Hiroshi Shirakawa

Bio: Hiroshi Shirakawa is an academic researcher from Tokyo Institute of Technology. The author has contributed to research in topics: Arbitrage & Martingale pricing. The author has an hindex of 10, co-authored 15 publications receiving 595 citations.

A Note of Option Pricing for Constant Elasticity of Variance Model

Abstract: We study the arbitrage free option pricing problem for constant elasticity of variance (CEV) model. To treat the stochastic aspect of the CEV model, we direct attention to the relationship between the CEV model and squared Bessel processes. Then we show the existence of a unique equivalent martingale measure and derive the Cox’s arbitrage free option pricing formula through the properties of squared Bessel processes. Finally we show that the CEV model admits arbitrage opportunities when it is conditioned to be strictly positive.

A Note on Option Pricing for the Constant Elasticity of Variance Model

Abstract: We study the arbitrage free optionpricing problem for the constant elasticity of variance (CEV) model. To treatthestochastic aspect of the CEV model, we direct attention to the relationship between the CEV modeland squared Bessel processes. Then we show the existence of a unique equivalentmartingale measure and derive the Cox's arbitrage free option pricing formulathrough the properties of squared Bessel processes. Finally we show that the CEVmodel admits arbitrage opportunities when it is conditioned to be strictlypositive.

Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes

Abstract: We study a continuous trading bond model where the associated forward rate curve follows a multidimensional Poisson-Gaussian process. the bond market is complete, and the unique arbitrage-free interest rate call option price is explicitly derived.

An Interest Rate Model with Upper and Lower Bounds

Abstract: We propose a new interest rate dynamicsmodel where the interest rates fluctuate in a bounded region. The model ischaracterised by five parameters which are sufficiently flexible to reflect theprediction of the future interest rates distribution. The interest rate convergesin law to a Beta distribution and has transition probabilities which arerepresented by a series of Jacobi polynomials. We derive the moment evaluationformula of the interest rate. We also derive the arbitrage free pure discountbond price formula by a weighted series of Jacobi polynomials. Furthermore wegive simple lower and upper bounds for the arbitrage free discount bond pricewhich are tight for the narrow interest rates region case. Finally we show thatthe numerical evaluation procedure converges to the exact value in the limitand evaluate the accuracy of the approximation formulas for the discount bondprices.

No Arbitrage Condition for Positive Diffusion Price Processes

Abstract: Using the Ray-Knight theorem we give conditions for anonnegative diffusion without drift to reach zero or not. These results also givenecessary and sufficient conditions for such a diffusion process to be a martingale (and notjust a local martinagle). We apply these results in order to give necessary and sufficientconditions for nonnegative diffusion to have equivalent local martingale measures.

Arbitrage Theory in Continuous Time

Abstract: 1 Introduction 2 The Binomial Model 3 A More General One Period Model 4 Stochastic Integrals 5 Differential Equations 6 Portfolio Dynamics 7 Arbitrage Pricing 8 Completeness and Hedging 9 Parity Relations and Delta Hedging 10 The Martingale Approach to Arbitrage Theory (For advanced readers) 11 The Mathematics of the Martingale Approach (For advanced readers) 12 Black-Scholes from a Martingale Point of View (For advanced readers) 13 Multidimensional Models: Classical Approach 14 Multidimensional Approach: Martingale Approach (For advanced readers) 15 Incomplete Markets 16 Dividends 17 Currency Derivatives 18 Barrier Options 19 Stochastic Optimal Control 20 Bonds and Interest Rates 21 Short Rate Models 22 Martingale Models for the Short Rate 23 Forward Rate Models 24 Change of Numeraire (For advanced readers) 25 LIBOR and Swap Market Models 26 Forwards and Futures Appendix A Measure and Integration (For advanced readers) Appendix B Probability Theory (For advanced readers) Appendix C Martingales and Stopping Times (For advanced readers) References Index

A Survey of Machine Scheduling Problems with Blocking and No-Wait in Process

Abstract: An important class of machine scheduling problems is characterized by a no-wait or blocking production environment, where there is no intermediate buffer between machines. In a no-wait environment, a job must be processed from start to completion, without any interruption either on or between machines. Blocking occurs when a job, having completed processing on a machine, remains on the machine until a downstream machine becomes available for processing. A no-wait or blocking production environment typically arises from characteristics of the processing technology itself, or from the absence of storage capacity between operations of a job. In this review paper, we describe several well-documented applications of no-wait and blocking scheduling models and illustrate some ways in which the increasing use of modern manufacturing methods gives rise to other applications. We review the computational complexity of a wide variety of no-wait and blocking scheduling problems and describe several problems which remain open as to complexity. We study several deterministic flowshop, jobshop, and openshop problems and describe efficient and enumerative algorithms, as well as heuristics and results about their performance. The literature on stochastic no-wait and blocking scheduling problems is also reviewed. Finally, we provide some suggestions for future research directions.

A Benchmark Approach to Quantitative Finance

Abstract: Preliminaries from Probability Theory.- Statistical Methods.- Modeling via Stochastic Processes.- Diffusion Processes.- Martingales and Stochastic Integrals.- The Ito Formula.- Stochastic Differential Equations.- to Option Pricing.- Various Approaches to Asset Pricing.- Continuous Financial Markets.- Portfolio Optimization.- Modeling Stochastic Volatility.- Minimal Market Model.- Markets with Event Risk.- Numerical Methods.- Solutions for Exercises.

Markowitz Revisited: Mean-Variance Models in Financial Portfolio Analysis

Abstract: Mean-variance portfolio analysis provided the first quantitative treatment of the tradeoff between profit and risk. We describe in detail the interplay between objective and constraints in a number of single-period variants, including semivariance models. Particular emphasis is laid on avoiding the penalization of overperformance. The results are then used as building blocks in the development and theoretical analysis of multiperiod models based on scenario trees. A key property is the possibility of removing surplus money in future decisions, yielding approximate downside risk minimization.