The Black–Scholes model as a determinant of the implied volatility smile: A simulation study

The paper represents an initial effort to shed light on the determinants of the implied volatility smile in financial (derivative) markets. It fully details the implications of the institutionalization of the Black–Scholes model in an uncertain world populated by individuals who are bounded by the amount of calculation or accounting which is technically possible. Combining model simulations, empirical analysis, and mathematical derivations, the paper proposes that the determinants of the volatility smile might be related to the behavior of traders. In pricing options, they use the widely accepted Black–Scholes formula with a measure of stock volatility that they derive from their subjective beliefs. Moreover, heterogeneity of traders’ beliefs and the way traders update their expectations have nontrivial effects, both on equilibrium prices and on the emergence of the implied volatility smile.     

基于实物期权的创业投资资本资产定价模型

创业投资的特质与实物期权方法有实质的契合性,表现在创业投资的风险水平同实物期权的波动率之间。创业投资的分期投资与实物期权的期权价值之间有着密切的关联性。这种内在契合性是运用实物期权方法研究创业投资定价研究的基础。基于Black-Scholes偏微分方程的实物期权模型构造的多期创业投资的实物期权定价模型,更具现实解释力。     

An enhanced implied tree model for option pricing: A study on Hong Kong property stock options

This paper empirically tests the practicability of the implied tree models on pricing the major HK real estate stock options and Hang Seng Index (HSI) Options, as an attempt to deal with the problem haunting the Black–Scholes Model in “volatility smiles”. Further, an iterative search procedure is originated to incorporate the idea of node-dependent interest rates to the implied binomial tree model. The results would then be compared with the original Cox, Ross, and Rubinstein (1979) [Cox, J., Ross, S. and Rubinstein, M. (1979), Option pricing: A simplified approach, Journal of Financial Economics, vol.7, no.3 (September), 229–264] tree models (CRR) in order to assess its performance, through an out-of-sample fitness test. The findings illustrate that the implied binomial trees, with node-dependent interest rates, provide a closer estimate of option prices than the original CRR tree models, when options are frequently traded in the market. Encouraging results are obtained from the in-sample fitness test on the implied trees to simulate the spot evolution of HSI options within a short period of time. However, the original CRR tree models outperform the implied tree models on either inactively traded property stock options, or options with distant time-to-maturity. Misrepresentation of future local volatilities, implied by the prices, and data constraints are likely the reasons hindering the development of the implied tree models.     

Do Aussie markets smile? Implied volatility functions and determinants

If options are correctly priced, the interpretation of volatility in the Black–Scholes model (as identifying the volatility of the underlying asset) is violated. The empirical relation between the model ‘implied volatility’ and the degree to which the option is in-the-money (moneyness) has been reported as resembling a U-shape (or ‘smile’) for options on currencies (and more of a ‘smirk’ for options on equities). In this article, using multivariate time-series analysis and employing an impulse response function, we investigate the structural relationships and dynamics of the volatility smile in relation to the option liquidity, key features of the underlying asset and market momentum. Our findings confirm evidence of a number of biases in the Black–Scholes model consistent with Chou et al. (2011) in regard to liquidity in both the underlying and the option itself, and with Peña et al. (1999) as to the importance of the option time to maturity. As well as delineating such biases as they co-relate both with each other and with the underlying asset volatility and momentum, we find that the pronounced smile is related to the differential sensitivities of in-the-money and out-of-the-money options, which itself suggests an explanation for the characteristic smile shape.     

Empirical of the Taiwan stock index option price forecasting model – applied artificial neural network

This work presents a novel neural network model for forecasting option prices using past volatilities and other options market factors. Out of different approaches to estimating volatility in the option pricing model, this study uses backpropagation neural network to forecast prices for Taiwanese stock index options. The ability to develop accurate forecasts of grey prediction volatility enables practitioners to establish an appropriate hedging strategy at in-the-money option.     

