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.     

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.     

Stackelberg financial-leader in insider trading model

In this paper, we extend the Jain-Mirman [Jain, N., & Mirman, L. (2000). Real and financial effects of insider trading with correlated signals. Economic Theory, 16, 333–353, Jain, N., & Mirman, L. (2002). Effects of insider trading under different market structures. The Quarterly Review of Economics and Finance, 42, 19–39] and the Daher-Mirman [Daher, W., & Mirman, L. (2006). Cournot duopoly and insider trading with two insiders. The Quarterly Review of Economics and Finance, 46, 530–551, Daher, W., & Mirman, L. (2007). Market structure and insider trading. International Review of Economics and Finance, 16, 306–331] papers on competition, and postulate that the competition among the insiders in the financial market be Stackelberg. However, an owner high in the organizational hierarchy, who designs manager compensation mechanisms and chooses a manager to serve his purpose, should have information on the manager's reaction and act as a Stackelberg leader in the financial sector. We show that owner's profit can definitely enlarged while the manager's profits may decrease or increase depending on the variances in the two sectors, which are the exogenous parameters.     

Re-examining the exchange rate pass-through into import prices using non-linear estimation techniques: Threshold cointegration

We document a significant threshold cointegrating relationship among effective nominal exchange rates and import prices. Using quarterly data for five industries of 16 OECD countries, we find that the degree of pass-through improves dramatically from the 50% average documented in the literature once threshold effects are recognized. The results of our threshold cointegration model show that import prices respond faster and by a larger extent to nominal exchange rate shocks than is the case for more conventional models. These findings give empirical support to the hypothesis that an equilibrium rate of pass-through exists (e.g. [Bacchetta, P., & Van Wincoop, E. (2005). A Theory of the currency denomination of international trade, Journal of International Economics 67, 295–319; Devereux, M., Engel, C., & Storgaard, P. (2004). Endogenous exchange rate pass-through when nominal prices are set in advance, Journal of International Economics 63(2), 263–291]).     

The dynamics of the Jones R & D growth model

The dynamics of most prominent endogenous growth models are well understood. One notable exception is the Jones R & D growth model [Jones, C.I., 1995. R & D based models of economic growth. Journal of Political Economy 103, 759–784]. This paper provides an analytical treatment of this model's transitional dynamics. It is shown that, given constant returns to labor in R & D (as conventionally assumed in R & D growth models), a unique trajectory converging to the balanced growth path exists. The equilibrium growth path can be monotonic or oscillatory. Moreover, applying a theorem from [Arnold, L.G., 2005. The dynamics of multi-country R & D growth models. University of Regensburg Discussion Papers in Economics, No. 404. February], this result can be used to characterize the dynamic behavior of the multi-country open-economy version of the model.     

Revisiting the long memory dynamics of the implied–realized volatility relationship: New evidence from the wavelet regression

The literature studying stock index options confirms severe biases and inefficiencies in using implied volatility as a forecast of future volatility. In this paper, we revisit the implied–realized volatility relationship with wavelet band least squares (WBLS) exploring the long memory of volatility, a possible cause of the bias. Using the S&P 500 and DAX monthly and bi-weekly option prices covering the recent financial crisis, we conclude that the implied–realized volatility relation is driven solely by the lower frequencies of the spectra representing long investment horizons. The findings enable improvement of future volatility forecasts as they support unbiasedness of implied volatility as a good proxy for future volatility in the long run.     

The determinants of exchange settlement practices and the implication of volatility smile: Evidence from the Taiwan Futures Exchange

This paper proposes that the Taiwan Futures Exchange (TAIFEX) adopts a linear extrapolation method to set the settlement price for the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX) options with less liquidity and thin trading. The empirical results indicate that the settlement-price-determined implied volatility is a smile function, consistent with the pattern of the market-price-determined implied volatility. Moreover, we examine the influence of economic factors on the TAIFEX's decision regarding the parameters of implied volatility function. Compared with the economic determinants of market-force-driven volatility parameters, the TAIFEX inappropriately values the impacts of the parameters of prior days, current stock returns, distribution of stock returns, long-term measurement of the stock market trend, market transaction cost, and time to maturity.     

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.

