基于涨跌幅限制的双边截断正态分布期权定价模型

标准Black Scholes期权定价公式假设股票价格服从对数正态分布,没有考虑股票价格涨跌幅的限制带来的影响.放松该假设条件,假设股票价格服从双边截断对数正态分布,考虑中国股票市场的涨跌幅限制,得到一个新的B-S期权定价公式来表达股价行为.双边截断正态分布假设下收益率的波动率要要比正态分布下的波动率小,所以新B-S公式计算出的期权价格就会比标准B-S公式计算出的价格低.     

On the option pricing for a generalization of the binomial model

In the paper, we give an elementary proof of the fact that the option pricing within the model in which variation in stock prices belongs to a limited range is reduced to a similar problem in the binomial model. We also find a hedging strategy. The result obtained allows us to calculate the option price for the market with random number of variations in stock prices. The proof is given for the homogeneous model. The proof for the heterogeneous model is similar. Further, we consider the European call option. Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I.     

基于观察信息的分数B-S市场的欧式幂期权定价模型

本文讨论了基于观察信息的分数Black-Scholes市场中的幂期权定价问题,利用基于可观察的信息下的股票价格的条件分布公式,推导出欧式幂期权的定价公式,推广了有关的分数Black-Scholes市场中的期权定价的一些结果.     

Multiscale analysis of a perpetual American option with the stochastic elasticity of variance

A perpetual American option is considered under a generalized model of the constant elasticity of variance model where the constant elasticity is perturbed by a small fast mean-reverting Ornstein–Uhlenbeck process. By using a multiscale asymptotic analysis, we find the impact of the stochastic elasticity of variance on option prices as well as optimal exercise prices. Our results improve the existing option price structure in view of flexibility and applicability through the market price of risk. The revealed results may provide useful information on real option problems.     

Dynamic linkages between stock prices,accrual earnings and cash flows: a cointegration analysis

This paper investigates the dynamic linkages between stock market prices, accrual earnings and cash flows using Finnish data. We find that stock returns lead accounting returns rather than vice versa. Thus, the thin Finnish stock market appears to produce important information about the future success of Finnish companies for decision making purposes. In addition, the cointegration analysis performed here indicates that the inclusion of the so-called error correction term based on non-stationary price variables significantly improves the observed association between stock market and accounting variables. Thus, in future research, the long-term adjustment between stock market and accounting variables should be analysed more carefully when investigating the causality between accounting earnings and stock markets.     

基于GARCH-GH模型的上证50ETF期权定价研究

上证50ETF期权是中国推出的首支股票期权.为描述上证50ETF收益率偏态、尖峰、时变波动率等特征,结合GARCH模型和广义双曲(Generalized Hyperbolic,GH)分布两方面的优势,建立GARCH-GH模型为上证50ETF期权定价.在等价鞅测度下,利用蒙特卡罗方法估计上证50ETF欧式认购期权价格.实证表明,相比较Black-Scholes模型和GARCH-Gaussian模型,GARCH-GH模型得到的结果更接近于上证50ETF期权的实际价格,其定价误差最小.     

The American put is log-concave in the log-price

We show that the American put option price is log-concave as a function of the log-price of the underlying asset. Thus the elasticity of the price decreases with increasing stock value. We also consider related contracts of American type, and we provide an example showing that not all American option prices are log-concave in the stock log-price.     

Microfoundations for diffusion price processes

We study microeconomic foundations of diffusion processes as models of stock price dynamics. To this end, we develop a microscopic model of a stock market with finitely many heterogeneous economic agents, who trade in continuous time, giving rise to an endogeneous pure-jump process describing the evolution of stock prices over time. When the number of agents in the market is large, we show that the price process can be approximated by a diffusion, with price-dependent drift and volatility coefficients that are determined by small excess demands and trading volume in the microscopic model. We extend the microscopic model further by allowing for non-market interactions between agents, to model herd behavior in the market. In this case, price dynamics can be approximated by a process with stochastic volatility. Finally, we demonstrate how heavy-tailed stock returns emerge when agents have a strong tendency towards herd behavior.     