Foreign equity option pricing under stochastic volatility model with double jumps

This paper considers the challenging problem advocated by Huang and Hung (2005), that is to incorporate the stochastic volatility into the foreign equity option pricing. Foreign equity options (quanto options) are contingent claims where the payoff is determined by an equity in one currency but the actual payoff is done in another currency. Huang and Hung (2005) priced foreign equity options under the Lévy processes. In Huang and Hung's paper, they considered jumps in the foreign asset prices and exchange rates and assumed the volatility as constant. However, many studies showed that constant volatility and jumps in returns are incapable of fully capturing the empirical features of equity returns or option prices. In this paper, the stochastic volatility with simultaneous jumps in prices and volatility is proposed to model foreign asset prices and exchange rates. The foreign equity option pricing formula is given by using the Fourier inverse transformation. The numerical results show that the use of stochastic volatility with simultaneous jumps in prices and volatility proposed to model foreign asset prices and exchange rates is necessary and this approach can help us to capture more accurately the foreign equity option prices.     

Optimality and Robustness of the English Auction

In Milgrom and Weber's (1982, Econometrica50, 1089–1122) “general symmetric model,” under a few additional regularity conditions, the English auction maximizes the seller's expected profit within the class of all posterior-implementable trading procedures and fails to do so among all interim incentive-compatible procedures in which “losers do not pay.” These results suggest that appropriate notions of robustness and simplicity which imply the optimality of the English auction for a risk-neutral seller must impose “bargaining-like” features on the set of feasible trading mechanisms. Journal of Economic Literature Classification Numbers: D44, D82.     

On derivatives and information costs

Information plays a central role in capital markets and in the process of asset pricing. The specific features of over-the-counter (OTC) markets require often an investment in information acquisition. Information costs can be defined in the context of Merton's [Merton, R. (1987). A simple model of capital market equilibrium with incomplete information. Journal of Finance, 42, 483–510] model of capital market equilibrium with incomplete information (CAPMI). In this context, hedging portfolios can be constructed and analytic formulas can be derived using the Black and Scholes technology or the martingale method. This paper presents a simple framework for the valuation of exotic derivatives and OTC traded securities in this context. We incorporate information costs into a model, and then use this new model to price a variety of exotic options using the general context in Bellalah [Bellalah, M. (2001). Market imperfections, information costs and the valuation of derivatives: Some general results. International Journal of Finance, 13, 1895–1928]. In each case, simple analytic formulae are derived.From a pedagogical viewpoint, we illustrate the methodology and propose simple analytic formulas for pay-on-exercise options, power derivatives, outperformance options, guaranteed exchange-rate contracts in foreign stock investments, equity-linked foreign exchange options and quantos in the same context. These formulae are simple and have the potential to explain some deviations with respect to the standard Black–Scholes model. We can use also stochastic volatilities and information costs to explain the smiles and skews found in options price data as in Bellalah, Prigent, and Villa [Bellalah, M., Prigent, J. L., & Villa, C. (2001). Skew without skewness: Asymmetric smiles, information costs and stochastic volatilitiy, International Journal of Finance, 2001, 1826, 1837] or Bellalah and Mahfoudh (2004) [Bellalah M. and Mahfoudh S. (2004). Option pricing under stochastic volatility with incomplete Information, Wilmott Magazine]. Our methodology can be applied for the valuation of several OTC and real options in the presence of incomplete information.     

Access pricing and investment: a real options approach

This paper examines a three-period model of an investment decision in a network industry characterized by demand uncertainty, economies of scale and sunk costs. In the absence of regulation we identify the market conditions under which a monopolist decides to invest early as well as the overall welfare generated by this decision. In a regulated environment, we consider a vertically integrated network provider that is required to provide access to downstream competitors and compare two distinct access pricing methodologies: the Efficient Component Pricing Rule (ECPR) and the Option to Delay Pricing Rule (ODPR). We identify the welfare-maximizing access prices using the unregulated market output as a benchmark and show that optimal access regulation depends on market conditions (that is, the nature of demand) with two possible outcomes: (i) access prices that provide a positive payoff to the incumbent, that is, provide a positive compensation to account for the option to delay; and (ii) access prices that yield a zero payoff to the incumbent. Moreover, unlike the earlier literature that argues in favor of an ECPR-type methodology to account for the interaction between irreversibility and demand uncertainty, we find that, except under very specific conditions, an access price that accounts for the option to delay value is welfare-superior to the ECPR.      

