An endogenous volatility approach to pricing and hedging call options with transaction costs

Standard delta hedging fails to exactly replicate a European call option in the presence of transaction costs. We study a pricing and hedging model similar to the delta hedging strategy with an endogenous volatility parameter for the calculation of delta over time. The endogenous volatility depends on both the transaction costs and the option strike prices. The optimal hedging volatility is calculated using the criterion of minimizing the weighted upside and downside replication errors. The endogenous volatility model with equal weights on the up and down replication errors yields an option premium close to the Leland [J. Finance, 1985 Leland, HE. 1985. Option pricing and replication with transaction costs. J. Finance, 40: 1283–1301. [Crossref], [Web of Science ®] , [Google Scholar], 40, 1283–1301] heuristic approach. The model with weights being the probabilities of the option's moneyness provides option prices closest to the actual prices. Option prices from the model are identical to the Black–Scholes option prices when transaction costs are zero. Data on S&P 500 index cash options from January to June 2008 illustrate the model.     

Dynamic liquidation under market impact

The optimal liquidation problem with transaction costs, which includes a positive fixed cost, and market impact costs, is studied in this paper as a constrained stochastic optimal control problem. We assume that trading is instantaneous and the dynamics of the stock to be liquidated follows a geometric Brownian motion. The solution to the impulse control problem is computed at each time step by solving a linear partial differential equation and a maximization problem. In contrast to results obtained from the static formulation of Almgren and Chriss [J. Risk, 2000 Almgren, R and Chriss, N. 2000. Optimal execution of portfolio transactions. J. Risk, 3: 5–39. [Crossref] , [Google Scholar], 3, 5–39], when risk is not considered, the optimal liquidation strategy from our stochastic control formulation depends on temporary market impact cost and permanent market impact cost parameters. In addition, our computational results indicate the following properties of the optimal execution strategy from the stochastic control formulation. Due to the existence of a no-transaction region, it may not be optimal for some individuals to sell their assets on some trading dates. As the value of the permanent market impact parameter increases, the expected optimal amount liquidated at the terminal time increases. As the value of the quadratic temporary impact cost parameter increases, the expected optimal amount liquidated at trading times tends to be uniform, and the no-transaction region shrinks. In the presence of quadratic temporary market impact costs, in contrast to optimal strategies that result from fixed and/or proportional transaction costs alone, portfolios in the selling region are neither re-balanced into the no-transaction region nor into the sell and no-transaction interface.     

Duality and convergence for binomial markets with friction

We prove limit theorems for the super-replication cost of European options in a binomial model with friction. Examples covered are markets with proportional transaction costs and illiquid markets. A dual representation for the super-replication cost in these models is obtained and used to prove the limit theorems. In particular, the existence of a liquidity premium for the continuous-time limit of the model proposed in Çetin et al. (Finance Stoch. 8:311–341, 2004) is proved. Hence, this paper extends the previous convergence result of Gökay and Soner (Math Finance 22:250–276, 2012) to the general non-Markovian case. Moreover, the special case of small transaction costs yields, in the continuous limit, the G-expectation of Peng as earlier proved by Kusuoka (Ann. Appl. Probab. 5:198–221, 1995).     

A BSDE approach to fair bilateral pricing under endogenous collateralization

Nie and Rutkowski (Int. J. Theor. Appl. Finance 18:1550048, 2015; Math. Finance, 2016, to appear) examined fair bilateral pricing in models with funding costs and an exogenously given collateral. The main goal of this work is to extend results from Nie and Rutkowski (Int. J. Theor. Appl. Finance 18:1550048, 2015; Math. Finance, 2016, to appear) to the case of an endogenous margin account depending on the contract’s value for the hedger and/or the counterparty. Comparison theorems for BSDEs from Nie and Rutkowski (Theory Probab. Appl., 2016, forthcoming) are used to derive bounds for unilateral prices and to study the range for fair bilateral prices in a general semimartingale model. The backward stochastic viability property, introduced by Buckdahn et al. (Probab. Theory Relat. Fields 116:485–504, 2000), is employed to examine the bounds for fair bilateral prices for European claims with a negotiated collateral in a diffusion-type model. We also generalize in several respects the option pricing results from Bergman (Rev. Financ. Stud. 8:475–500, 1995), Mercurio (Actuarial Sciences and Quantitative Finance, pp. 65–95, 2015) and Piterbarg (Risk 23(2):97–102, 2010) by considering contracts with cash-flow streams and allowing for idiosyncratic funding costs for risky assets.     

