Degree Of Moneyness Research Articles

The pricing of U.S. Treasury floating rate notes

Since January 2014, the U.S. Treasury has been issuing floating rate notes (FRNs). These notes pay quarterly interest based on an average of the constant maturity rates of newly issued three-month T-bills during the quarter. We show how to price such FRNs. We estimate that they have been paying excess interest between 3 and 42 basis points above the implied interest of other Treasury securities. We interpret this fact through the lens of a model where money-like assets differ in their degrees of moneyness. Additional empirical evidence supports this interpretation.

Patterns of 50 ETF Options Implied Volatility in China: On Implied Volatility Functions

The aim of this study is to examine the volatility smile based on the European options on Shanghai stock exchange 50 ETF. The data gives evidence of the existence of a well-known U-shaped implied volatility smile for the SSE 50 ETF options market in China. For those near-month options, the implied volatility smirk is also observed. And the implied volatility remains high for the short maturity and decreases as the maturity increases. The patterns of the implied volatility of SSE 50 ETF options indicate that in-the-money options and out-of-the-money options are more expensive relative to at-the-money options. This makes the use of at-the-money implied volatility for pricing out-of- or in-the-money options questionable. In order to investigate the implied volatility, the regression-based implied volatility functions model is considered employed to study the implied volatility in this study as this method is simple and easy to apply in practice. Several classical implied volatility functions are investigated in this paper to find whether some kind of implied volatility functions could lead to more accurate options pricing values. The potential determinants of implied volatility are the degree of moneyness and days left to expiration. The empirical work has been expressed by means of simple ordinary least squares framework. As the study shows, when valuing options, the results of using volatility functions are mixed. For far-month options, using at-the-money implied volatility performs better than other volatility functions in option valuation. For near-month options, the use of volatility functions can improve the valuation accuracy for deep in-the-money options or deep out-of-the-money options. However, no particular implied volatility function performs very well for options of all moneyness level and time to maturity.

Dynamic Jump Intensities and Risk Premiums in Crude Oil Futures and Options Markets

A tremendous amount of theoretical and empirical research has been devoted to modeling the dynamics of stock returns and applying this knowledge to valuing equity derivatives. The statistical evidence indicates that the returns process exhibits time-varying diffusive volatility and stochastic jumps in returns, and probably in volatility as well. Moreover, the parameters governing this process appear to drift over time. Yet prices for crude oil and other commodities have not been explored nearly as much, although they are volatile, crucially important to the real economy, and have actively traded futures and options. In this article, the authors go a long way toward correcting this lacuna for derivatives based on crude oil. Their approach is at the current frontier for research on equity derivatives, or indeed beyond it since they allow the jump intensity to vary stochastically over time. Their large sample of daily data spans nearly 25 years of crude oil futures and options, including multiple maturities and degrees of moneyness on each date. Bringing information from both the futures and options markets into the estimation allows much greater statistical power and, more importantly, enforces consistency in the modeling of both derivatives and their underlying. This is a significant advance in our understanding of the price dynamics of the most important commodity, and the futures and option contracts that are based on it.

The evolving dynamics of the Australian SPI 200 implied volatility surface

This paper is concerned with the evolutionary behaviour of implied volatility patterns, which identifies vega uncertainty. Using a principal component analysis (PCA), we compare reported results in US and European markets with our findings here for Australian markets. In this way, we seek to establish the degree to which prior findings have “universality” as opposed to being strictly the outcome of a particular market at a particular time. In a broad sense, we are able to reproduce prior findings. But there are differences. Prior studies find that prevailing shocks impact primarily uniformly across options independently of moneyness (a “parallel shift”) with a second effect (a “Z-shaped twist”) that impacts differentially in relation to the option's degree of moneyness. We find that the “parallel shift” can be interpreted as applying primarily to in-the-money (ITM) options and the Z-shaped twist to out-of-the-money (OTM) options. As a result, the overall effects are interpreted in relation to a volatility smile.

Empirical Patterns of Time Value Decay in Options

I conduct and empirical analysis of the pattern of time value decay in listed equity options, considering both call and put options and various degrees of moneyness for both classes of options. I find that empirical patterns differ from model or theory based predictions in important ways. While model-based simulations commonly predict slow decay in time value with rapidly accelerating decay as the option approaches expiry, the empirical results show that time value decay is often very rapid early in the holding period of an option. This result holds regardless of holding period duration (30, 60 and 90 days are considered) and moneyness. Further analysis reveals the differences between empirical results and model-based predictions are largely due to changes in stock price during the holding period, with deviations in the market price of the option from model-based prices being a minor factor. The only options to exhibit rapidly accelerating time value decay are out-the-money calls or puts purchased in low-volatility environments. I discuss the implications of these results for the management of option positions.

