Efficiency of the foreign currency options market

This paper provides a new test of the efficiency of the currency option markets for four major currencies — British Pound, Euro, Swiss Frank and Japanese Yen vis-à-vis the U.S. dollar. The approach is to simulate trading strategies to see if the well-accepted no-arbitrage condition of put–call parity (PCP) holds in a trading environment. Augmented Dickey–Fuller and Philips–Perron tests are used to check for the presence of unit roots in the data, followed by a formal econometric analysis. The results indicate that the most currency option prices do not violate the PCP conditions, when transaction costs are allowed for.     

General equilibrium pricing of currency and currency options

This paper presents a consumption-based general equilibrium model for valuing foreign exchange contingent claims. The model identifies a novel economic mechanism by exploiting highly but imperfectly shared consumption disaster with variable intensities which are the concerns to the representative investor under recursive utility. When applied to the data, the model simultaneously replicates (i) the moderate option-implied volatilities; (ii) substantial variations in the risk-neutral skewness of currency returns; (iii) the uncovered interest rate parity puzzle; and (iv) the first two moments of carry trade returns. Furthermore, the model rationalizes salient features of the aggregate stock, government bonds, and equity index options.     

Option pricing: A general equilibrium approach

This article examines option valuation in a general equilibrium framework. We focus on the general equilibrium implications of price dynamics for option valuation. The general equilibrium considerations allow us to derive an alternative option valuation formula that is as simple as the Black and Scholes formula, and that exhibits different behavior with respect to the exercise price and time to expiration. They also help us clarify comparative-statics properties of option valuation formulas in general and of the Black and Scholes model in particular.     

American bond option pricing in one-factor dynamic term structure models

Arbitrage-tree pricing of American options on bonds in one-factor dynamic term structure models is investigated. We re-derive a general decomposition result which states that the American bond option premium can be split into the value of an otherwise equivalent European option and anearly exercise premium. This extends earlier work on American equity options by e.g. Kim (1990), Jamshidian (1992) and Carr, Jarrow, and Myneni (1992) and parallels recent work by Jamshidian (1991, 1992, 1993) and Chesney, Elliott, and Gibson (1993). We examine a Gaussian class of special cases in some detail and provide a variety of numerical valuation results.An earlier version of the paper was entitled American Bond Option Pricing in One-Factor Spot Interest Rate Models.I am grateful for many helpful comments from two anonymous referees, the participants of the Second Nordic Symposium on Contingent Claims Analysis in Finance held in Bergen, Norway in May of 1994 and from the participants of the EIASM Doctoral Tutorial held in connection with the 1994 EFA annual meeting in Bruxelles. I am particularly indebted to Krishna Ramaswamy for his help and advice during my stay as visiting doctoral fellow at the Wharton School of the University of Pennsylvania. Financial support from the Aarhus University Research Foundation (Grants # E-1994-SAM-1-1-72 & E-1995-SAM-1-59), the Danish Social Science Research Council, and the Danish Research Academy is gratefully acknowledged. All errors and omissions are my own.     

Pseudospectral methods for pricing options

Models with two or more risk sources have been widely applied in option pricing in order to capture volatility smiles and skews. However, the computational cost of implementing these models can be large—especially for American-style options. This paper illustrates how numerical techniques called ‘pseudospectral’ methods can be used to solve the partial differential and partial integro-differential equations that apply to these multifactor models. The method offers significant advantages over finite-difference and Monte Carlo simulation schemes in terms of accuracy and computational cost.     

A dynamic programming approach for pricing CDS and CDS options

We propose a flexible framework for pricing single-name knock-out credit derivatives. Examples include Credit Default Swaps (CDSs) and European, American and Bermudan CDS options. The default of the underlying reference entity is modelled within a doubly stochastic framework where the default intensity follows a CIR++ process. We estimate the model parameters through a combination of a cross sectional calibration-based method and a historical estimation approach. We propose a numerical procedure based on dynamic programming and a piecewise linear approximation to price American-style knock-out credit options. Our numerical investigation shows consistency, convergence and efficiency. We find that American-style CDS options can complete the credit derivatives market by allowing the investor to focus on spread movements rather than on the default event.     