Asymptotic arbitrage with small transaction costs

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ _n on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λ _n -consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λ _n >0 on market n; there does not exist any form of asymptotic arbitrage. In one case, (λ _n ) can even converge to 0, but not too fast.     

Generalized stochastic target problems for pricing and partial hedging under loss constraints��application in optimal book liquidation

We consider a singular version with state constraints of the stochastic target problems studied in Soner and Touzi (SIAM J. Control Optim. 41:404?C424, 2002; J. Eur. Math. Soc. 4:201?C236, 2002) and more recently Bouchard et al. (SIAM J. Control Optim. 48:3123?C3150, 2009), among others. This provides a general framework for the pricing of contingent claims under risk constraints. Our extended version perfectly fits the market models with proportional transaction costs and the order book liquidation issues. Our main result is a direct PDE characterization of the associated pricing function. As an example application, we discuss the valuation of VWAP-guaranteed-type book liquidation contracts, for a general class of risk functions.     

There's more to volatility than volume

It is widely believed that fluctuations in transaction volume, as reflected in the number of transactions and to a lesser extent their size, are the main cause of clustered volatility. Under this view bursts of rapid or slow price diffusion reflect bursts of frequent or less frequent trading, which cause both clustered volatility and heavy tails in price returns. We investigate this hypothesis using tick by tick data from the New York and London Stock Exchanges and show that only a small fraction of volatility fluctuations are explained in this manner. Clustered volatility is still very strong even if price changes are recorded on intervals in which the total transaction volume or number of transactions is held constant. In addition the distribution of price returns conditioned on volume or transaction frequency being held constant is similar to that in real time, making it clear that neither of these are the principal cause of heavy tails in price returns. We analyse recent results of Ane and Geman (2000 Ane, T and Geman, H. 2000. Order flow, transaction clock, and normality of asset returns. J. Finance, 55(5): 2259–2284. [Crossref], [Web of Science ®] , [Google Scholar]: J. Finance, 55, 2259–2284) and Gabaix et al. (2003 Gabaix, X, Gopikrishnan, P, Plerou, V and Stanley, H.E. 2003. A theory of power-law distributions in financial market fluctuations. Nature, 423: 267–270. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]: Nature, 423, 267–270), and discuss the reasons why their conclusions differ from ours. Based on a cross-sectional analysis we show that the long-memory of volatility is dominated by factors other than transaction frequency or total trading volume.     

Optimal dividend policies for a class of growth-restricted diffusion processes under transaction costs and solvency constraints

In this paper, we consider a company whose surplus follows a rather general diffusion process and whose objective is to maximize expected discounted dividend payments. With each dividend payment, there are transaction costs and taxes, and it is shown in Paulsen (Adv. Appl. Probab. 39:669?C689, 2007) that under some reasonable assumptions, optimality is achieved by using a lump sum dividend barrier strategy, i.e., there is an upper barrier $\bar{u}^{*}$ and a lower barrier $\underline{u}^{*}$ so that whenever the surplus reaches $\bar{u}^{*}$ , it is reduced to $\underline{u}^{*}$ through a dividend payment. However, these optimal barriers may be unacceptably low from a solvency point of view. It is argued that, in that case, one should still look for a barrier strategy, but with barriers that satisfy a given constraint. We propose a solvency constraint similar to that in Paulsen (Finance Stoch. 4:457?C474, 2003); whenever dividends are paid out, the probability of ruin within a fixed time T and with the same strategy in the future should not exceed a predetermined level ??. It is shown how optimality can be achieved under this constraint, and numerical examples are given.     

Price discovery in the presence of boundedly rational agents

In this paper we propose a sequential model of security trading which, compared to existing models, is extended along the notions of (Simon, H.A., A behavioral model of rational choice. Quart. J. Econ., 1955 Simon, HA. 1955. A behavioral model of rational choice. Quart. J. Econ., 64: 99–118.  [Google Scholar], 64, 99–118; Rubinstein, A., Modeling Bounded Rationality, Zeuthen Lecture Book Series, 1998 (MIT Press: Cambridge, MA), and Odean, T., Do investors trade too much? Am. Econ. Rev., 1999, 89(5), 1279–1298) by adding boundedly rational traders. Our results indicate that both momentum and mean-reversion in asset prices can be attributed to the presence of agents who are subject to systematic errors in the process of forecasting the liquidation value of a risky security. The length of the momentum period is inversely related to both the amount of information-based trading in the market and the rate at which asset specific information is learned by boundedly rational agents. Furthermore, the model allows explicitly to establish a link between the component of the bid–ask spread that can be explained by bounded rationality and both momentum and reversal.     

