Option pricing with random volatilities in complete markets

This article presents the theory of option pricing with random volatilities in complete markets. As such, it makes two contributions. First, the newly developed martingale measure technique is used to synthesize results dating from Merton (1973) through Eisenberg, (1985, 1987). This synthesis illustrates how Merton's formula, the CEV formula, and the Black-Scholes formula are special cases of the random volatility model derived herein. The impossibility of obtaining a self-financing trading strategy to duplicate an option in incomplete markets is demonstrated. This omission is important because option pricing models are often used for risk management, which requires the construction of synthetic options.Second, we derive a new formula, which is easy to interpret and easy to program, for pricing options given a random volatility. This formula (for a European call option) is seen to be a weighted average of Black-Scholes values, and is consistent with recent empirical studies finding evidence of mean-reversion in volatilities.Helpful comments from an anonymous referee are greatly appreciated.     

A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities

This paper sets up a model for the valuation of traditional participating life insurance policies. These claims are characterized by their explicit interest rate guarantees and by various embedded option elements, such as bonus and surrender options. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation.The eventual benefits (or pay-offs) from the contracts considered crucially depend on the history of returns on the insurance company's assets during the contract period. This path-dependence prohibits the derivation of closed-form valuation formulas but we demonstrate that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts. We also demonstrate how the fundamental financial model can be extended to allow for mortality risk and we provide a wide range of numerical pricing results.     

Incentive Efficiency of Stock versus Options

This paper examines the relative incentive costs of using stockversus options in management incentive contracts that use market priceas the performance measure. We establish that if the manager'seffort has little or no effect on a firm's operating risk, thenthe cost of incentive risk is less using stock rather than options.However, this result is reversed if the manager's effort has asignificant impact on the firm's operating risk.     

Mortgage prepayment with an uncertain holding period

A discrete-time-option pricing model is developed to value a mortgage and its embedded prepayment option when the effective life of the mortgage is a random variable with a probability distribution of known parameters. The model can be applied when the borrower's ex ante expectation of his tenure follows any probability distribution bounded to the left at zero. The Gamma distribution is used to illustrate the model.The pricing model is further applied to determine the conditions under which financially motivated prepayment is optimal. The results show that the certainty model understates the Interest Rate Differential needed to justify prepayment (IRD) for short Expected Holding Period (EHP) borrowers and overstates the IRD for long EHP borrowers. When the EHP is relatively long, the certainty model provides relatively good estimates of IRD during the beginning years of the mortgage life. Under most other conditions, the estimates of the certainty holding period model are biased.     

Microfoundations of a mortgage prepayment function

This article focuses on the following question: how much of an interest rate decline is needed to justify refinancing a typical home mortgage? Modern option pricing theory is used to answer the question; this theory indicates that the answer depends upon several factors, which include the volatility of interest rates and the expected holding period of the borrower. The analysis suggests that the commonly espoused “rule of thumb” refinance if the interest rate declines by 200 basis points — is a fair approximation to the more precisely derived differential for many households. We also construct the prepayment behavior of a pool of mortgages in which the expected holding periods of the borrowers in the pool vary. The prepayment behavior of this simulated pool is used to generate a series of empirically testable hypotheses regarding the likely shape of an actual prepayment function and its determinants. Finally, actual prepayment data are used to estimate a hazard function that explains prepayment behavior. We find that the estimated model understates prepayment behavior relative to that predicted by the simulation model, which suggests that the simple option pricing model is not adequate to explain aggregate prepayment behavior.     

A Refined Binomial Lattice for Pricing American Asian Options

We present simple and fast algorithms for computing very tight upper and lower bounds on the prices of American Asian options in the binomial model. We introduce a new refined version of the Cox-Ross-Rubinstein (1979) binomial lattice of stock prices. Each node in the lattice is partitioned into nodelets, each of which represents all paths arriving at the node with a specific geometric stock price average. The upper bound uses an interpolation idea similar to the Hull-White (1993) method. From the backward-recursive upper-bound computation, we estimate a good exercise rule that is consistent with the refined lattice. This exercise rule is used to obtain a lower bound on the option price using a modification of a conditional-expectation based idea from Rogers-Shi (1995) and Chalasani-Jha-Varikooty (1998). Our algorithms run in time proportional to the number of nodelets in the refined lattice, which is smaller than n^4/20 for n > 14 periods.     

我国对外贸易存在的问题及对策探讨

改革开放以来,我国在对外贸易方面取得了巨大成就,但也应该清醒地看到,我国在对外贸易方面存在的问题也很多:一是长期以来我国出口企业经营策略趋同现象明显,表现在我国出口企业都热衷于短期趋利行为,竞争策略过于单一并且习惯采取统一的经营管理模式;二是入世以来我国的出口贸易受技术性贸易壁垒限制严重;三是我国将迎来贸易摩擦频发期。针对我国对外贸易存在的诸多问题,我国政府应该努力为企业创造公平竞争的市场环境,出口企业应该不断强化自身经营策略的创新性,在市场定位、管理和服务等方面的经营策略上保持创新性;推进对外贸易发展方式的转变,提高出口商品质量、信誉和效益。     

Stock options and capital structure

We show that value-maximizing CEOs compensated with stock options prefer debt to equity. Our pecking order result does not depend on managerial risk aversion, managerial firm-specific human capital, or asymmetric information. Moreover, our result holds at least weakly regardless of the distribution of firm cash flows and strictly as long as the support of the cash flow distribution is big enough to bring all features of the stock option contract into play with positive probability JEL Classification Numbers: G0, G3 An earlier version of this paper was completed while Page was visiting CERMSEM at Paris 1 and the University of Warwick. Page gratefully acknowledges the support and hospitality of CERMSEM, Paris 1 and Warwick. Page also gratefully acknowledges financial support from the Department of Economics, Finance, and Legal Studies and the Culverhouse College of Business at the University of Alabama. Both authors are grateful to seminar participants in the Financial Markets Group Workshop at LSE for many helpful comments and both authors are especially grateful to an anonymous referee whose detailed and insightful comments led to substantial improvements in the paper