Stylized patterns of implied volatility in India: a case study of NSE Nifty options

Purpose – The aim of this study is to examine the “volatility smile” or/and “skew”, term structure and implied volatility surfaces based on those European options written in the standard and poor (S&P) Nifty equity index. The stochastic nature of implied volatility across strike price, time-to-expiration and moneyness violates the core assumption of the Black–Scholes option pricing model. Design/methodology/approach – The potential determinants of implied volatility are the degree of moneyness, time-to-expiration and the liquidity of the strikes. The empirical work has been expressed by means of a simple ordinary least squares (OLS) framework and presents the estimation results according to moneyness, time-to-expiration and liquidity of options. Findings – The options data give evidence of the existence of a classical U-shaped volatility smile for the Indian options market. Indeed, there is some evidence that the “volatility smirk” which pertains to 30-day options and also implied volatility remain higher for the shorter maturity options and decrease as the time-to-expiration increases. The results lead us to believe that in-the-money calls and out-of-the-money puts are of higher volatility than at-the-money options. Conclusion was drawn due to the persistence of the smile in the options market. Practical implications – The practical implication of studying stylized patterns of implied volatility is that it educates the volatility traders about how in-the-money and out-of-the-money options are priced in the options market, and provides an estimate of volatility for the pricing of future options. Originality/value – This study is an extension of previous work. The undertaking has been to examine the case of a more liquid and transparent options market, which is missing from the earlier work. The current study is more relevant because, since 2008, significant changes have been observed in the futures and options market in India.

Relative Option Prices and Risk-Neutral Skew as Predictors of Index Returns

Much real-world research on options has focused on the Black–Scholes implied volatility smile/skew. What causes it? How does it behave? What information does it contain, and can it be used somehow to predict future returns on the underlying asset? Some evidence in the literature suggests that the skew contains a small amount of information about future returns, with a positive skew being a weak signal that the asset’s price will rise the next day. In this article, Ratcliff explores whether and how returns respond to the behavior of the skew, as measured by the implied volatility (IV) difference between an out-of-the-money (OTM) call and an OTM put with the same degree of moneyness.

Apreçamento de opções sobre taxa de câmbio R$/US$ negociadas no Brasil: uma comparação entre os modelos Black e redes neurais artificiais

In this study, a multilayer neural network model was applied to the pricing of R$/USD exchange rate call options traded on the Sao Paulo Securities, Commodities and Futures Exchange (BM&FBovespa) from January 2004 to December 2007. Based on the actual market prices, the performances of a neural network model and the Black model were compared, using the usual error metrics and statistical tests. Overall, the results showed that the artificial intelligence model outperformed the Black model for the different degrees of moneyness.

Money and Liquidity in Financial Markets

We argue that there is a connection between the interbank market for and the broader financial markets, which has its basis in demand for by banks. Tightness in the interbank market for leads banks to engage in what we term liquidity pull-back, which involves selling financial assets either by banks directly or by levered investors. Empirical tests support this hypothesis. While our data covers part of the recent crisis period, our results are not driven by the crisis. Our general point is that money matters in financial markets. Different financial assets have different degrees of moneyness (liquidity) and, as a result, there are systematic cross-sectional variations in trading activity as the price of liquidity, or the level of tightness, in the interbank market fluctuates.

The Downside of High Water Marks: An Empirical Study

Using a large sample of hedge funds, I study the effects of the high water mark (HWM) on fund performance, risk, and fund closure. I find that as funds fall below the HWM, the standard deviation of future returns increases, the future expected Sharpe ratio decreases, and the incidence of fund closure increases. In addition to supporting predictions from models in the literature, these results resonate well with economic intuition: HWM contracts function as if the fund manager holds call options on the fund's returns which have varying degrees of moneyness depending on how far the fund is from the HWM.

The early exercise premia of America put options on stocks

Using the put-call parity, this paper finds that early exercise premia of short-lived American put options on stocks account for a significant portion of put prices. This finding holds even for out-of-the-money put options. The magnitude of the early exercise premia of American put options with no dividend is positvely related to the degree of moneyness, time to maturity of the put option, and the volatility. The magnitude of the early exercise premia of American put options with dividend is positvely related to the degree of moneyness and the risk-free interest rates.