Skew-Brownian motion and pricing European exchange options

This article derives a closed-form pricing formula for European exchange options under a non-Gaussian framework for the underlying assets, intending to resolve mispricing associated with a geometric Brownian motion. The dynamics of each of the two correlated underlying assets are assumed to be governed by the exponential of a skew-Brownian motion, which is specified as a sum of a standard Brownian motion and an independent reflected Brownian motion. The proposed pricing formula does not incur additional computational costs than the standard Black–Scholes framework, which one can quickly recover as a particular case of the proposed framework. Finally, we present some numerical experiments followed by a valuable discussion on the results.     

An adjusted binomial model for pricing Asian options

We propose a model for pricing both European and American Asian options based on the arithmetic average of the underlying asset prices. Our approach relies on a binomial tree describing the underlying asset evolution. At each node of the tree we associate a set of representative averages chosen among all the effective averages realized at that node. Then, we use backward recursion and linear interpolation to compute the option price.     

Central bank digital currency and the effectiveness of negative interest rate policy: A DSGE analysis

Implementing a negative interest rate policy (NIRP) in the traditional fiat system is less effective than desired because of the zero lower bound (ZLB) constraint on interest rates and the cash barrier. Would this problem be solved if a new form of currency was introduced, i.e., central bank digital currency (CBDC), in the economy? To answer this question, we construct a dynamic stochastic general equilibrium (DSGE) model to analyze the effectiveness of NIRP upon the introduction of CBDC. The results suggest that: (i) The CBDC can eliminate the ZLB constraint and stabilize the economic fluctuations caused by NIRP. (ii) The central bank can implement NIRP by directly adjusting the interest rate of digital currency to stimulate consumption, investment, and output and to accelerate macroeconomic recovery. (iii) Welfare analysis shows that the central bank can effectively choose different NIRP rules according to the economic objectives.     

Static hedging and pricing American knock-in put options

This paper extends the static hedging portfolio (SHP) approach of  and  to price and hedge American knock-in put options under the Black–Scholes model and the constant elasticity of variance (CEV) model. We use standard European calls (puts) to construct the SHPs for American up-and-in (down-and-in) puts. We also use theta-matching condition to improve the performance of the SHP approach. Numerical results indicate that the hedging effectiveness of a bi-monthly SHP is far less risky than that of a delta-hedging portfolio with daily rebalance. The numerical accuracy of the proposed method is comparable to the trinomial tree methods of  and . Furthermore, the recalculation time (the term is explained in Section 1) of the option prices is much easier and quicker than the tree method when the stock price and/or time to maturity are changed.     

Stock index dynamics and derivatives pricing with stochastic interest rates

The paper analyzes the equilibrium valuation of stock index derivatives in an economy with stochastic interest rates and with a representative agent having time-additive power utility. The equilibrium short interest rate dynamics and the equilibrium term structure of interest rates are described by an affine one-factor term structure model. In equilibrium the value of the stock index is a non-trivial function of the short interest rate. The paper investigates the consequences of the induced stock index dynamics for the theoretical spreads between index forward prices and index futures prices and the consequences for the valuation of options on stock index futures.The paper was written while the author was a visiting scholar at Department of Finance, Kellogg Graduate School of Management, Northwestern University. I thank for helpful comments and suggestions from Gurdip Bakshi, Avi Bick, Menachem Brenner (the editor), Zhiwu Chen, San-Lin Chung, Mark Fisher, Andreas Höger, Marti Subrahmanyam, two anonymous referees, and participants at the Western Finance Association meeting in San Diego, the European Financial Management Association meeting in Istanbul, the European Finance Association meeting in Vienna, and the Center of Analytical Finance workshop at University of Aarhus. Financial support from the Danish Natural Science and Social Science Reasearch Councils is gratefully acknowledged.     

