CONTENTS -- Preface -- Program -- Mean Square Error for the Leland-Lott Hedging Strategy M. Gamys and Y. Kabanov -- 1. Introduction -- 1.1 Formulation of the Main Result -- 2. Proof of Theorem 1.2 -- 2.1 Preparatory Manipulations -- 2.2 Tools -- 2.3 Explicit Formulae and Useful Bounds -- 2.4 Analysis of the Principal Terms -- 2.5 Analysis of the Residual Rn1 -- 2.6 Analysis of the Residual Rn2 -- 3. Asymptotics of Gaussian Integrals -- Acknowledgement -- References -- Variance Reduction for MC/QMC Methods to Evaluate Option Prices J.-P. Fouque, C.-H. Han and Y. Lai -- 1. Introduction -- 2. Multi-Factor Stochastic Volatility Models and Option Price Approximations -- 2.1 Vanilla European Option Price Approximations -- 3. Monte Carlo Simulations: Two Variance Reduction Methods -- 3.1 Importance Sampling -- 3.2 Control Variate Method -- 3.3 Numerical Results -- 3.3.1 One-Factor SV Models -- 3.3.2 Two-Factor SV Models -- 4. Quasi Monte Carlo Method and a Counterexample -- 4.1 Introduction to Quasi Monte Carlo Method -- 4.2 Low-Biased Estimate of American Put Option Price -- 5. A Smooth Estimator: Control Variate for MC/QMC Methods -- 5.1 European Call Option Estimation -- 5.2 Accuracy Results -- 5.3 Delta Estimation -- 6. Conclusion -- References -- Estimation of the Local Volatility of Discount Bonds Using Market Quotes for Coupon-Bond Options H. Fujiwara, M. Kijima and K. Nishide -- 1. Introduction -- 2. The Local Volatility Model for Bond Options -- 2.1 Discount Bonds -- 2.2 Coupon Bonds -- 3. The Proposed Method -- 3.1 Relation Between Coupon-Bond Options and Discount Bonds -- 3.2 The Crude Approximation -- 3.3 Numerical Experiments -- 4. Application to the JGB Market -- 4.1 Market Data -- 4.2 Implied Volatilities of the Coupon-Bond Options -- 4.3 Local Volatility Function of Discount Bonds -- 5. Conclusion -- A. Duprire's Local Volatility Model.

B. Volatility Function of Coupon Bonds -- References -- Real Options in a Duopoly Market with General Volatility Structure M. Kijima and T. Shibata -- 1. Introduction -- 2. The Model and Some Preliminaries -- 2.1 The Setup -- 2.2 The Resolvent Operator -- 2.3 The Value Functions -- 3. A Duopoly Market -- 3.1 Follower -- 3.2 Leader -- 4. Equilibria -- 4.1 Strategic Substitution -- 4.2 Strategic Complement -- 5. Conclusions -- Acknowledgment -- Appendix -- References -- Arbitrage Pricing Under Transaction Costs: Continuous Time E. Denis -- 1. Introduction -- 2. Generalized Arbitrage in Abstract Setting -- 3. Proofs -- 3.1 Proof of Proposition 2.1 -- 3.2 Proof of Theorems 2.2 and 2.3 -- 3.3 Proof of Theorem 2.4 -- 4. Application to Finance -- 4.1 The Y-Model -- 4.2 Generalized Arbitrage for the Y-Model -- 4.3 Examples -- References -- Leland's Approximations for Concave Pay-off Functions E. Denis -- 1. Introduction -- 2. Main Results -- 3. Estimates -- 3.1 Explicit Formulae -- 3.2 Inequalities -- 4. Proof of Theorem 2.1 -- References -- Option Pricing Based on Geometric Stable Processes and Minimal Entropy Martingale Measures Y. Miyahara and N. Moriwaki -- 1. Introduction -- 2. [GLP & MEMM] and [GSP & MEMM] Models -- 2.1 Geometric Lévy Process (GLP) -- 2.1.1 Variance Gamma Process -- 2.1.2 CGMY Process -- 2.1.3 Stable Model -- 2.1.4 Merton Jump-Di usion Model -- 2.1.5 NIG Process -- 2.2 Minimal Entropy Martingale Measure (MEMM) Next we will give the definition of the MEMM. -- 2.3 [GSP & MEMM] Model -- 3. Reproducibility of the Volatility Smile/Smirk Properties 1 -- 3.1 Volatility Smile/Smirk Properties -- 3.2 [Geometric Variance Gamma Process & MEMM] Model -- 3.3 [Geometric CGMY Process & MEMM] Model -- 3.4 [Geometric Stable Process & MEMM] Model -- 4. Application to Dollar-Yen Currency Options 2 -- 4.1 Pricing Error for Option Price.

4.2 Minimization Problem -- 4.3 Results -- 4.3.1 In-Sample Analysis -- 4.3.2 Out-of-Sample Analysis -- 4.3.3 Volatility-Based Calibration -- 5. Conclusions and Remarks -- Acknowledgement -- References -- The Impact of Momentum Trading on the Market Price and Trades K. Nishide -- 1. Introduction -- 2. Model Setup -- 3. Market Prices -- 4. Discussions -- 5. Conclusions -- Acknowledgment -- Appendix -- A. Proof of Theorem 3.1 -- B. Proof of Proposition 3.1 -- C. Proofs of Propositions 3.2 to 3.4 -- References -- Investment Game with Debt Financing M. Nishihara and T. Shibata -- 1. Introduction -- 2. Monopoly -- 2.1 Unlevered Firm -- 2.2 Levered Firm -- 3. Duopoly -- 3.1 Competition Between Unlevered Firms -- 3.2 Competition Between Two Symmetric Firms -- 3.3 Competition Between the Levered and Unlevered Firms -- 3.4 Case of Q2 > 0 -- 4. Oligopoly -- 4.1 Competition Among n Levered Firms -- 4.2 Social Loss Due to Preemption -- 5. Numerical Examples -- 6. Conclusion -- References -- The Valuation of Callable Financial Commodities with Two Stopping Boundaries K. Sawaki, A. Suzuki and K. Yagi -- 1. Introduction -- 2. Model Formulation -- 3. Some Examples -- 4. Analytical Properties -- 5. Conclusion -- Acknowledgment -- References -- Statistical Properties of Covariance Estimator of Microstructure Noise: Dependence, Rare Jumps and Endogeneity M. Ubukata and K. Oya -- 1. Introduction -- 2. Definitions and PreviousWorks -- 2.1 Notation and Microstructure Noise -- 2.2 Noise Cross and Autocovariance Estimators -- 2.2.1 Noise Cross-Covariance Estimator -- 2.2.2 Noise Autocovariance Estimator -- 3. Rare Jumps and Endogenous Noise -- 3.1 Rare Jumps and Noise Covariance Estimator -- 3.2 Endogenous Noise and Noise Covariance Estimator -- 4. Monte Carlo Simulation -- 4.1 The Impact of Rare Jumps on the Noise Covariance Estimator.

4.2 The Impact of Endogenous Noise on the Estimator -- 5. Conclusion -- Acknowledgement -- References -- Quanto Pre-washing for Jump Diffusion Models H. Y. Wong and K. Y. Lau -- 1. Introduction -- 2. Quanto Options -- 2.1 The Jump Diffusion Model -- 3. Quanto Pre-washing -- 4. The Merton Jump Diffusion Model -- 4.1 Closed Form Solutions -- 4.2 Laplace Transform Solutions -- 5. Conclusion -- References.