外汇市场、股票市场与房地产市场的风险传染研究——基于三元VAR-BEKK-GARCH模型实证分析

本文将人民币汇率、房价和股价三者纳入一个统一的分析框架中,从水平变动和波动风险两个方面考虑时变异方差和变量间的风险传递效应,使用“二次汇改”后的2010年6月到2017年12月的月度数据,采用三元GARCH和BEKK时序模型研究人民币汇率、房价和股价之间的动态影响关系及其波动风险互动机制。研究发现,三个市场相互之间具有明显的影响,特别是价格波动的风险传染上,房地产市场与股票之间、股票市场与汇率市场之间或长期或短期都存在风险的传递效应。具体而言,市场在均值溢出方面,人民币升值会促进房价和股价的上涨;但房价与股价之间的价格影响关系并不明显。在波动溢出方面,房价和股价之间的波动溢出效应明显,同时存在ARCH和GARCH型波动效应,而股价对汇率的波动影响也同时存在ARCH和GARCH型波动效应,但汇率对股价仅有GARCH型波动效应。     

Option pricing under a normal mixture distribution derived from the Markov tree model

We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal distributions. Using this normal mixture distribution and risk-neutral pricing, we derive a closed-form expression for European call option prices. We also suggest a regression tree-based method for estimating three volatility parameters σ, σ⁺, and σ⁻ required to apply the MT model. We apply the MT model to price call options on 89 non-dividend paying stocks from the S&P 500 index. For each stock symbol on a given day, we use the same parameters to price options across all strikes and expires. Comparing against the Black–Scholes model, we find that the MT model’s prices are closer to market prices.     

Heuristic option pricing with neural networks and the neuro-computer synapse 3

Today’s option and warrant pricing is based on models developed by Black, Scholes and Merton in 1973 and Cox, Ross and Rubinstein in 1979. The price movement of the underlying asset is modeled by continuous-time or discrete-time stochastic processes. Unfortunately these models are based on severely unrealistic assumptions. Permanently an unsatisfactory and quite artificial adaption to the true market conditions is necessary (future volatility of the underlying price). Here, an alternative heuristic approach with a highly accurate neural network approximation is presented. Market prices of options and warrants and the values of the influence variables form the usually very large output/ input data set. Thousands of multi-layer perceptrons with various topologies and with different weight initializations are trained with a fast sequential quadratic programming (SQP) method. The best networks are combined to an expert council network to synthesize market prices accurately. All options and warrants can be compared to single out overpriced and underpriced ones for each trading day. For each option and warrant overpriced and underpriced trading days can be used to ascertain a better buy and sell timing. Furthermore the neural model gains deep insight into the market price sen-sitivities (option Greeks), e.g., ?, Г, Θ and Ω. As an illustrative example we inves-tigate BASF stock call warrants. Time series from the beginning of 1996 to mid 1997 of 74 BASF call warrant prices at the Frankfurter Wertpapierborse (Frankfurt Stock Exchange) form the data basis. Finally a possible speed up of the training with the neuro-computer SYNAPSE 3 is briefly discussed     

A simple model for market booms and crashes

Multiple equilibria models are one of the major categories of theoretical models for stock market crashes. The main objective of this paper is to model multiple equilibria and demonstrate how market prices move from one regime into another in a continuous time framework. As a consequence of this, a multiple jump structure is obtained with both booms and crashes, which are defined as points of discontinuity of the stock price process. For the constructed model, we prove that the stock price is a càdlàg semimartingale process, find the conditional distributions for the time of the next jump, the type of the next jump and the size of the next jump, given the public information available to market participants, and conduct a number of numerical studies.     

Impact of introducing make-to-order options in a make-to-stock environment

Firms engaged in consumer product sales often implement a strict make-to-stock approach, applying a single price to all customers. In such systems, customers can get the product at the given price upon availability on the shelf. However, consumers can often tolerate a delay between order placement and demand satisfaction under a price discount. Recognizing this phenomenon, a supplier may consider offering a menu of delivery-price options to consumers, where longer delay-time options imply lower prices. Demands from customers willing to wait provide advance demand information to the supplier. This paper studies strategies to exploit this additional information to improve profitability and service levels. Primarily assuming that delivery times are set exogenously, we determine optimal prices and stock levels under the new delayed demand satisfaction options. In addition, we develop analytical models to characterize the system performance gains under the new demand fulfillment option.     