Truncation and acceleration of the Tian tree for the pricing of American put options

We present a new method for truncating binomial trees based on using a tolerance to control truncation errors and apply it to the Tian tree together with acceleration techniques of smoothing and Richardson extrapolation. For both the current (based on standard deviations) and the new (based on tolerance) truncation methods, we test different truncation criteria, levels and replacement values to obtain the best combination for each required level of accuracy. We also provide numerical results demonstrating that the new method can be 50% faster than previously presented methods when pricing American put options in the Black–Scholes model.     

Revisiting the Tourinho real options model: outstanding issues 30 years later

This article presents and extends the first known model in real options, proposed in Tourinho (1979), and provides thoughts on addressing issues that are still outstanding 30 years later. It discusses the need to ensure the existence of market equilibrium when applying real options valuation to price assets, once all agents behave as suggested by the solution to the pricing equation. It argues that this can be achieved by using a stochastic process for the price that is sufficiently general to respond to supply and demand imbalances in the market for the resource. Once the individual decision rules are derived, the parameters of the process must be determined to ensure market equilibrium exists. For reserves of natural resources, this can be done by using a mean-reverting process for the price of the commodity and ensuring that the long-term price to which it reverts equals the trigger price for development of the marginal reserve.     

探索支持个人本外币兑换特许业务的发展路径

个人本外币兑换特许业务自2008年试点以来,尤其在2012年国家外汇管理局对特许业务的管理办法进行修订以来,业务量和机构家数增长迅速。但与国际货币兑换公司相比,国内仍存在业务量较低、对银行的依赖较大、业务范围较窄等问题。文章回顾了该业务在我国的发展现状,借鉴成熟国际特许机构的发展经验,对促进我国特许业务发展提出相关政策建议。     

Discussion of “Which approach to accounting for employee stock options best reflects market pricing?”

The objective of the Landsman, Peasnel, Pope and Yeah paper (in this issue) is to compare, for current shareholders, the value relevance of four methods of accounting for employee stock options (ESOs). My discussion provides a unifying framework for the theoretical analyses and the link between the theoretical analyses and the empirical investigation.     

American option valuation under stochastic interest rates

By applying Ho, Stapleton and Subrahmanyam's (1997, hereafter HSS) generalised Geske–Johnson (1984, hereafter GJ) method, this paper provides analytic solutions for the valuation and hedging of American options in a stochastic interest rate economy. The proposed method simplifies HSS's three-dimensional solution to a one-dimensional solution. The simulations verify that the proposed method is more efficient and accurate than the HSS (1997) method. We illustrate how the price, the delta, and the rho of an American option vary between the stochastic and non-stochastic interest rate models. The magnitude of this effect depends on the moneyness of the option, interest rates, volatilities of the underlying asset price and the bond price, as well as the correlation between them. This revised version was published online in June 2006 with corrections to the Cover Date.     

Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach

Simple analytical pricing formulae have been derived, by different authors and for several derivatives, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulas under the most general stochastic volatility specification of the Duffie and Kan (1996) model. Using Gaussian Arrow-Debreu state prices, first order stochastic volatility approximate pricing solutions will be derived only involving one integral with respect to the time-to-maturity of the contingent claim under valuation. Such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate.     

An option pricing approach to corporate dividends and the capital investment financing decision

In light of a growing trend toward viewing dividends as an investable asset class, this article opens up a new perspective on their valuation. We show that dividends can be viewed as options on the cash flow of the firm. That is, a firm either pays zero dividends, in which case the option expires out‐of‐the‐money, or it pays a positive dividend, the value of which corresponds to the option's moneyness. The exercise price is determined by the capital budget, the flexibility of the company to use external financing, and whether it has minimum and maximum dividends. The model is also capable of accommodating a stochastic capital budget, which allows for uncertain growth opportunities and their correlation with the firm's cash flows. We also present an application of the model using actual data for a large multinational company.