     

ENDOGENOUS CYCLICAL GROWTH WITH A SIGMOIDAL DIFFUSION OF INNOVATIONS

The model we propose in this paper is an extension of the one described in Freeman et al. [Freeman, S., Hong, D. and Peled, D. (1999) Endogenous Cycles and Growth with Indivisible Technological Developments. Review of Economics Dynamics, 2, 403–432]. In our model, we incorporate the process of diffusion of major innovations and analyze macroeconomic effects on consumption, capital and aggregate output. Following Bresnahan and Trajtenberg [Bresnahan, T. and Trajtenberg, M. (1995) General Purpose Technologies: Engines of Growth?. Journal of Econometrics, 65, 83–108.], Helpman [Helpman, E. (ed.) (1998) General Purpose Technologies and Economic Growth. MIT Press] and Lipsey et al. [Lipsey, R.G., Carlaw, K. and Bekar, C. (2005) Economic Transformations: General Purpose Technologies and Long Term Economic Growth. Oxford University Press.] we assimilate major innovations with the emergence of certain GPTs, and we suggest that the diffusion process for these technologies, at a large scale, might follow an S-shaped pattern. The proposed model presents optimum stationary solutions which are cyclical and have a wave dynamic within each cycle. The cycles are characterized by certain co-movements in consumption, R&D investment, capital accumulation and output. Consideration of the innovation diffusion process highlights new aspects of endogenous cycles and long-run growth.     

A test of the Wagner's hypothesis for the Fiji islands

In this article we examine Wagner's law for Fiji for the period 1970 to 2002. Using the Johansen (1988 Johansen, S. 1988. Statistical analysis of cointegrating vectors. Journal of Economic Dynamics and Control, 12: 231–54. [Crossref], [Web of Science ®] , [Google Scholar]) test for cointegration, we find one cointegration relationship between national output and government expenditure. Using five different long run estimators, we find robust results on the impact of national income on government expenditure. The elasticity ranges from 1.36 to 1.44, implying that a 1% increase in income leads to a 1.36–1.44% increase in government expenditure. Moreover, we find that in the long run national income Granger causes government expenditure. While these results are consistent with Wagner's law, we warn policy makers that because Fiji's total debt stands at around 69% of GDP, in future the bulk of expenditure will go towards debt financing at the expense of productive sectors.     

The payoff and implied pricing kernel in REITs

This article explores the hybrid character (i.e. the resemblance of both stock and bond) of Real Estate Investment Trust (REIT) through the implied pricing kernel behind REITs prices. We use the Empirical Pricing kernel method (Rosenberg and Engle, 2002 Rosenberg, J and Engle, RF. 2002. Empirical pricing kernels. Journal of Financial Economics, 64: 341–72. [Crossref], [Web of Science ®] , [Google Scholar]) to explore their Payoff probability density and extract the implied pricing kernel. To estimate payoff probability density, we use asymmetric GARCH model. Results indicate that implied pricing kernels flatten in all ranges of low rate of returns and decrease exponentially in ranges of high rate of returns. This means the REIT pricing kernel resembles a bond when rate of return is low, and a stock when it is high. The pattern is consistent between 1970 and 2000.     

Mutual Insurance,Individual Savings,and Limited Commitment

We examine a dynamic model of mutual insurance when households can also engage in self-insurance by storage. We assume that there is no enforcement mechanism, so that any insurance is informal and must be self-enforcing. We show that consumption allocations satisfy a modified Euler condition and that an enhanced storage technology can either improve or diminish welfare. Furthermore we show that the ex ante transfers introduced into dynamic informal insurance models recently by Gauthier et al. (Gauthier, C., Poitevin, M., and González, P. (1997). Journal of Economic Theory76, 106–144) are only used here in the first period, with the role of ex ante transfers being replaced by differential individual storage. Journal of Economic Literature Classification Numbers: C61, C73, D90, E21.     

On the asymmetric impact of macro–variables on volatility

We extend the GARCH–MIDAS model to take into account possible different impacts from positive and negative macroeconomic variations on financial market volatility: a Monte Carlo simulation which shows good properties of the estimator with realistic sample sizes. The empirical application is performed on the daily S&P500 volatility dynamics with the U.S. monthly industrial production and national activity index as additional (signed) determinants. We estimate the Relative Marginal Effect of macro variable movements on volatility at different lags. In the out-of-sample analysis, our proposed GARCH–MIDAS model not only statistically outperforms the competing specifications (GARCH, GJR-GARCH and GARCH–MIDAS models), but shows significant utility gains for a mean-variance investor under different risk aversion parameters. Attention to robustness is given by choosing different samples and estimating the model in an international context (six different stock markets).     

