arXiv subjects

Svetlozar T. Rachev

Publications and source records attributed to Svetlozar T. Rachev.

52 records · Page 3Linked to original sources

arXiv2022

ESG-Valued Portfolio Optimization and Dynamic Asset Pricing

ESG ratings provide a quantitative measure for socially responsible investment. We present a unified framework for incorporating numeric ESG ratings into dynamic pricing theory. Specifically, we introduce an ESG-valued return that is a linearly constrained transformation of financial return and ESG score. This leads to a more complex portfolio optimization problem in a space governed by reward, risk and ESG score. The framework preserves the traditional risk aversion parameter and introduces an ESG affinity parameter. We apply this framework to develop ESG-valued: portfolio optimization; capital market line; risk measures; option pricing; and the computation of shadow riskless rates.

q-fin.PM↗

arXiv2021

Market Complete Option Valuation using a Jarrow-Rudd Pricing Tree with Skewness and Kurtosis

Applying the Cherny-Shiryaev-Yor invariance principle, we introduce a generalized Jarrow-Rudd (GJR) option pricing model with uncertainty driven by a skew random walk. The GJR pricing tree exhibits skewness and kurtosis in both the natural and risk-neutral world. We construct implied surfaces for the parameters determining the GJR tree. Motivated by Merton's pricing tree incorporating transaction costs, we extend the GJR pricing model to include a hedging cost. We demonstrate ways to fit the GJR pricing model to a market driver that influences the price dynamics of the underlying asset. We supplement our findings with numerical examples.

q-fin.MF↗

arXiv2021

Global and Tail Dependence: A Differential Geometry Approach

Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant conditional probabilities, and do not provide a complete framework in which to compare extreme dependence between two random variables. In fact, for many important classes of bivariate distributions, these coefficients take on non-informative boundary values. We propose a new approach by first considering global measures based on the surface area of the conditional cumulative probability in copula space, normalized with respect to departures from independence and scaled by the difference between the two boundary copulas of co-monotonicity and counter-monotonicity. The measures could be approached by cumulating probability on either the lower left or upper right domain of the copula space, and offer the novel perspective of being able to differentiate asymmetric dependence with respect to direction of conditioning. The resulting TDCs produce a smoother and more refined taxonomy of tail dependence. The empirical performance of the measures is examined in a simulated data context, and illustrated through a case study examining tail dependence between stock indices.

stat.AP↗

arXiv2020

Option Pricing Incorporating Factor Dynamics in Complete Markets

Using the Donsker-Prokhorov invariance principle we extend the Kim-Stoyanov-Rachev-Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny-Shiryaev-Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete markets where the stock price dynamics depends on the log-return dynamics of a market influencing factor. In the discrete case, we extend the results of this new approach to a financial market with informed traders employing a statistical arbitrage strategy involving trading of forward contracts. Our findings are illustrated with numerical examples employing US financial market data. Our work provides further support for the conclusion that any option pricing model must preserve valuable information on the instantaneous mean log-return, the probability of the stock's upturn movement (per trading interval), and other market microstructure features.

q-fin.MF↗

arXiv2020

Option Pricing in Markets with Informed Traders

The objective of this paper is to introduce the theory of option pricing for markets with informed traders within the framework of dynamic asset pricing theory. We introduce new models for option pricing for informed traders in complete markets where we consider traders with information on the stock price direction and stock return mean. The Black-Scholes-Merton option pricing theory is extended for markets with informed traders, where price processes are following continuous-diffusions. By doing so, the discontinuity puzzle in option pricing is resolved. Using market option data, we estimate the implied surface of the probability for a stock upturn, the implied mean stock return surface, and implied trader information intensity surface.

q-fin.MF↗

arXiv2020

Option Pricing with Mixed Levy Subordinated Price Process and Implied Probability Weighting Function