Exchange rate pass-through in New Member States and candidate countries of the EU

This paper studies the degree of exchange rate pass-through to the prices of imports of some New Member States (NMSs) of the European Union plus Turkey, coming from the euro area. I estimate industry-specific rates of pass-through across and within countries using the methodology proposed by Campa and González-Mínguez [Campa, J.M. and González-Mínguez, J.M. (2006). Differences in Exchange Rate Pass-Through in the Euro Area. European Economic Review, 50, 121–145.] which estimates the short- and long-run pass-through elasticities. I did not find evidence either in favour of the hypothesis of Local Currency Pricing (zero pass-through) or the hypothesis of Producer Currency Pricing (complete pass-through) for all the countries except for Slovenia and Cyprus. With reference to the results by industry, the lowest values for exchange rate pass-through are in Manufacturing sectors. However, I did observe a exchange rate pass-through decline through the pricing chain.     

House Allocation with Transfers

We consider the Shapley–Scarf house allocation problem where monetary transfers are allowed. We characterize the class of mechanisms that are strategy-proof, ex post individually rational, ex post budget-balanced, and “collusion-proof.” In these mechanisms, the price of each object is fixed in advance, and the objects are reallocated according to the (unique) core assignment of the Shapley–Scarf economy associated with the prices. The special case in which all prices are zero is the core mechanism studied by Shapley and Scarf. Our mechanisms are compelling alternatives to the Groves mechanisms, which satisfy neither budget balance nor our condition of collusion-proofness. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

A nonparametric kernel regression approach for pricing options on stock market index

Previous options studies typically assume that the dynamics of the underlying asset price follow a geometric Brownian motion (GBM) when pricing options on stocks, stock indices, currencies or futures. However, there is mounting empirical evidence that the volatility of asset price or return is far from constant. This article, in contrast to studies that use parametric approach for option pricing, employs nonparametric kernel regression to deal with changing volatility and, accordingly, prices options on stock index. Specifically, we first estimate nonparametrically the volatility of asset return in the GBM based on the Nadaraya–Watson (N–W) kernel estimator. Then, based on the N–W estimates for the volatility, we use Monte Carlo simulation to compute option prices under different settings. Finally, we compare the index option prices under our nonparametric model with those under the Black–Scholes model and the Stein–Stein model.     

经理人股权薪酬合约结构的理论与启示

经理人股权薪酬合约中限制性股票和股票期权如何配置与其激励特性及经理人股票期权价值相关。本文使用布莱克——斯科尔斯模型衡量经理人期杈价值时存在没有考虑经理人异质风险态度、风险构成对期权定价的影响。介绍了3个不同模型支撑下的股权薪酬合约结构的理论,并联系我国的实际情况提出了对我国上市公司制定股权薪酬合约计划的启示和建议。     

Ad-Hoc Black–Scholes vis-à-vis TSRV-based Black–Scholes: Evidence from Indian Options Market

This research paper examines one-day-ahead out-of-sample performance of the volatility smirk-based options pricing models, namely, Ad-Hoc-Black–Scholes (AHBS) models on the CNX Nifty index options of India. Further, we compare the performance of these models with that of a TSRV-based Black–Scholes (BS) model. For the purpose, the study uses tick-by-tick data. The results on the AHBS models are highly satisfactory and robust across all the subgroups considered in the study. Notably, a daily constant implied volatility based ad-hoc approach outperforms the TSRV-based BS model substantially. The performance of the ad-hoc approaches improves further when the smile/smirk effect is considered. For the estimation of the implied volatility smile, we apply three weighting schemes based on the Vega and liquidity of the options. All the schemes offer equally competing results. The major contribution of the study to the existing literature on options pricing is in terms of the ex-ante examination of the ad-hoc approaches to price the options by calibrating volatility smile/smirk on a daily basis.