Market calibration under a long memory stochastic volatility model

In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock.     

Monte Carlo analysis of convertible bonds with reset clauses

This paper analyzes some features of non-callable convertible bonds with reset clauses via both analytic and Monte Carlo simulation approaches. Assume that the underlying stock receives no dividends and that it has credit risk of the issuer. We mean by reset that the conversion price is adjusted downwards if the underlying stock price does not exceed pre-specified prices. Reset convertibles are usually issued when the outlook for the issuer is unfavorable. The price of any convertible bonds can be approximately viewed as a sum of values of an otherwise identical non-convertible bond plus an embedded option to convert the bond into the underlying stock. In this paper, we first develop an exact formula for the conversion option value of the European riskless convertible in the classical Black–Scholes–Merton framework. It is shown by Monte Carlo simulation that conversion option value estimates of the American risky convertible are located in a certain region defined by this formula. From estimates of the conversion probability, it is also shown that there exists an optimal reset time in the latter half of the trading interval.     

面对成比例交易成本的情况下外汇期权的定价

The purpose of present work is to examine the financial problem of finding the universal reservation prices of a European call option written on exchange rate when there is proportional transaction costs of trading foreign currency in the market. An approach is suggested to compute the reservation bid-ask price of foreign currency call option based on maximizing the investor's expected utility. Option prices are determined from the investor's basic portfolio selection problem, without the need to solve a more complex optimization problem involving the insertion of the option payoffs into the terminal value function. Option prices are computed numerically in a Markov chain approximation for the case of exponential utility.Numerical results show that the option price bounds are almost independent of the alternative risk aversion parameter, but the bounds of NT region becomes narrower and the range of values of the initial holding for which the fair price lies within the bid-ask spread is shifted to a lower value when the risk aversion parameter increases.     

Modeling investment behavior under price cap regulation

Motivated by the frequently observed criticism of the regulatory practice arising from companies in the industries concerned, we investigate the impact of regulation on investment behavior. Therefore, we model the investment timing and volume of a firm acting in a regulated market. When capping prices, the regulatory authority imposes a price ceiling on market prices. Accordingly, we use a real option approach where the price cap that limits possible future firm values enters the firm’s portfolio in form of a short call option position. By comparing this framework to a competitive benchmark model, we derive an optimal price setting rule for regulators. Moreover, it can be shown how deviations from this optimum affect the investment behavior of firms.      

FOREIGN CURRENCY OPTION PRICING WITH PROPORTIONAL TRANSACTION COSTS

The purpose of present work is to examine the financial problem of finding the universal reservation prices of a European call option written on exchange rate when there is proportional transaction costs of trading foreign currency in the market. An approach is suggested to compute the reservation bid-ask price of foreign currency call option based on maximizing the investor＇s expected utility. Option prices are determined from the investor＇s basic portfolio selection problem, without the need to solve a more complex optimization problem involving the insertion of the option payoffs into the terminal value function. Option prices are computed numerically in a Markov chain approximation for the case of exponential utility. Numerical results show that the option price bounds are almost independent of the alternative risk aversion parameter, but the bounds of NT region becomes narrower and the range of values of the initial holding for which the fair price lies within the bid-ask spread is shifted to a lower value when the risk aversion parameter increases.     

股价遵循分数跳扩散的混合型双标的两值期权定价

应用风险中性定价原理,研究标的股价服从分数跳扩散过程的混合型双标的两值期权的定价问题,并得出定价公式,并与股价服从标准布朗运动的定价公式做出比较分析.     

国内外利率为随机的双币种重置型期权定价

双币种重置期权的特征是指在终端期T时的收益依赖于预先设定的t<,0>时刻标的资产的价格与执行价K>0(事先给定)的大小关系重新设置期权的执行价从而给出其定价,这种期权是投资于外国资产的一种合约,其风险不仅依赖外国资产价格的变化,还受外国货币的汇率以及国内外两种利率波动的影响,所以在实际应用方面十分广泛.本文首先就标的资...