Leveraged Lévy processes as models for stock prices

Adopting a constant elasticity of variance formulation in the context of a general Lévy process as the driving uncertainty we show that the presence of the leverage effect? ?One explanation of the documented negative relation between market volatilities and the level of asset prices (the ‘smile’ or ‘skew’), we term the ‘leverage effect’, argues that this negative relation reflects greater risk taking by the management, induced by a fall in the asset price, with a view of maximizing the option value of equity shareholders. in this form has the implication that asset price processes satisfy a scaling hypothesis. We develop forward partial integro-differential equations under a general Markovian setup, and show in two examples (both continuous and pure-jump Lévy) how to use them for option pricing when stock prices follow our leveraged Lévy processes. Using calibrated models we then show an example of simulation-based pricing and report on the adequacy of using leveraged Lévy models to value equity structured products.     

Do financial returns have finite or infinite variance? A paradox and an explanation

One of the major points of contention in studying and modelling financial returns is whether or not the variance of the returns is finite or infinite (sometimes referred to as the Bachelier–Samuelson Gaussian world versus the Mandelbrot stable world). A different formulation of the question asks how heavy the tails of the financial returns are. The available empirical evidence can be, and has been, interpreted in more than one way. The apparent paradox, which has puzzled many a researcher, is that the tails appear to become less heavy for less frequent (e.g. monthly) returns than for more frequent (e.g. daily) returns, a phenomenon not easily explainable by the standard models. Inspired by the prelimit theorems of Klebanov, Rachev and Szekely (1999 Klebanov, L, Rachev, S and Szekely, G. 1999. Pre-limit theorems and their applications. Acta Applicandae Mathematicae, 58: 159–174.  [Google Scholar]) and Klebanov, Rachev and Safarian (2000 Klebanov, L, Rachev, S and Safarian, M. 2000. Local prelimit theorems and their applications to finance. Appl. Math. Lett., 13: 73–78.  [Google Scholar]), we provide an explanation of this paradox. We show that, for financial returns, a natural family of models are those with tempered heavy tails. These models can generate observations that appear heavy tailed for a wide range of aggregation levels before becoming clearly light tailed at even larger aggregation scales. Important examples demonstrate the existence of a natural scale associated with the model at which such an apparent shift in the tails occurs.     

Political influences on the costs of banking crises in emerging market economies: testing the U-shaped veto player hypothesis

While there has been considerable research on the consequences of financial crises, there has been little empirical research on the possible effects of the role of domestic political institutions that influence a government's ability to implement crisis management policies. This paper investigates the impact of domestic institutions, characterized by a U-shaped veto player framework, on the output costs of banking crises. The analysis extends MacIntyre's qualitative study (2001 MacIntyre, Andrew. 2001. Institutions and investors: The politics of the economic crisis in Southeast Asia. International Organization, 55(1): 81–122. [Crossref], [Web of Science ®] , [Google Scholar]) of the relationship between veto players and policy risks in the Asian financial crises. For a large sample of emerging market economies, we find support for McIntyre's hypotheses that both too few and too many veto players are associated with greater costs of banking crises.     

Turbo warrants under stochastic volatility

Turbo warrants have experienced huge growth since they first appeared in late 2001. In some European countries, buying and selling turbo warrants constitutes 50% of all derivative trading nowadays. In Asia, the Hong Kong Exchange and Clearing Limited (HKEx) introduced the callable bull/bear contracts, which are essentially turbo warrants, to the market in 2006. Turbo warrants are special types of barrier options in which the rebate is calculated as another exotic option. It is commonly believed that turbo warrants are less sensitive to the change in volatility of the underlying asset. Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]) has considered the pricing of turbo warrants under the Black–Scholes model. However, the pricing and characteristics of turbo warrants under stochastic volatility are not known. This paper investigates the valuation of turbo warrants considered by Eriksson (2005 Eriksson, J. 2005. Explicit pricing formulas forturbo warrants. Uppsala Dissertation in Mathematics, 45 [Google Scholar]), but extends the analysis to the CEV, the fast mean-reverting stochastic volatility and the two time-scale volatility models. We obtain analytical solutions for turbo warrants under the aforementioned models. This enables us to examine the sensitivity of turbo warrants to the implied volatility surface.     

