ( 2 ) 37 - 57 2015.12

Research paper (scientific journal), Joint Work, Accepted

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Dimension Reduction for Pricing Options under Multidimensional Levy Processes

Junichi Imai

Asia-Pacific Financial Markets (Springer)  22 ( 1 ) 1 - 26 2015

Research paper (scientific journal), Single Work, Accepted

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米国金先物市場におけるアメリカンオプションの価格評価分析

杉浦大輔, 今井 潤一

ジャフィー・ジャーナル 金融工学と市場計量分析 (朝倉書店)   2015

Research paper (scientific journal), Joint Work, Accepted

Pricing Derivative Securities Using Integrated Quasi-Monte Carlo Methods with Dimension Reduction and Discontinuity Realignment

Junichi Imai and Ken Seng Tan

SIAM Journal on Scientific Computing (SIAM)  36 ( 5 ) A2101 - A2121 2014

Research paper (scientific journal), Joint Work, Accepted

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Distributional Bounds for Portfolio Risk with Tail Dependence

Kunio So and Junichi Imai

Methodology and Computing in Applied Probability  2014

Research paper (scientific journal), Joint Work, Accepted

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Comparison of low discrepancy mesh methods for pricing Bermudan options under a Levy process

Junichi Imai

Mathematics and Computers in Simulation 100   54 - 71 2014

Research paper (scientific journal), Single Work, Accepted

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Numerical Inverse Levy Measure Method for Infinite Shot Noise Series Representation

J.Imai and R. Kawai

Journal of Computational and Applied Mathematics 253   264 - 283 2013.04

Research paper (scientific journal), Joint Work, Accepted

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Time-changed Lévy過程の下でのアメリカンオプションの評価

杉浦大輔, 今井潤一

ジャフィー・ジャーナル (朝倉書店)   2013.04

Research paper (scientific journal), Joint Work, Accepted

Pricing Portfolio Credit Derivatives with Stochastic Recovery and Systematic Factor

Yuko Otani and Junichi Imai

IAENG International Journal of Applied Mathematics 43 ( 4 ) 264 - 283 2013

Research paper (scientific journal), Joint Work, Accepted

Comparison of random number generators via Fourier transform

Junichi Imai

Monte Carlo Methods and Applications 19 ( 3 ) 237 - 259 2013

Research paper (scientific journal), Single Work, Accepted

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In this paper, we investigate simple yet practical schemes to generate random variates from the characteristic function of any continuous distribution. We discuss the generation of non-uniform random variates from a uniform random number generator. The inverse of the cumulative distribution function is derived from its characteristic function via the fast Fourier transform. We conduct several numerical experiments to assess the accuracy and efficiency of the schemes.

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実質次元減少法によるQMCを用いたポートフォリオのリスク指標の推定

鈴木悠也，今井潤一

日本オペレーションズ・リサーチ学会和文論文誌 55   177-193 2012

Research paper (scientific journal), Joint Work, Accepted

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On finite truncation of infinite shot noise series representation of tempered stable laws

Junichi Imai and Reiichiro Kawai

Physica A: Statistical Mechanics and Applications 390 ( 23-24 ) 4411-4425 2011.11

Research paper (scientific journal), Joint Work, Accepted

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フランチャイズビジネスにおける最適契約～商品の廃棄を考慮したロイヤルティ形態の比較～

川地由也，今井潤一

リアルオプション研究 4 ( 1 ) 1--32 2011.03

Research paper (scientific journal), Joint Work, Accepted

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On Monte Carlo and Quasi-Monte Carlo Methods for Series Representation of Infinitely Divisible Laws

R. Kawai and J. Imai

Monte Carlo and Quasi-Monte Carlo Methods 2010 (Springer)  23   471 - 486 2011

Research paper (scientific journal), Accepted

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Infinitely divisible random vectors and Lévy processes without Gaussian component admit representations with shot noise series. To enhance efficiency of the series representation in Monte Carlo simulations, we discuss variance reduction methods, such as stratified sampling, control variates and importance sampling, applied to exponential interarrival times forming the shot noise series. We also investigate the applicability of the generalized linear transformation method in the quasi-Monte Carlo framework to random elements of the series representation. Although implementation of the proposed techniques requires a small amount of initial work, the techniques have the potential to yield substantial improvements in estimator efficiency, as the plain use of the series representation in those frameworks is often expensive. Numerical results are provided to illustrate the effectiveness of our approaches.