It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this paper, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method of subordination which has been proposed in the literature by including business (intrinsic, market) time. We define a mixed Levy subordinated model by adding a single subordinated Levy process to the well-known log-normal model, resulting in a new log-price process. We apply the proposed models to study the behavioral finance notion of "greed and fear" disposition from the perspective of rational dynamic asset pricing theory. The greedy or fearful disposition of option traders is studied using the shape of the probability weighting function. We then derive the implied probability weighting function for the fear and greed deposition of option traders in comparison to spot traders. Our result shows the diminishing sensitivity of option traders. Diminishing sensitivity results in option traders overweighting the probability of big losses in comparison to spot traders.

q-fin.MF↗

arXiv2020

Equity Premium Puzzle or Faulty Economic Modelling?

In this paper, we revisit the equity premium puzzle reported in 1985 by Mehra and Prescott. We show that the large equity premium that they report can be explained by choosing a more appropriate distribution for the return data. We demonstrate that the high-risk aversion value observed by Mehra and Prescott may be attributable to the problem of fitting a proper distribution to the historical returns and partly caused by poorly fitting the tail of the return distribution. We describe a new distribution that better fits the return distribution and when used to describe historical returns can explain the large equity risk premium and thereby explains the puzzle.

econ.GN↗

arXiv2019

A Rational Finance Explanation of the Stock Predictability Puzzle

In this paper, we address one of the main puzzles in finance observed in the stock market by proponents of behavioral finance: the stock predictability puzzle. We offer a statistical model within the context of rational finance which can be used without relying on behavioral finance assumptions to model the predictability of stock returns. We incorporate the predictability of stock returns into the well-known Black-Scholes option pricing formula. Empirically, we analyze the option and spot trader's market predictability of stock prices by defining a forward-looking measure which we call "implied excess predictability". The empirical results indicate the effect of option trader's predictability of stock returns on the price of stock options is an increasing function of moneyness, while this effect is decreasing for spot traders. These empirical results indicate potential asymmetric predictability of stock prices by spot and option traders. We show in pricing options with the strike price significantly higher or lower than the stock price, the predictability of the underlying stock's return should be incorporated into the option pricing formula. In pricing options that have moneyness close to one, stock return predictability is not incorporated into the option pricing model because stock return predictability is the same for both types of traders. In other words, spot traders and option traders are equally informed about the future value of the stock market in this case. Comparing different volatility measures, we find that the difference between implied and realized variances or variance risk premium can potentially be used as a stock return predictor.

q-fin.MF↗

arXiv2019

A New Set of Financial Instruments

In complete markets, there are risky assets and a riskless asset. It is assumed that the riskless asset and the risky asset are traded continuously in time and that the market is frictionless. In this paper, we propose a new method for hedging derivatives assuming that a hedger should not always rely on trading existing assets that are used to form a linear portfolio comprised of the risky asset, the riskless asset, and standard derivatives, but rather should design a set of specific, most-suited financial instruments for the hedging problem. We introduce a sequence of new financial instruments best suited for hedging jump-diffusion and stochastic volatility market models. The new instruments we introduce are perpetual derivatives. More specifically, they are options with perpetual maturities. In a financial market where perpetual derivatives are introduced, there is a new set of partial and partial-integro differential equations for pricing derivatives. Our analysis demonstrates that the set of new financial instruments together with a risk measure called the tail-loss ratio measure defined by the new instrument's return series can be potentially used as an early warning system for a market crash.

q-fin.PR↗

arXiv2019

Modelling Crypto Asset Price Dynamics, Optimal Crypto Portfolio, and Crypto Option Valuation

