Smooth convergence in the binomial model

In this article, we consider a general class of binomial models with an additional parameter λ. We show that in the case of a European call option the binomial price converges to the Black–Scholes price at the rate 1/n and, more importantly, give a formula for the coefficient of 1/n in the expansion of the error. This enables us, by making special choices for λ, to prove that convergence is smooth in Tian’s flexible binomial model and also in a new center binomial model which we propose. Ken Palmer was supported by NSC grant 93-2118-M-002-002.     

The analysis and valuation of interest rate options

This paper provides a simple, alternative model for the valuation of European-style interest rate options. The assumption that drives the hedging argument in the model is that the forward prices of bonds follow an arbitrary two-state process. Later, this assumption is made more specific by postulating that the discount on a zero-coupon bond follows a multiplicative binomial process. In contrast to the Black-Scholes assumption applied to zero-coupon bonds, the limiting distribution of this process has the attractive features that the zero-bond price has a natural barrier at unity (thus precluding negative interest rates), and that the bond price is negatively skewed. The model is used to price interest rate options in general, and interest rate caps and floors in particular. The model is then generalized and applied to European-style options on bonds. A relationship is established between options on swaps and options on coupon bonds. The generalized model then provides a computationally simple formula, closely related to the Black-Scholes formula, for the valuation of European-style options on swaps.     

The volatility term structure in a lognormal process for the short rate

One-factor Markov models are widely used by practitioners for pricing financial options. Their simplicity facilitates their calibration to the intial conditions and permits fast computer Implementations. Nevertheless, the danger remains that such models behave unrealistically, if the calibration of the volatility is not properly done. Here, we study a lognormal process and investigate how to specify the volatility constraints in such a way that the term structure of volatility at future times, as implied by the short rate process, has a realistic and stable shape. However, the drifting down of the volatility term structure is unavoidable. As a result, there is a tendency to underestimate option prices.     

Achieving smooth asymptotics for the prices of European options in binomial trees

A new binomial approximation to the Black–Scholes model is introduced. It is shown that, for digital options and vanilla European call and put options, a complete asymptotic expansion of the error in powers of n ^?1 exists. This is the first binomial tree for which an asymptotic expansion has been shown to exist.     

Valuation and incentive effects of hurdle rate executive stock options

Traditional executive stock options are often criticized for inherently weak links between pay and performance. Hurdle rate executive stock options represent a viable improvement. However, valuing these options presents extraordinary analytic difficulties. With a constant dividend yield the strike price becomes a path-dependent function of the stock price and exact analytic valuation is intractable. To solve this problem, we apply the Monte Carlo valuation approach developed by Longstaff and Schwartz (Rev Financ Stud 4:113–147, 2001) to estimate the value of path-dependent American options. We also extend the methodology to incorporate the theoretical framework by Ingersoll (J Bus 79:453–487, 2006) to permit subjective valuation influenced by an executive’s risk aversion.

The Trading Volume of Currency Options and the Spot Exchange Rate

This paper estimates the interrelation between the spot exchange rate of the Israeli currency, the new Israeli shekel, to the U.S. dollar, and the trading volumes of put and call options on the U.S. dollar in the Tel Aviv Stock Exchange. An increase in the trading volume of calls is positively correlated with an increase in the spot exchange rate of the dollar on the same day and the following day, but with a lower coefficient. Similarly, an increase in the trading volume of puts is related to a decrease in the spot price of the dollar on the same day of trade, with a smaller effect on the following day.     

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.     

The role of the national institutional environment in IFRS convergence: a new approach

This study uses an ideal setting to capture the influence of the national institutional environment on outcomes (i.e., earnings quality) of IFRS convergence using a within-country approach. We show that earnings quality in terms of discretionary accruals and persistence has increased, while conservatism has decreased after IFRS convergence. The results are more pronounced in companies with a strong institutional environment. Our results are robust after considering incentives and other confounding factors. Our findings show differences in earnings quality in firms within a country adopting the same standards, let alone in firms worldwide. This indicates the context embeddedness of accounting standards.     

The Expected Return and Exercise Time of Merton-style Real Options

We analyse the rate of return and expected exercise time of Merton-style options (1973) employed in many real option situations where the possibility of exercise is both perpetual and American in nature. Using risk-neutral and risk-adjusted pricing techniques, Merton-style options are shown to have an expected return that is a constant percentage of the option value and independent of the proximity to the critical exercise boundary. Merton options thus remain at the same point on the Security Market Line, unlike European options whose position and rate of return change dynamically. We also present formulae for the expected time and discounted times to exercise and analyse the dependency of these variables on volatility.     

Generalizations of Ho–Lee’s binomial interest rate model I: from one- to multi-factor

In this paper a multi-factor generalization of Ho–Lee model is proposed. In sharp contrast to the classical Ho–Lee, this generalization allows for those movements other than parallel shifts, while it still is described by a recombining tree, and is a process with stationary independent increments to be compatible with principal component analysis. Based on the model, generalizations of duration-based hedging are proposed. A continuous-time limit of the model is also discussed. This research was supported by Open Research Center Project for Private Universities: matching fund subsidy from MEXT, 2004–2008 and also by Grants-in-Aids for Scientific Research (No. 18540146) from the Japan Society for Promotion of Sciences.     