Hedging with a Volatility Term Structure

Because of transaction costs and other execution problems, hedging portfolios are readjusted only periodically, usually once a day. The question is whether the hedge ratio should reflect the instantaneous variance, the average variance over the life of the option as in the Black-Scholes model, or a combination of the two volatility measures. In this article, the authors show that for path-independent options the option value depends only on the average volatility, while the hedge ratio depends also on the path of future volatility. The sensitivity of the hedge ratio to short-term volatility depends on the degree of moneyness of the option. This is shown to be a more serious problem for short-term than for long-term options.

ON THE ST. LOUIS EQUATION AND AN ALTERNATIVE DEFINITION OF THE MONEY SUPPLY

IN THEIR WELL KNOWN and controversial paper, Andersen and Jordan [2] presented evidence that, when responses of GNP to monetary and fiscal actions are analyzed, only money matters. The equation from which these results were derived has since been subjected to much criticism. This criticism has centered mostly on the statistical specification of the St. Louis equation (e.g., [14]) and on the reversecausation argument (e.g., [12]). In perhaps its most popularized form, the St. Louis equation measures monetary actions by employing changes in the narrowly defined money stock (?\M1). Fiscal actions are measured by changes in high employment federal expenditures (AE). In addition, statistical constraints are imposed upon the equation for estimation purposes. These constraints are: 1) each independent variable has the same lag length, 2) the distributed lag weights are estimated by a fourth degree polynomial by the Almon technique with both endpoints constrained to zero. Schmidt and Waud [14] show that if the statistical constraints are removed, estimation of the St. Louis equation indicates that money matters, but so do fiscal actions. Lombra and Torto [12] demonstrate that, if the variable employed to measure monetary actions is adjusted to account for the conclusion derived from the St. Louis equation is that money still matters, but again, so do fiscal actions. In spite of these criticisms, the St. Louis equation continues to be used in its original form (e.g., [4]). The purpose of this paper is to show that, even if 1) the Andersen-Jordan constraints are imposed upon the equation, and 2) the monetary variable is not adjusted for reverse-causation, estimation of the St. Louis equation with a weighted aggregate money stock variable leads to conclusions different from those discovered by Andersen and Jordan. The money stock variable considered in this paper, arbitrarily called Mw, is derived and more fully explained in a recent paper by the author [9]. MW is a weighted average of six financial assets and is an attempt to take into account Gurley's suggestion that assets be weighted according to their degree of moneyness in determining a money stock.' Moreover, in comparison with both the weighted average case and the case of combinations of unweighted sums of the component assets, it was found that MW satisfies the Friedman-Meiselman dual criteria for

A FACTOR ANALYTIC APPROACH TO AN EMPIRICAL DEFINITION OF MONEY

IN RECENT YEARS, several attempts have been made to develop an empirical definition of money. Not only have different methodologies been employed in arriving at the empirical definitions of money, but the definitions vary widely from study to study. Friedman and Meiselman [6] define money to be that set of financial assets which best explains nominal income. Friedman and Meiselman [6, p. 181] employ two criteria in determining the set of assets which defines the money supply. The first criterion is that the sum of the assets should have the highest correlation with income. The second criterion is that the sum of the assets should have a higher correlation with income than any of the components taken separately. Using these criteria, Friedman and Meiselman conclude that a proper empirical definition of money is the sum of currency, demand deposits, and time deposits at commercial banks. Using the same dual criteria, Timberlake and Fortson [13] argue that time deposits have insignificant explanatory power in predicting income, and Kaufman [10] argues that the definition of money changes depending upon whether financial assets are related to income in preceding, concurrent, or later periods. Another approach to defining money empirically is the employment of elasticities of substitution among financial assets [3], [5]. For example, Chetty [3, p. 278] estimates elasticities of substitution and uses these elasticities to take into account Gurley's [7] suggestion that financial assets be weighted by their corresponding degree of moneyness in defining the money supply. Chetty concludes that the money supply should be a weighted sum of currency, demand desposits, time deposits, deposits in mutual savings banks, and liabilities of savings and loan associations. In this paper, a methodological and statistical approach different from the studies previously cited is employed. The analysis involves a twostage procedure. In the first stage, a set of financial assets is considered simultaneously to determine relationships among the assets within the set. The dimension of the set of assets is then reduced by the multivariate statistical technique of factor analysis. In the second stage of the analysis, the Friedman-Meiselman dual criteria are applied to the factor analytic results to determine an empirical definition of money. It will be seen that the money supply is defined to be a weighted arithmetic average of the assets considered. The factor analysis model is presented in section I, and estimated results are presented in section II of this paper. In