光滑树图期权定价模型的叉熵分析法

为了克服CRR模型收敛的波动性,以及强调历史信息的预测作用的情况,提出了一个新奇的光滑收敛的树图模型.新模型基于历史信息,运用最小叉熵原理
来推导树图的关键参数p,u,d, 然后使用倒推法推断期权的价格.显然,新模型所得的期权的价格隐含着历史信息.由于最小叉熵原理是一个凸规划问题,能求得唯一的最优解,所以,新模型也适用于不完全金融市场期权定价.最后,数值算例表明,相比于CRR模型,新模型收敛光滑平稳且有更高的计算精度;对上涨(下跌)的二元期权、欧式期权,新模型都能光滑收敛于B-S公式.     

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.     

Option pricing for a logstable asset price model

The paper generalises the celebrated Black and Scholes [1] European option pricing formula for a class of logstable asset price models. The theoretical option prices have the potential to explain the implied volatility smiles evident in the market.     

An analytic pricing formula for lookback options under stochastic volatility

In this work, an analytic pricing formula for floating strike lookback options under Heston’s stochastic volatility model is derived by means of the homotopy analysis method. The fixed strike lookback options can then be priced on the basis of the results of floating strike and the put–call parity relation for lookback options.     

The pricing of derivatives on assets with quadratic volatility

The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model guarantees positive asset prices. In this paper, it is shown that the pricing partial differential equation can be solved for level-dependent volatility which is a quadratic polynomial. If zero is attainable, both absorption and negative asset values are possible. Explicit formulae are derived for the call option: a generalization of the Black-Scholes formula for an asset whose volatiliy is affine, the formula for the Bachelier model with constant volatility, and new formulae in the case of quadratic volatility. The implied Black-Scholes volatilities of the Bachelier and the affine model are frowns, the quadratic specifications imply smiles.     

随机利率Vasicek模型下的欧式缺口期权的定价研究

研究随机利率Vasicek模型下欧式缺口期权的定价问题,利用偏微分方程方法给出了欧式缺口看涨期权和看跌期权的定价公式,并且是Vasicek利率模型下标准欧式期权定价公式的一种推广.     

跳跃过程下的汇率连动期权的定价

假设汇率变化过程服从带跳的几何布朗运动,股票价格遵循带跳的O-U过程,建立汇率连动期权市场模型,利用保险精算方法和Girsanov公式,给出了汇率连动期权的定价公式,获得了欧式看涨和看跌期权定价公式及平价公式．     

Eurodollar futures pricing in log-normal interest rate models in discrete time

We demonstrate the appearance of explosions in three quantities in interest rate models with log-normally distributed rates in discrete time. (1) The expectation of the money market account in the Black, Derman, Toy model, (2) the prices of Eurodollar futures contracts in a model with log-normally distributed rates in the terminal measure and (3) the prices of Eurodollar futures contracts in the one-factor log-normal Libor market model (LMM). We derive exact upper and lower bounds on the prices and on the standard deviation of the Monte Carlo pricing of Eurodollar futures in the one factor log-normal Libor market model. These bounds explode at a non-zero value of volatility, and thus imply a limitation on the applicability of the LMM and on its Monte Carlo simulation to sufficiently low volatilities.     

中国国债期货与隐含择券期权定价

本文提出了一种双树拼接的改进BDT模型,在此基础上发展出两种方法为中国市场上的国债期货和择券期权定价。其中"直接定价法"直接使用双树拼接树图,"两步定价法"则是经期权调整的持有成本模型。对中国TF1403和T1603国债期货合约的实证研究表明,两种方法都是合理的,且各有优势,"两步定价法"与市场价格差异较小,"直接定价法"与市场价格同步性较高。     

汇率连动期权的保险精算定价

利用保险精算方法给出了汇率连动期权的定价公式,获得了欧式看涨期权和看跌期权价格的表达式及平价关系。     

Assessment and propagation of input uncertainty in tree‐based option pricing models

This paper aims to provide a practical example of assessment and propagation of input uncertainty for option pricing when using tree‐based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices are as unknown as the inputs they are based on. Option pricing formulas are tools whose validity is conditional not only on how close the model represents reality, but also on the quality of the inputs they use, and those inputs are usually not observable. We show three different approaches to integrating out the model nuisance parameters and show how this translates into model uncertainty in the tree model space for the theoretical option prices. We compare our method with classical calibration‐based results assuming that there is no options market established and no statistical model linking inputs and outputs. These methods can be applied to pricing of instruments for which there is no options market, as well as a methodological tool to account for parameter and model uncertainty in theoretical option pricing. Copyright © 2008 John Wiley & Sons, Ltd.     