On the convergence rate of fixed-width sequential confidence intervals

Abstract

Let X _f1, X _f2, ... be a sequence of i.i.d. random variables with mean µ and variance σ²∈ (0, ∞). Define the stopping times N(d)=min {n:n ^?1 Σ ⁿ _i=1} (X _i&#x2212;X _n)²+n ^?1?nd ²/a ²}, d>0, where X n =n ^?1 Σ ⁿ _i=1} Xi and (2π)^?½ ∫ ^a _?a exp (?u ²/2) du=α ∈(0,1). Chow and Robbins (1965) showed that the sequence I_n,d =[X_n ?d, X _n + d], n=1,2, ... is an asymptotic level -α fixed-width confidence sequence for the mean, i.e. lim_d→0 P(µ∈I_N(d),d )=α. In this note we establish the convergence rate P(µ∈I_N(d),d )=α + O(d½?δ) under the condition E|X₁|^3+?+5/(28) < ∞ for some δ ∈ (0, ½) and ??0. The main tool in the proof is a result of Landers and Rogge (1976) on the convergence rate of randomly selected partial sums.     

Volatility of the short rate in the rational lognormal model

A recent article of Flesaker and Hughston introduces a one factor interest rate model called the rational lognormal model. This model has a lot to recommend it including guaranteed finite positive interest rates and analytic tractability. Consequently, it has received a lot of attention among practioners and academics alike. However, it turns out to have the undesirable feature of predicting that the asymptotic value of the short rate volatility is zero. This theoretical result is proved rigorously in this article. The outcome of an empirical study complementing the theoretical result is discussed at the end of the article. European call options are valued with the rational lognormal model and a comparably calibrated mean reverting Gaussian model. unsurprisingly, rational lognormal option values are considerably lower than the analogous mean reverting Gaussian option values. In other words, the volatility in the rational lognormal model declines so quickly that options are severely undervalued.     

The anticipated and concurring effects of the EMU: exchange rate volatility, institutions and growth

Reduced exchange rate volatility and higher and less heterogeneous quality of institutional rules and macroeconomic policies are two of the main (anticipated and concurring) effects expected from a currency union.In this paper, we measure the magnitude of these two effects for the Eurozone countries looking at real effective exchange rates (REER) and at different indicators of quality of institutional rules and macroeconomic policies (QIRMP). We find that the first effect is much stronger than the second when we compare relative changes for Eurozone countries and the rest of the world in the relevant period.We further evaluate the impact of both effects on economic growth on a larger sample of countries. Our findings show that both have significant impact on levels (more robust) and on rates of growth (weaker) of per capita GDP.     

Measuring the convergence of national accounting standards with international financial reporting standards: The application of fuzzy clustering analysis

A single set of accounting standards is considered the path to achieving accounting convergence globally. Given the important role that formal harmonization/convergence plays in the accounting profession and global capital markets, this study focuses on the methods and methodology for the measurement of formal accounting convergence. Based on our review and evaluation of the existing methods for measuring the level of harmonization/convergence between any two sets of accounting standards, we propose using a new method of matching and fuzzy clustering analysis to assess the convergence progress of national accounting standards (NAS) with International Financial Reporting Standards (IFRS) from whole and single standards, respectively. Single standards are clustered according to their convergence level, which may indicate further convergence emphasis. As an illustrative example, the achievements made in China are evaluated using this new method. The results reveal that this new method can measure the convergence level of NAS with IFRS more clearly and informatively.     

贸易保护对汇率的影响——基于资本流动性及汇率收敛视角

对资本开放程度及汇率收敛度进行分类的框架下,考察贸易保护对汇率的影响。研究发现：在不同分类的国家,同样提升关税,对名义汇率的影响不尽相同;在汇率收敛的国家,提升关税会伴随资本控制程度降低而会导致名义汇率升值;在汇率不收敛情况下,提升关税会伴随资本控制程度降低而导致名义汇率贬值;从升值角度向绝对收敛状态转移时,低资本控制度及汇率收敛使汇率收敛度越接近于绝对收敛,在关税上升情况下会加剧名义汇率升值。使用动态系统GMM模型对66个国家2000-2014年样本数据进行实证分析,有力支撑了理论分析的结果。同时,对非关税措施进行实证分析,得出一般情况下贸易保护政策的确会造成汇率的升值,该结果在一般情况下是稳健的。     

The impact of monetary policy on the exchange rate: A high frequency exchange rate puzzle in emerging economies

This study investigates the impact of monetary policy shocks on the exchange rates of Brazil, Mexico and Chile. We find that even a focus on 1 day exchange rate changes following policy events – which reduces the potential for reverse causality considerably – fails to lend support for the view that associates unexpected interest rate hikes with immediate appreciations. This lack of empirical backing for the predictions of standard open economy models persists irrespective of whether we use the US Dollar or effective exchange rates, whether changes in the policy rate that were followed by exchange rate interventions are excluded, whether “contaminated” events are dropped from the analysis or whether we allow for non-linearities. We argue that it is difficult to attribute this stronger version of the exchange rate puzzle to fiscal dominance, as unexpected rate increases are not associated with increases in risk premia, and similar results are obtained in the case of Chile – a country that has had the highest possible short-term credit rating since 1995 and a debt/GDP ratio below 10%.     

Adjustable rate mortgages and housing demand: The impact of initial rate discounts

This article investigates the impact of ARM initial rate (teaser) discounts on mortgage choice and housing demand. Because discounted ARM loans may reduce expected user costs, theoretical models predict a positive impact on housing expenditures. To test the hypothesis, a simultaneous model of housing expenditures conditioned upon mortgage instrument choice is estimated using a national sample of transactions for the 1986 to 1988 period. The results indicate that overall housing demand would have been reduced by approximately 13 percent during the period in the absence of ARM loans.