Industry cost of equity capital: European evidence for multifactor models

We estimate the costs of equity capital for 117 industries from 16 European countries employing the CAPM and 8 multifactor asset pricing models as well as a variety of different econometric techniques. In doing so, we extend previous research on cost of equity estimation in mainly two ways. First, our study involves European instead of US or UK industries, which are investigated in previous research, and we find that cost of equity estimates obtained from the CAPM or multifactor asset pricing models are as imprecise for European industries as for US and UK industries. Second, in addition to the CAPM, the Fama and French [1993 Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56. doi: 10.1016/0304-405X(93)90023-5[Crossref], [Web of Science ®] , [Google Scholar]. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56] three-factor model, and the Carhart [1997 Carhart, Mark M. 1997. “On Persistence in Mutual Fund Performance.” The Journal of Finance 52 (1): 57–82. doi: 10.1111/j.1540-6261.1997.tb03808.x[Crossref], [Web of Science ®] , [Google Scholar]. “On Persistence in Mutual Fund Performance.” The Journal of Finance 52 (1): 57–82] four-factor model, which are usually employed, our study includes six multifactor models that have not yet been examined on their ability to provide precise estimates of the costs of equity: the five-factor model of Fama and French [1993 Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56. doi: 10.1016/0304-405X(93)90023-5[Crossref], [Web of Science ®] , [Google Scholar]. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33: 3–56] as well as the multifactor models of Pástor and Stambaugh [2003 Pástor, Lubos, and Robert F. Stambaugh. 2003. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy 111 (3): 642–685. doi: 10.1086/374184[Crossref], [Web of Science ®] , [Google Scholar]. “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy 111 (3): 642–685]; Campbell and Vuolteenaho [2004 Campbell, John Y., and Tuomo Vuolteenaho. 2004. “Bad Beta, Good Beta.” American Economic Review 94 (5): 1249–1275. doi: 10.1257/0002828043052240[Crossref], [Web of Science ®] , [Google Scholar]. “Bad Beta, Good Beta.” American Economic Review 94 (5): 1249–1275]; Hahn and Lee [2006 Hahn, Jaehoon, and Hangyong Lee. 2006. “Yield Spreads as Alternative Risk Factors for Size and Book-To-Market.” Journal of Financial &; Quantitative Analysis 41 (2): 245–269. doi: 10.1017/S0022109000002052[Crossref], [Web of Science ®] , [Google Scholar]. “Yield Spreads as Alternative Risk Factors for Size and Book-To-Market.” Journal of Financial &; Quantitative Analysis 41 (2): 245–269]; Petkova [2006 Petkova, Ralitsa. 2006. “Do the Fama–French Factors Proxy for Innovations in Predictive Variables?” The Journal of Finance 61 (2): 581–612. doi: 10.1111/j.1540-6261.2006.00849.x[Crossref], [Web of Science ®] , [Google Scholar]. “Do the Fama–French Factors Proxy for Innovations in Predictive Variables?” The Journal of Finance 61 (2): 581–612]; and Koijen, Lustig, and van Nieuwerburgh [2010 Koijen, Ralph S., Hanno N. Lustig, and Stijn G. van Nieuwerburgh. 2010. “The Cross-Section and Time-Series of Stock and Bond Returns.” Working Paper, University of Chicago, University of California at Los Angeles, New York University. [Google Scholar]. “The Cross-Section and Time-Series of Stock and Bond Returns.” Working Paper, University of Chicago, University of California at Los Angeles, New York University]. Our results suggest that these models provide even more imprecise cost of equity estimates. One main reason for these inaccurate estimates is the large temporal variation of the risk loadings on the non-traded factors in these models.     

Variance matters (in stochastic dividend discount models)

Stochastic dividend discount models (Hurley and Johnson in Financ Anal J 50–54. http://?www.?jstor.?org/?stable/?4479761, 1994, J Portf Manag 27–31. doi:10.?3905/?jpm.?1998.?409658, 1998; Yao in J Portf Manag 99–103. doi:10.?3905/?jpm.?1997.?409618, 1997) present expressions for the expected value of stock prices when future dividends, periodically received by shareholders as a reward for their risky investment, evolve through time in a Markovian setting by the means of a discretely distributed random rate of growth. Such result extends and makes more flexible the classical textbook formula for stock prices known as Gordon model. This paper introduces a closed-form expression for the variance of random stock prices, determines how their variance is affected by the variance of the dividend rate of growth, establishes that, in this framework, the dividend process is non-stationary, and perform a simple econometric analysis applying real market data.     