Correcting the Merton and Henriksson timing model

This article provides evidence of a common bias found in traditional timing models, which is related with a negative correlation between timing and stock-picking abilities resulting in spurious coefficients. We consider as a possible cause for this bias the failure to include in the timing models the cost of the option implied in timing activities, and on this basis we opt for a corrected version of the Merton and Henriksson's model (1981 Merton, R. C. and Henriksson, R. D. 1981. On market timing and investment performance II: statistical procedures for evaluating forecasting skills. Journal of Business, 54: 513–34. [Crossref] , [Google Scholar]). As far as we know, this correction has not previously been applied. Our results confirm both the existence of this bias and the correction of the problem when the cost of the option is included in timing models.     

Collective behavior and options volatility smile: An agent-based explanation

This paper represents an initial effect to shed light on the determinants of option implied volatility smile from the micro perspective of traders' behavior. We compare the zero intelligence behavior and the collective behavior with the agent-based simulation. We find that the constant implied volatility, which is the assumption of the Black–Scholes model, can be obtained under the environment of the zero intelligence traders; while the smile shape of implied volatility, which is more consistent with the practical option market worldwide, can be explained by traders' collective behavior. Moreover, different degrees of collective behavior are tested to result that with the increasing of collective degree the implied volatility curve becomes steeper.     

Tax evasion and social interactions

The paper extends the standard tax evasion model by allowing for social interactions. In Manski's [Manski, C.F. (1993). Identification of Endogenous Social Effects: The Reflection Problem. Review of Economic Studies 60(3), 531–542.] nomenclature, our model takes into account endogenous interactions, i.e., social conformity effects, exogenous interactions, i.e., fairness effects, and correlated effects. Our model is tested using experimental data. Participants must decide how much income to report given individual and group tax rates and audit probabilities, and given a feedback on the other members' reporting behavior. Myopic and self-consistent expectations are considered in the analysis. In the latter case, the estimation is based on a two-limit simultaneous tobit with fixed group effects. A unique social equilibrium exists when the model satisfies coherency conditions. In line with Brock and Durlauf [Brock, W.A., Durlauf, S.N. (2001b). Interactions-Based Models, in J. Heckman and E. Leamer, eds., Handbook of Econometrics 5, Elsevier Science B.V., 3297–380.], the intrinsic nonlinearity between individual and group responses helps identify the model. Our results provide evidence of fairness effects but reject social conformity.     

Schelling's spatial proximity model of segregation revisited

Schelling [Schelling, T.C., 1969. Models of Segregation. American Economic Review, Papers and Proceedings, 59, 488-493, Schelling, T.C., 1971a. Dynamic Models of Segregation. Journal of Mathematical Sociology, 1 (2), 143–186, Schelling, T.C., 1971b. On the Ecology of Micromotives. The Public Interest, 25, 61–98, Schelling, T.C., 1978. Micromotives and Macrobehavior. New York: Norton.] presented a microeconomic model showing how an integrated city could unravel to a rather segregated city, notwithstanding relatively mild assumptions concerning the individual agents' preferences, i.e., no agent preferring the resulting segregation. We examine the robustness of Schelling's model, focusing in particular on its driving force: the individual preferences. We show that even if all individual agents have a strict preference for perfect integration, best-response dynamics may lead to segregation. This raises some doubts on the ability of public policies to generate integration through the promotion of openness and tolerance with respect to diversity. We also argue that the one-dimensional and two-dimensional versions of Schelling's spatial proximity model are in fact two qualitatively very different models of segregation.     

Inflation,openness, and exchange-rate regimes: The quest for short-term commitment

This paper further tests Romer's [Romer, D., 1993. Openness and inflation: theory and evidence. Quarterly Journal of Economics 58, 869–903] extension of Kydland and Prescott's [Kydland, F., Prescott, E., 1977. Rules rather than discretion: the inconsistency of optimal plans. Journal of Political Economy 85, 473–491] predictions for dynamic inconsistency problems in open economies. In a panel data set of developed and developing countries from 1973 to 1998, I find that openness does not play a role in restricting inflation in the short run. On the other hand, a fixed exchange-rate regime plays a significant role. The results are robust to controlling for other variables that determine inflation, performing sensitivity analysis, and using a de facto exchange-rate regime classification.     

Zermelo and the Early History of Game Theory

In the modern literature on game theory there are several versions of what is known as Zermelo's theorem. It is shown that most of these modern statements of Zermelo's theorem bear only a partial relationship to what Zermelo really did. We also give a short survey and discussion of the closely related but almost unknown work by König (1927, Acta Sci. Math. Szeged, 3, 121–130) and Kálmar (1928/29, Acta Sci. Math. Szeged, 4, 65–85). Their papers extend and considerably generalize Zermelo's approach. A translation of Zermelo's paper is included in the Appendix. Journal of Economic Literature Classification Numbers: B19; C70; C72.