On Pricing Exponential Square Root Barrier Knockout European Options

A barrier option is one of the most popular exotic options which is designedto give a protection against unexpected wild fluctuation of stock prices.Protection is given to both the writer and holder of such an option.Kunitomo and Ikeda (1992) analytically obtained a pricing formula forexponential double barrier knockout options. Since the logarithm of theirproposed barriers for the stock price process S(t), whichisassumed to be geometric Brownian motion, are nothing but straight lineboundaries, the protection provided by them is not uniform over time. Toremedy this problem, we propose square root curved boundaries±btfor the underlying Brownian motion process W(t). Since thestandarddeviation of Brownian motion is proportional to t, theseboundaries(after transformation) can be made to provide more uniform protectionthroughout the life time of the option. We will apply asymptoticexpansions of certain conditional probabilities obtained by Morimoto (1999)to approximate pricing formulae for exponential square root double barrierknockout European call options. These formulae allow us to computenumerical values in a very short time (t < 10^–6sec), whereas it takesmuch longer to perform Monte Carlo simulations to determine optionpremiums.     

Asset-Backed Securitization in Singapore: Value of Embedded Buy-Back Options

Asset backed securities have been promoted as an important financing instrument for property developers to raise capital in Singapore. In 1999 alone, S$1.92 billion worth of bonds have been issued via the securitization of six commercial properties and one residential condominium project under construction. Buy-back option is a unique feature embedded in the asset-backed securitization (ABS) in Singapore, which allow the originator to retain a contingent claim on the upside potential of the asset price. Based on the multi-period binomial option pricing framework proposed by Cox et al. (1979), the prices of the options embedded in the ABS contracts are estimated. Using the securitization of the 132,111 square feet 268 Orchard Road office building for illustration, the premium of the options embedded in the 10-year ABS deal was estimated at S$28.47 million, or 15.48 percent of the bond value. Recognition of the value of embedded options is important for structuring a fair and transparent ABS deal.     

Pricing and hedging power options

In this paper we study the pricing and hedging of options whose payoff is a polynomial function of the underlying price at expiration; so-called ‘power options’. Working in the well-known Black and Scholes (1973) framework we derive closed-form formulas for the prices of general power calls and puts. Parabola options are studied as a special case. Power options can be hedged by statically combining ordinary options in such a way that their payoffs form a piecewise linear function which approximates the power option's payoff. Traditional delta hedging may subsequently be used to reduce any residual risk.     

Z-Transform and preconditioning techniques for option pricing

In the present paper, we convert the usual n-step backward recursion that arises in option pricing into a set of independent integral equations by using a z-transform approach. In order to solve these equations, we consider different quadrature procedures that transform the integral equation into a linear system that we solve by iterative algorithms and we study the benefits of suitable preconditioning techniques. We show the relevance of our procedure in pricing options (such as plain vanilla, lookback, single and double barrier options) when the underlying evolves according to an exponential Lévy process.     

Multiplicative noise,fast convolution and pricing

In this work we detail the application of a fast convolution algorithm to compute high-dimensional integrals in the context of multiplicative noise stochastic processes. The algorithm provides a numerical solution to the problem of characterizing conditional probability density functions at arbitrary times, and we apply it successfully to quadratic and piecewise linear diffusion processes. The ability to reproduce statistical features of financial return time series, such as thickness of the tails and scaling properties, makes these processes appealing for option pricing. Since exact analytical results are lacking, we exploit the fast convolution as a numerical method alternative to Monte Carlo simulation both in the objective and risk-neutral settings. In numerical sections we document how fast convolution outperforms Monte Carlo both in speed and efficiency terms.     

我国风电企业排污权期权交易研究

由于经济发展导致了环境恶化,我国日益重视发展风电等新能源产业,并允许排污权交易以改善环境。在剖析排污权期权含义与定价模型的基础上,分析我国风电企业排污权交易市场建立的条件以及排污权期权交易的条件。最后,提出我国风电企业排污权期权交易的原则、组织机构与主体。     

BookReview

We compare the bias in binomial trees against that in certain analytical/numerical valuation techniques with which they disagree. We consider the CRR tree, the COS method and the Leisen–Reimer as well as the Prekopa–Szantai exponentially smoothed method. We conclude that the binomial trees are unbiased and that the exponentially smoothed method is biased.     

PRICING AND HEDGING SHORT STERLING OPTIONS USING NEURAL NETWORKS

This paper compares the performance of artificial neural networks (ANNs) with that of the modified Black model in both pricing and hedging short sterling options. Using high‐frequency data, standard and hybrid ANNs are trained to generate option prices. The hybrid ANN is significantly superior to both the modified Black model and the standard ANN in pricing call and put options. Hedge ratios for hedging short sterling options positions using short sterling futures are produced using the standard and hybrid ANN pricing models, the modified Black model, and also standard and hybrid ANNs trained directly on the hedge ratios. The performance of hedge ratios from ANNs directly trained on actual hedge ratios is significantly superior to those based on a pricing model, and to the modified Black model. Copyright © 2012 John Wiley & Sons, Ltd.     