Nonlinear dynamics in economics and finance and unit root testing

The recent financial crisis exposed the inability of traditional theoretical and empirical models to parsimoniously capture the rich dynamics of the economic environment. This has stimulated the interest of both academics and practitioners in the development and application of more sophisticated models. By allowing for the presence of nonlinearities, complex dynamics, multiple equilibria, structural breaks and spurious trends, these latter models resemble more closely the properties of economic and financial time series. In this article, we illustrate the flexibility of a family of econometric models, namely the exponential smooth transition autoregressive (ESTAR), to encompass several of the above characteristics. We then re-assess the power of the ESTAR unit root test developed by Kapetanios, Shin and Snell ((2003) Kapetanios, G., Shin, Y. and Snell, A. 2003. Testing for a unit root in the nonlinear STAR framework. Journal of Econometrics, 112(2): 359–79. (doi:10.1016/S0304-4076(02)00202-6)[Crossref], [Web of Science ®] , [Google Scholar]) in the presence of nuisance parameters typically encountered in the literature and compare its performance with that of the augmented Dickey-Fuller and the Enders and Granger ((1998) Enders, W. and Granger, C. W.J. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics, 16(3): 304–11. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) tests. Our results show the lack of dominance of any particular test and that the power is not independent to priors about the nuisance parameters. Finally, we examine several asset price deviations from fundamentals and one hyper-inflation series and find contradictory results between the nonlinear fitted models and unit root tests. The findings highlight that new testing procedures with higher power are desirable in order to shed light on the behavior of financial and economic series.     

Physiological Age,Health Costs,and Their Interrelation

We demonstrate the impact of an observable health-related quantity on the evaluation of individual physiological ages by extending the phase-type aging model proposed by Lin and Liu in 2007 Lin, X. S., and X. Liu. 2007. Markov Aging Process and Phase-Type Law of Mortality. North American Actuarial Journal 11: 92–109.[Taylor &; Francis Online] , [Google Scholar]. In their model, an individual of a given calendar age has a determinable distribution of his or her physiological age. In our article, we use observable information to refine this distribution, thereby better connecting physiological age with the health of the individual. We illustrate our model using health cost data, and we investigate the impact of an observed health cost on the distribution of an individual’s physiological age. We also explore the impact on the expected present value of future health costs.     

q-Optimal Martingale Measures for Discrete Time Models

We focus on a backward induction of the q-optimal martingale measure for discrete-time models, where 1  <  q  <  ∞. As for the bounded asset price process case, the same backward induction has been obtained by Grandits (Bernoulli, 5:225–247, 1999). To remove the boundedness, we shall discuss a sufficient condition under which there exists a signed martingale measure whose density is in the ${\mathcal {L}^q}$ -space, which topic is our second aim.     

On the game interpretation of a shadow price process in utility maximization problems under transaction costs

To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S ^?, lying in the bid/ask price interval $[\underline{S}, \overline{S}]$ . Such a process S ^? is called a shadow price if it provides the same optimal utility value as in the original model with bid-ask spread. We call S ^? a generalized shadow price if the above property is true for the relaxed utility function in the frictionless model. This relaxation is defined as the lower semicontinuous envelope of the original utility, considered as a function on the set $[\underline{S}, \overline{S}]$ , equipped with some natural weak topology. We prove the existence of a generalized shadow price under rather weak assumptions and mark its relation to a saddle point of the trader/market zero-sum game, determined by the relaxed utility function. The relation of the notion of a shadow price to its generalization is illustrated by several examples. Also, we briefly discuss the interpretation of shadow prices via Lagrange duality.     

An Associative Approach to Risk Perception: Measuring the Effects of Risk Communications Directly and Indirectly<1?tpb=-6pt?>

Risk perception is often measured by a direct method, e.g., a questionnaire. This mainly reveals the deliberate evaluation of a risk (a so‐called secondary evaluative process), whereas risk perception can also be based on a first, spontaneous reaction (a primary evaluative process). An indirect test such as the Extrinsic Affective Simon Task (EAST, De Houwer, 2003 De Houwer, J. 2003. The Extrinsic Affective Simon Task. Experimental Psychology, 50: 77–85. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) may be needed to reveal this first, spontaneous reaction. In this study, a questionnaire and an EAST measured the effects of varying risk communications (high risk, low risk or control article), about high‐voltage power lines. The results of the EAST showed that the respondents associated power lines stronger with unhealthy than with healthy. However, the questionnaire results did not seem to indicate that the respondents considered power lines as risky. The EAST did not reveal an effect of article variation on the associations of power lines with (un)healthy. Conversely, the questionnaire results showed that article variation influenced the secondary evaluative process. Further, our findings demonstrated that the direct and indirect measures were unrelated. An indirect test may complement a direct test to get an overall picture of how people evaluate risks.