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ゲーム理論的リアルオプションアプローチによる中小企業と大企業の特許権取得競争分析

青木一生，今井潤一

リアルオプション研究 4 ( 2 ) 169-206 2011

Research paper (scientific journal), Joint Work, Accepted

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Quasi-Monte Carlo method for infinitely divisible random vectors via series representations

IMAI Junichi and Kawai Reiichiro

SIAM Journal on Scientific Computing 32 ( 4 ) 1879-1897 2010

Research paper (scientific journal), Joint Work, Accepted

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Dimension Reduction Approach To Simulating Exotic Options In A Meixner Levy Market

Junichi Imai and Ken Seng Tan

IAENG International Journal of Applied Mathematics 39 ( 4 ) 265-275 2009.09

Research paper (scientific journal), Joint Work, Accepted

A Generalized Linear Transformation Method for Simulating Meixner Levy Process

Junichi Imai and Ken Seng Tan

Proceedings of the World Congress on Engineering 2009 (IAENG(International Association of Engineers))  II   pp1406-1411 2009.07

Research paper (conference, symposium, etc.), Joint Work, Accepted

マルコフ完全均衡と離散選択モデルを用いたイノベーションのジレンマの分析

今井潤一

リアルオプション研究 2   65-87 2009

Research paper (scientific journal), Single Work, Accepted

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This paper investigates the equilibrium investment policies of two different firms under consumers’ preference uncertainty. The incumbent firm, which owns a superior old technology, produces merchandise that can satisfy current consumers at the beginning of the investment game. The startup firm, which possesses an inferior old technology, does not capture the consumers satisfaction but it has a possibility to cultivate a new technology that can attract the consumers in the future if the customers’ preference is changed. We consider two types of equilibria in our valuation model. The first one is a price equilibrium at each time derived from the Bertrand competition. To represent customers’ diversity and products differentiation we use a discrete choice model. The other one is a Markov perfect equilibrium where each firm can invest either in the old technology or in the new technology depending on customers’ preference, which is modeled as a Markov process.

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An accelerating quasi-MonteCarlo method for option pricing under the generalized hyperbolic Le'vy process

Junichi Imai and Ken Seng Tan

SIAM Journal on Scientific Computing (SIAM)  31 ( 3 ) 2282-2302 2009

Research paper (scientific journal), Joint Work, Accepted

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In this paper, we develop a simple and yet practically efficient algorithm for simulating high-dimensional exotic options. Our method is based on an extension of Imai and Tan's linear transformation method, which is originally proposed in the context of simulating a Gaussian process. By generalizing this method to other stochastic processes and exploiting the numerical inversion method of Hormann and Leydold, this method can be used to enhance quasi-Monte Carlo method in a wide range of applications. We demonstrate the relative efficiency of our proposed simulation technique using exotic option examples including Asian, lookback, barrier, and cliquet options for which the underlying asset price follows an exponential generalized hyperbolic Lévy process. We also illustrate the impact of our proposed method on dimension reduction.


Read More: https://epubs.siam.org/doi/10.1137/080727713


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A Generalized Linear Transformation Method for Simulating Meixner Levy Processes

Junichi Imai, Ken Seng Tan

WORLD CONGRESS ON ENGINEERING 2009, VOLS I AND II (INT ASSOC ENGINEERS-IAENG)  II   1406 - + 2009

Accepted,  ISSN  2078-0958

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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.

NIGレヴィ過程下における効率的な準モンテカルロ法を用いたオプション評価

今井 潤一

数理解析研究所講究録 (京都大学数理解析研究所)  1580   114-123 2008.02

Research paper (conference, symposium, etc.), Single Work

Computation of Optimal Portfolios Using Simulation-based Dimension Reduction

Phelim Boyle, Junichi Imai and Ken Seng Tan

Insurance: Mathematics and Economics 43 ( 3 ) 327 - 338 2008

Research paper (scientific journal), Joint Work, Accepted

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This paper describes a simple and efficient method for determining the optimal portfolio for a risk averse investor. The portfolio selection problem is of long standing interest to finance scholars and it has obvious practical relevance. In a complete market the modern procedure for computing the optimal portfolio weights is known as the martingale approach. Recently, alternative implementations of the martingale approach based on Monte Carlo methods have been proposed. These methods use Monte Carlo simulation to compute stochastic integrals. This paper examines the efficient implementation of one of these methods due to [Cvitanic, J., Goukasian, L., Zapatero, F. 2003. Monte Carlo computation of optimal portfolios in complete markets. J. Econom. Dynam. Control 27, 971–986]. We explain why a naive application of the quasi-Monte Carlo method to this problem is often only marginally more efficient than the classical Monte Carlo method. Using the dimension reduction technique of [Imai, J., Tan, K.S., 2007. A general dimension reduction method for derivative pricing. J. Comput. Financ. 10 (2), 129–155] it is possible to significantly reduce the effective dimension of the problem. The paper shows why the proposed technique leads to a dramatic improvement in efficiency.