A Model of Equity Based Compensation with Tax

In this paper, we develop a two‐stage continuous time model of employee stock option (ESO) valuation under different tax regimes. We show that tax rules can have significant effects on ESO exercise behavior. In addition, we find that incentive stock options (ISO) are the optimal form of compensation for all levels of employees in the UK. In the US, restricted stock plans are preferred, and tax breaks offered by incentive schemes are only beneficial to employees with high liquid wealth (or small option holdings relative to wealth) or low risk aversion. We also analyze 83b elections for restricted stock plans in the US and find that making an election is a sub‐optimal decision for both the employee and the firm.     

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.     

股票期权的个人所得税问题探讨

股票期权制度是一种新型的薪酬激励制度。股票期权制度作为富有成效的激励制度之一，在发达国家得到了广泛的应用，已成为市场经济国家和地区的企业对员工进行长期激励的非常普遍的方式。近两年来，股票期权成为我国企业改革和发展的一个热门话题，并在部分企业开始实施。如何针对股票期权所得的特点，并借鉴国外经验，制定相应的税收政策，是我们迫切需要解决的问题。本对我国股票期权所得税目、纳税义务发生时间、计税依据、税收优惠及税收征管等作了较为详细的探讨。     

Tighter Option Bounds from Multiple Exercise Prices

Optionbounds are determined by state discount factors limited by prices of a riskless bond and the underlying asset. Usually the asset has at least two market-traded options for each maturity, further limiting the factors. Tighter bounds result from incorporating the prices of all existing options of the same maturity. The tightened bounds are particularly applicable to appraising the consistency of all options trading on a single underlying security, notably index options. Constructed examples indicate a potential improvement of eighty percent in bound width; index data reveals a lower reduction, but extensive arbitrage opportunities from violations of the tighter bounds. This revised version was published online in November 2006 with corrections to the Cover Date.     

An analytical approximation for pricing VWAP options

This paper proposes a unified approximation method for various options whose pay-offs depend on the volume weighted average price (VWAP). Despite their popularity in practice, very few pricing models have been developed in the literature. Also, in previous works, the underlying asset process has been restricted to a geometric Brownian motion. In contrast, our method is applicable to the general class of continuous Markov processes such as local volatility models. Moreover, our method can be used for any type of VWAP options with fixed-strike, floating-strike, continuously sampled, discretely sampled, forward-start and in-progress transactions.     

世界大国增值税类型选择的规律——以美国、印度和欧盟为例

本文认为,世界各国尤其是国土面积最大的几个国家,在打破税制路径依赖的过程中,在认识和采纳消费型增值税过程中,面对国内维持现状的政治和经济因素的强大影响,增值税改革的决策是异常痛苦的过程。美国迄今为止未实行增值税,印度的增值税改革也未能在全国范围内铺开,欧盟作为增值税改革的成功实践者,其改革进程也充斥着政策妥协与延期实施。本文通过对世界大国增值税类型选择规律的分析,有助于我们重新认识中国增值税转型改革的路径和方案,权衡各方面利益,保证改革在曲折中前行。     

Valuing qualitative options with stochastic volatility

We find a closed-form formula for valuing a time-switch option where its underlying asset is affected by a stochastically changing market environment, and apply it to the valuation of other qualitative options such as corridor options and options in foreign exchange markets. The stochastic market environment is modeled as a Markov regime-switching process. This analytic formula provides us with a rapid and accurate scheme for valuing qualitative options with stochastic volatility.     

An empirical investigation of the factors that determine the pricing of Dutch index warrants

This paper investigates the pricing of Dutch index warrants. It is found that when using the historical standard deviation as an estimate for the volatility, the Black and Scholes model underprices all put warrants and call warrants on the FT-SE 100 and the CAC 40, while it overprices the call warrants on the DAX. When the implied volatility of the previous day is used the model prices the index warrants fairly well. When the historical standard deviation is used the mispricing of the call and the put warrants depends in a strong way on the mispricing of the previous trading day, and on the moneyness (in a non-linear way), the volatility, and the dividend yield. When the implied standard deviation of the previous trading day is used the mispricing of the call warrants is only related to the moneyness and to the estimated volatility, while the mispricing of put index warrants depends in a strong way on the moneyness, the volatility, the dividend yield and the remaining time to maturity.     

Pricing U.S. Dollar Index Futures Options: An Empirical Investigation

This paper develops a pricing model and empirically tests the pricing efficiency of options on the U.S. Dollar Index (USDX) futures contract. Empirical tests of the model indicate that the market consistently overprices these options relative to the derived model. This overpricing is more pronounced for out‐of‐the‐money options than for in‐the‐money options and more pronounced for put options than for call options. To validate the above results, delta neutral portfolios are created for one‐ and two‐day holding periods and consistently generate positive arbitrage profits, indicating that on average the market overprices the options on the USDX futures contracts.     

The effect of option listing on financing decisions

This paper investigates the effect of option listing on corporate financing decisions. Firms experience a significant drop in leverage, which is driven mainly by an increase in new equity issues. This effect is more prominent in firms with greater information asymmetry and lower percentages of quasi-index and transient investors before listing and those with active options trading after listing. After options are listed, the newly listed firms hold more cash and engage in more acquisitions, which are funded mainly by equity issues. These findings suggest that option listing has a significant impact on financing decisions because of lower information asymmetry and that firms use the post-listing equity to build up financial slack and support major investments, such as acquisitions.