Despite being described as a medium of exchange, cryptocurrencies do not have the typical attributes of a medium of exchange. Consequently, cryptocurrencies are more appropriately described as crypto assets. A common investment attribute shared by the more than 2,500 crypto assets is that they are highly volatile. An investor interested in reducing price volatility of a portfolio of crypto assets can do so by constructing an optimal portfolio through standard optimization techniques that minimize tail risk. Because crypto assets are not backed by any real assets, forming a hedge to reduce the risk contribution of a single crypto asset can only be done with another set of similar assets (i.e., a set of other crypto assets). A major finding of this paper is that crypto portfolios constructed via optimizations that minimize variance and Conditional Value at Risk outperform a major stock market index (the S$\&$P 500). As of this writing, options in which the underlying is a crypto asset index are not traded, one of the reasons being that the academic literature has not formulated an acceptable fair pricing model. We offer a fair valuation model for crypto asset options based on a dynamic pricing model for the underlying crypto assets. The model was carefully backtested and therefore offers a reliable model for the underlying crypto assets in the natural world. We then obtain the valuation of crypto options by passing the natural world to the equivalent martingale measure via the Esscher transform. Because of the absence of traded crypto options we could not compare the prices obtained from our valuation model to market prices. Yet, we can claim that if such options on crypto assets are introduced, they should follow closely our theoretical prices after adjusting for market frictions and design feature nuances.

q-fin.RM↗

arXiv2019

Multiple Subordinated Modeling of Asset Returns

Subordination is an often used stochastic process in modeling asset prices. Subordinated Levy price processes and local volatility price processes are now the main tools in modern dynamic asset pricing theory. In this paper, we introduce the theory of multiple internally embedded financial time-clocks motivated by behavioral finance. To be consistent with dynamic asset pricing theory and option pricing, as suggested by behavioral finance, the investors' view is considered by introducing an intrinsic time process which we refer to as a behavioral subordinator. The process is subordinated to the Brownian motion process in the well-known log-normal model, resulting in a new log-price process. The number of embedded subordinations results in a new parameter that must be estimated and this parameter is as important as the mean and variance of asset returns. We describe new distributions, demonstrating how they can be applied to modeling the tail behavior of stock market returns. We apply the proposed models to modeling S&P 500 returns, treating the CBOE Volatility Index as intrinsic time change and the CBOE Volatility-of-Volatility Index as the volatility subordinator. We find that these volatility indexes are not proper time-change subordinators in modeling the returns of the S&P 500.

q-fin.MF↗

arXiv2017

Option pricing for Informed Traders

In this paper we extend the theory of option pricing to take into account and explain the empirical evidence for asset prices such as non-Gaussian returns, long-range dependence, volatility clustering, non-Gaussian copula dependence, as well as theoretical issues such as asymmetric information and the presence of limited arbitrage opportunities

q-fin.MF↗

arXiv2017

Pricing derivatives in Hermite markets

We present a new framework for Hermite fractional financial markets, generalizing the fractional Brownian motion and fractional Rosenblatt markets. Considering pure and mixed Hermite markets, we introduce a strategy-specific arbitrage tax on the rate of transaction volume acceleration of the hedging portfolio as the prices of risky assets change, allowing us to transform Hermite markets with arbitrage opportunities to markets with no arbitrage opportunities within the class of Markov trading strategies.

q-fin.MF↗

arXiv2016

Pricing Derivatives in Hermite Markets

We introduce Hermite fractional financial markets, where market uncertainties are described by multidimensional Hermite motions. Hermite markets include as particular cases financial markets driven by multivariate fractional Brownian motion and multivariate Rosenblatt motion. Conditions for no-arbitrage and market completeness for Hermite markets are derived. Perpetual derivatives, bonds forwards, and futures are priced. The corresponding partial and partial-differential equations are derived.

q-fin.MF↗

arXiv2015

$ν$-Generalized Hyperbolic Distributions

A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these distributions are studied. It seems, that this class may be useful for asset returns modeling.

math.PR↗

arXiv2011

Multivariate heavy-tailed models for Value-at-Risk estimation

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals to have different tail thickness. After a discussion of relevant estimation and simulation issues, we conduct a backtesting study on a set of portfolios containing derivative instruments, using historical US stock price data.

q-fin.RM↗