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The Investment Game under Uncertainty: An Analysis of Equilibrium Values in the Presence of First or Second Mover Advantage

Junichi Imai and Takahiro Watanabe

Stochastic Processes and Applications to Mathematical Finance:Proceedings of the 6th Ritsumeikan Conference (World Scientific)     151 - 172 2007

Research paper (scientific journal), Joint Work, Accepted

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In this paper we develop a valuation model when there exist two competitive firms that face irreversible investment decisions under the demand uncertainty. We propose a numerical procedure to derive both project values and equilibrium strategies in the duopolistic environment. In numerical examples we consider two different economic conditions, which are labelled first mover advantage and second mover advantage, and examine the effects of these conditions on the equilibrium strategies as well as the project values. We show that these conditions cause significant changes in the equilibrium strategies of both firms.

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A General Dimension Reduction Technique for Derivative Pricing

Junichi Imai and Ken Seng Tan

Journal of Computational Finance 10 ( 2 ) 129-155 2007

Research paper (scientific journal), Joint Work, Accepted

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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.



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競争状況下でのリアルオプションと柔軟性の罠

今井潤一, 渡辺隆裕

現代ファイナンス 22   75-95 2007

Research paper (scientific journal), Joint Work, Accepted

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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．

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Minimizing Effective Dimension Using Linear Transformation

Junichi Imai and Ken Seng Tan

Monte Carlo and Quasi-Monte Carlo Methods 2002: Proceedings of a Conference held at the National University of Singapore    275 - 292 2003

Research paper (scientific journal), Joint Work, Accepted

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Enhanced Quasi-Monte Carlo Methods with Dimension Reduction

Junichi Imai and Ken Seng Tan

Proceedings of the 2002 Winter Simulation Conference    1502 - 1510 2003

Research paper (conference, symposium, etc.), Joint Work, Accepted

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Dynamic Fund Protection

Junichi Imai and Phelim Boyle

North American Actuarial Journal (Society of Actuaries)  5 ( 3 ) 31-51 2001

Research paper (scientific journal), Joint Work, Accepted

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Dynamic fund protection provides an investor with a floor level of protection during the investment period. This feature generalizes the concept of a put option, which provides only a floor value at a particular time. The dynamic protection feature ensures that the fund value is upgraded if it ever falls below a certain threshold level. Gerber and Pafumi (2000) have recently derived a closed-form expression for the price of this protection when the basic portfolio follows geometric Brownian motion. In this paper we examine the pricing of this feature under the constant elasticity of variance process. Two approaches are used to obtain numerical results. First, we show how to extend the basic Monte Carlo approach to handle the particular features of dynamic protection. When a discrete-time simulation approach is used to value a derivative that is subject to continuous monitoring, there is a bias. We show how to remove this bias. Second, a partial differential equation approach is used to price dynamic protection. We demonstrate that the price of the dynamic protection is sensitive to the investment assumptions. We also discuss a discrete time modification of the dynamic protection feature that is suitable for practical implementation. The paper deals just with pricing and does not consider the important question of reserving for these contracts.

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A Real Option Analysis of An Oil Refinery Project

Junichi Imai and Mutsumi Nakajima

Financial Practice and Education (Financial Management Association International)  10 ( 2 ) 78-91 2000

Research paper (scientific journal), Joint Work, Accepted

破産企業の資産処分に関する経済分析

佐山展生, 今井潤一

経営財務情報の経済分析 (日本経営財務研究学会編，中央経済社出版)     123-148 1999.10

Research paper (scientific journal), Single Work, Accepted,  ISSN  4-502-35193-8 C3334

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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．

柔軟性を持つ投資プロジェクトに対する非完備市場下での最適戦略

今井 潤一

コーポレートファイナンスの理論と実証 (日本経営財務研究学会編，中央経済社出版)     109-133 1998.09

Research paper (scientific journal), Single Work, Accepted,  ISSN  4-502-34613-6 C3334

取引コストが存在する場合のアメリカン・オプションの上・下限価格の導出法

今井 潤一

日本経営工学学会論文誌 47 ( 6 ) 434-442 1997.02

Research paper (scientific journal), Single Work, Accepted

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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．

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為替レートの変動に対応する生産拠点の選択

今井潤一, 古川浩一

経営財務諸研究の新潮流 (日本経営財務研究学会編，中央経済社出版)     1 - 42 1997.01

Research paper (scientific journal), Joint Work, Accepted,  ISSN  4-502-33633-5 C3334

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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．