     

Accounting for the impact of higher order moments in foreign equity option pricing model

This paper investigates the pricing of foreign equity option whose value depends on foreign equity prices and exchange rate. We assume that the underlying asset returns of foreign equity option is not a Brownian motion, and use the Gram-Charlier series expansion to augment a normal density with two additional terms to capture the effects of skewness and kurtosis. The empirical study shows that the higher order moments (skewness and kurtosis) clearly affect the estimated prices of foreign equity options. This approach enables us to capture more accurately the foreign equity option prices.     

A comparison of pricing and hedging performances of equity derivatives models

This article investigates the pricing/hedging conundrum, i.e. the observation of a mismatch between derivatives models’ pricing and hedging performances, that has so far been under-emphasized as the literature tends to focus on increasingly complicated option pricing models, without adequately addressing hedging performance. Hence, we analyse the ability of the Black–Scholes, Practitioner Black–Scholes, Heston–Nandi and Heston models to Delta-hedge a set of call options on the S&P500 index and Apple stock. We extend earlier studies in that we consider the impact of asset dynamics, apply a stringent payoff replication strategy, look at the impact of moneyness at maturity and test for the robustness to the parameters’ calibration frequency and Delta-Vega hedging. The study shows that adding risk factors to a model, as stochastic volatility, should only be considered in light of the data dynamics. Even then, however, more complicated models generally fare poorly for hedging purposes. Hence, a better fit of a model to option prices is not a good indicator of its hedging performance, and so of its ability to describe the underlying dynamics. This can be understood for reasons of over-fitting. Those findings hint to a potentially appealing hedging-based calibration of models’ parameters, rather than the standard pricing-based one.     

Influence and inefficiency in the internal capital market

I model inefficient resource allocations in M-form organizations due to influence activities by division managers that skew capital budgets in their favor. Corporate headquarters receives two types of signals about investment opportunities: private signals that can be distorted by managers, and public signals that are undistorted but noisy. Headquarters faces a tradeoff between the cost of attaining an accurate private signal and the value of the information the signal provides. In contrast to existing models of “socialism” in internal capital markets, I show that investment sensitivity to Tobin's Q is higher than first-best in firms where division managers hold equity (a result consistent with evidence presented in Scharfstein, 1998). When managers face high private costs from distorting information (equity holdings), headquarters may commit to investment contracts that place “too little” weight on private signals and “too much” weight on public signals (i.e. Q). This result has implications for managers in the design of capital budgeting processes and incentive compensation systems.     

碳交易及补贴机制下供应链差别定价研究

研究了碳交易机制、补贴机制以及碳交易及补贴机制下,一个二级供应链中普通产品和低碳产品竞争的差别定价策略,通过求解Stackelberg博弈模型得出单一的补贴政策并不能激励制造商进行节能减排,应与碳交易机制结合使用,其节能减排效果优于单一的碳交易机制。最后通过一个算例分析验证了碳交易及补贴机制的有效性。研究表明：碳交易价格升高到一定程度时,普通产品的零售价批发价均升高,低碳产品的价格均下降,普通产品的销量下降,低碳产品销量上升,碳排放总量下降;随着低碳补贴的增加,普通产品的零售价,低碳产品的批发价、零售价均降低,普通产品的销量下降,低碳产品的销量上升,其中低碳产品的价格和需求量对低碳补贴的反应更加敏感,使碳排放量降低的同时还提高了制造商和零售商的利润。     

A high-frequency analysis of price resolution and pricing barriers in equities on the adoption of a new currency

We use ultra high frequency (trade by trade) data to demonstrate that equity price clustering and pricing predictability around psychologically important prices in Greece switches away from drachma-focused with the introduction of the euro, but does not immediately switch to euro-clustering. The change in trader price focus around the euro introduction addresses an open debate in the clustering literature on whether the presence of clustering is a bias related to the current prices or anchoring to past prices. Our findings of a decline in drachma clustering, but lack of switch to euro effects supports the case for clustering being a trading feature that is slow to transfer to new pricing regimes. A key advantage of the ultra high frequency dataset is we are also able to demonstrate the presence of psychological pricing barriers related to each currency that are not detectable in daily data.