Narrow Results

US tax laws provide investors an incentive to time the sales of their bonds to minimize tax liability. This grants a tax timing option that affects bond value. In reality, corporate bond investors’ tax-timing strategy is complicated by risk of default. In this chapter, we assess the effects of taxes and stochastic interest rates on the timing option value and equilibrium price of corporate bonds by considering discount and premium amortization, multiple trading dates, transaction costs, and changes in the level and volatility of interest rates. We find that the value of tax-timing option account for a substantial proportion of corporate bond price and the option value increases with bond maturity and credit risk.

In this study, we document a novel lead–lag relation between historical and implied volatilities based on China’s CSI300 Index options. We show that historical volatilities have incremental information when we predict implied volatilities, and this pattern tends to be more stable for put options than for call options. Moreover, we reveal that this lead– lag relation is relevant to option terms and time horizons of historical volatilities, which means implied volatilities of long-term options are more likely to be properly predicted by long-term historical volatilities on average. Finally, we find that speculative trading might explain our results.

This paper considers a portfolio problem with control on downside losses. Incorporating the worst-case portfolio outcome in the objective function, the optimal policy is equivalent to the hedging portfolio of a European option on a dynamic mutual fund that can be replicated by market primary assets. Applying the Black-Scholes formula, a closed-form solution is obtained when the utility function is HARA and asset prices follow a multivariate geometric Brownian motion. The analysis provides a useful method of converting an investment problem to an option pricing model.

In this paper, a novel algorithm for numerical solutions of American option models is presented in terms of the precision integration and wavelet. We discretize the space variable employing quasi–wavelet appropriately so that the resulting semi–discrete system of equations is a system of ordinary differential equation, and then we apply precise integration method to the semi-discrete system. Numerical results show that the proposed algorithm is practicable and efficient.

In this paper, an algorithm for numerical solutions of American option models is presented in terms of the precision integration. We discretize the space variable employing finite differences appropriately so that the resulting semi-discrete system of equations is a system of ordinary differential equation, and then we apply precise integration method to the semi-discrete system, and analyze errors of the method. Numerical results show that the proposed algorithm is practicable and efficient.

The following sections are included:

• INTRODUCTION

• DISCRETE AND CONTINUOUS RANDOM VARIABLES

• PROBABILITY DISTRIBUTIONS FOR DISCRETE RANDOM VARIABLES
  • Probability Distribution
  • Probability Function and Cumulative Distribution Function

• EXPECTED VALUE AND VARIANCE FOR DISCRETE RANDOM VARIABLES
  • Expected Value for Earnings per Share
  • Expected Value of Ages of Students
  • Expected Value and Variance: Defective Tires
  • Expected Value and Variance: Commercial Lending Rate

• THE BERNOULLI PROCESS AND THE BINOMIAL PROBABILITY DISTRIBUTION
  • The Bernoulli Process
  • Binomial Distribution
  • Probability Function
  • Mean and Variance

• THE HYPERGEOMETRIC DISTRIBUTION
  • The Hypergeometric Formula
  • Mean and Variance

• THE POISSON DISTRIBUTION AND ITS APPROXIMATION TO THE BINOMIAL DISTRIBUTION
  • The Poisson Distribution
  • The Poisson Approximation to the Binomial Distribution

• JOINTLY DISTRIBUTED DISCRETE RANDOM VARIABLES
  • Joint Probability Function
  • Marginal Probability Function
  • Conditional Probability Function
  • Independence

• EXPECTED VALUE AND VARIANCE OF THE SUM OF RANDOM VARIABLES
  • Covariance and Coefficient of Correlation Between Two Random Variables
  • Expected Value and Variance of the Summation of Random Variables X and Y
  • Expected Value and Variance of Sums of Random Variables

• Summary

• Appendix 6A The Mean and Variance of the Binomial Distribution

• Appendix 6B Applications of the Binomial Distribution to Evaluate Call Options
  • What Is an Option?
  • The Simple Binomial Option Pricing Model
  • The Generalized Binomial Option Pricing Model¹⁰

• Questions and Problems

US tax laws provide investors an incentive to time the sales of their bonds to minimize tax liability. This grants a tax timing option that affects bond value. In reality, corporate bond investors’ tax-timing strategy is complicated by risk of default. In this chapter, we assess the effects of taxes and stochastic interest rates on the timing option value and equilibrium price of corporate bonds by considering discount and premium amortization, multiple trading dates, transaction costs, and changes in the level and volatility of interest rates. We find that the value of tax-timing option account for a substantial proportion of corporate bond price and the option value increases with bond maturity and credit risk.