A GARCH option pricing model with α-stable innovations

We develop an option pricing model which is based on a GARCH asset return process with α-stable innovations with truncated tails. The approach utilizes a canonic martingale measure as pricing measure which provides the possibility of a model calibration to market prices. The GARCH-stable option pricing model allows the explanation of some well-known anomalies in empirical data as volatility clustering and heavy tailedness of the return distribution. Finally, the results of Monte Carlo simulations concerning the option price and the implied volatility with respect to different strike and maturity levels are presented.     

Pricing bivariate option under GARCH processes with time-varying copula

This paper develops a method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. As the association between the underlying assets may vary over time, the dynamic copula with time-varying parameter offers a better alternative to any static model for dependence structure and even to the dynamic copula model determined by dynamic dependence measure. Therefore, the proposed method proves to play an important role in pricing bivariate options. The approach is illustrated with one type of better-of-two-markets claims: call option on the better performer of Shanghai and Shenzhen Stock Composite Indexes. Results show that the option prices obtained by the time-varying copula model differ substantially from the prices implied by the static copula model and even the dynamic copula model derived from the dynamic dependence measure. Moreover, the empirical work displays the advantages of the suggested method.     

考虑公司信息披露情绪的欧式脆弱期权定价

从公司信息披露的角度来看,定量数据直观地反映了公司的经营和财务状况,而描述性的非结构文本信息是对定量数据的有效补充。本文从公司年报中挖掘信用违约文本信息,构建语调变量情绪指标,以调控脆弱期权的违约临界值,改进经典的Klein欧式脆弱期权定价模型。研究表明:随着语调变量指标的增大,欧式看涨看跌期权价格呈递减趋势,且指标越接近1,期权价格递减速度越快,说明期权价格对负向情绪更加敏感,符合金融市场实际情况。此外,应用研究发现不考虑情绪指标的Klein模型倾向于低估期权价格,考虑公司信息披露情绪的脆弱期权定价模型能更准确地分析财务困境对信用风险的影响,结果更贴近实际情况。     

基于不确定指数O-U过程带有浮动利率模型的亚式期权定价

不确定金融是不确定理论在现代金融领域的一种应用,在解决金融问题中发挥着越来越重要的作用。而利率是一个重要的经济指标,经常受到一些不确定因素的影响,在研究期权定价时,有必要考虑浮动利率。本文提出了一种新的不确定指数Ornstein-Uhlenbeck过程模型,假设利率服从不确定均值回复过程,研究了期权定价问题,运用α-轨道方法,分别推导了亚式看涨期权和看跌期权定价公式。最后,设计了计算期权价格的数值算法,并给出数值算例。     

American Options under Proportional Transaction Costs: Pricing, Hedging and Stopping Algorithms for Long and Short Positions

American options are studied in a general discrete market in the presence of proportional transaction costs, modelled as bid-ask spreads. Pricing algorithms and constructions of hedging strategies, stopping times and martingale representations are presented for short (seller’s) and long (buyer’s) positions in an American option with an arbitrary payoff. This general approach extends the special cases considered in the literature concerned primarily with computing the prices of American puts under transaction costs by relaxing any restrictions on the form of the payoff, the magnitude of the transaction costs or the discrete market model itself. The largely unexplored case of pricing, hedging and stopping for the American option buyer under transaction costs is also covered. The pricing algorithms are computationally efficient, growing only polynomially with the number of time steps in a recombinant tree model. The stopping times realising the ask (seller’s) and bid (buyer’s) option prices can differ from one another. The former is generally a so-called mixed (randomised) stopping time, whereas the latter is always a pure (ordinary) stopping time.     

SDP Relaxation of Arbitrage Pricing Bounds Based on?Option Prices and Moments

This paper develops a semidefinite programming approach to computing bounds on the range of allowable absence of arbitrage prices for a European call option when option prices at other strikes and expirations are available and when moment related information on the underlying is known. The moment related information is incorporated in the problem through the fictitious prices of polynomial valued securities. The optimization then comes from relaxing a risk neutral pricing optimization problem in terms of moments of measures from a decomposition of the risk neutral pricing measure. We demonstrate this optimization formulation with computations using moment data from the standard Black-Scholes option pricing model and Merton’s jump diffusion model.     

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     

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.     

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.