The Quality Delivery Option in Treasury Bond Futures Contracts

This paper uses three methods to estimate quality option values for CBOT Treasury bond futures contracts. It presents evidence regarding: (1) payoffs from exercising this option at delivery, (2) estimates from a T-bond futures pricing model that incorporates this option, and (3) estimates obtained from an exchange option pricing formula. The results indicate that this option is worth considerably less than reported by Kane and Marcus (1986a) . For example, payoffs obtained by switching from the bond cheapest to deliver three months prior to delivery to the one cheapest at time of delivery average less than 0.30 percentage points of par.     

Invisible Parameters in Option Prices

This paper characterizes contingent claim formulas that are independent of parameters governing the probability distribution of asset returns. While these parameters may affect stock, bond, and option values, they are “invisible” because they do not appear in the option formulas. For example, the Black-Scholes ( 1973 ) formula is independent of the mean of the stock return. This paper presents a new formula based on the log-negative-binomial distribution. In analogy with Cox, Ross, and Rubinstein's ( 1979 ) log-binomial formula, the log-negative-binomial option price does not depend on the jump probability. This paper also presents a new formula based on the log-gamma distribution. In this formula, the option price does not depend on the scale of the stock return, but does depend on the mean of the stock return. This paper extends the log-gamma formula to continuous time by defining a gamma process. The gamma process is a jump process with independent increments that generalizes the Wiener process. Unlike the Poisson process, the gamma process can instantaneously jump to a continuum of values. Hence, it is fundamentally “unhedgeable.” If the gamma process jumps upward, then stock returns are positively skewed, and if the gamma process jumps downward, then stock returns are negatively skewed. The gamma process has one more parameter than a Wiener process; this parameter controls the jump intensity and skewness of the process. The skewness of the log-gamma process generates strike biases in options. In contrast to the results of diffusion models, these biases increase for short maturity options. Thus, the log-gamma model produces a parsimonious option-pricing formula that is consistent with empirical biases in the Black-Scholes formula.     

Static-arbitrage upper bounds for the prices of basket options

In this paper we investigate the possible values of basket options. Instead of postulating a model and pricing the basket option using that model, we consider the set of all models which are consistent with the observed prices of vanilla options, and, within this class, find the model for which the price of the basket option is largest. This price is an upper bound on the prices of the basket option which are consistent with no-arbitrage. In the absence of additional assumptions it is the lowest upper bound on the price of the basket option. Associated with the bound is a simple super-replicating strategy involving trading in the individual calls.     

Development Value: A Real Options Approach Using Empirical Data

This paper combines an empirical methodology and a theoretical options approach to determine the real option values of development and delay for vacant parcels of land in the City of Chicago. A theoretical options model provides an option price that incorporates future uncertainty. The data allow for disaggregation down to specific land use categories and results show option values vary across zoning categories and within zoning categories for specific land uses.     

A fast Fourier transform technique for pricing American options under stochastic volatility

This paper develops a non-finite-difference-based method of American option pricing under stochastic volatility by extending the Geske-Johnson compound option scheme. The characteristic function of the underlying state vector is inverted to obtain the vector’s density using a kernel-smoothed fast Fourier transform technique. The method produces option values that are closely in line with the values obtained by finite-difference schemes. It also performs well in an empirical application with traded S&P 100 index options. The method is especially well suited to price a set of options with different strikes on the same underlying asset, which is a task often encountered by practitioners.     

On the range of options prices

In this paper we consider the valuation of an option with time to expiration and pay-off function which is a convex function (as is a European call option), and constant interest rate , in the case where the underlying model for stock prices is a purely discontinuous process (hence typically the model is incomplete). The main result is that, for “most” such models, the range of the values of the option, using all possible equivalent martingale measures for the valuation, is the interval , this interval being the biggest interval in which the values must lie, whatever model is used.     

Efficiency tests with overlapping data: an application to the currency options market

This paper presents the results of an empirical study into the efficiency of the currency options market. The methodology derives from a simple model often applied to the spot and forward markets for foreign exchange. It relates the historic volatility of the underlying asset to the implied volatility of an option on the underlying at a specified prior time and then proceeds to test obvious hypotheses about the values of the coefficients. The study uses panel regression to address the problem of overlapping data which leads to dependence between observations. It also uses volatility data directly quoted on the market in order to avoid the biases which may occur when ‘backing out’ volatility from specific option pricing models. In general, the evidence rejects the hypothesis that the currency option market is efficient. This suggests that implied volatility is not the best predictor of future exchange rate volatility and should not be used without modification: the models presented in this paper could be a way of producing revised forecasts.     

Valuation of American partial barrier options

This paper concerns barrier options of American type where the underlying asset price is monitored for barrier hits during a part of the option’s lifetime. Analytic valuation formulas of the American partial barrier options are provided as the finite sum of bivariate normal distribution functions. This approximation method is based on barrier options along with constant early exercise policies. In addition, numerical results are given to show the accuracy of the approximating price. Our explicit formulas provide a very tight lower bound for the option values, and moreover, this method is superior in speed and its simplicity.     

Dispersion trading: Empirical evidence from U.S. options markets

This paper develops empirical evidence on the viability of a form of volatility trading known as “dispersion trading.” The results shed light on the efficiency with which U.S. options markets price volatility.Using end-of-day implied volatilities extracted from equity option prices for the stocks that comprise the S&P 500, the implied volatility of the S&P 500 is computed using a modification of the Markowitz variance equation. This Markowitz-implied volatility is then compared to the implied volatility of the S&P 500 extracted directly from index options on the S&P 500. These contemporaneous measures of implied volatility are then examined for exploitable discrepancies both with and without transaction costs. The study covers the period October 31, 2005 through November 1, 2007.It is shown that, from a trader's perspective, index option implied volatility tended to be more often “rich” and component volatilities tended to be more often “cheap.” Nevertheless, there were times when the opposite was true; suggesting that potential dispersion trades can run in either direction.     

Option pricing under a stressed-beta model

Empirical studies have concluded that stochastic volatility is an important component of option prices. We introduce a regime-switching mechanism into a continuous-time Capital Asset Pricing Model which naturally induces stochastic volatility in the asset price. Under this Stressed-Beta model, the mechanism is relatively simple: the slope coefficient—which measures asset returns relative to market returns—switches between two values, depending on the market being above or below a given level. After specifying the model, we use it to price European options on the asset. Interestingly, these option prices are given explicitly as integrals with respect to known densities. We find that the model is able to produce a volatility skew, which is a prominent feature in option markets. This opens the possibility of forward-looking calibration of the slope coefficients, using option data, as illustrated in the paper.     

Real options under a double exponential jump-diffusion model with regime switching and partial information

We consider the irreversible investment in a project which generates a cash flow following a double exponential jump-diffusion process and its expected return is governed by a continuous-time two-state Markov chain. If the expected return is observable, we present explicit expressions for the pricing and timing of the option to invest. With partial information, i.e. if the expected return is unobservable, we provide an explicit project value and an integral-differential equation for the pricing and timing of the option. We provide a method to measure the information value, i.e. the difference between the option values under the two different cases. We present numerical solutions by finite difference methods. By numerical analysis, we find that: (i) the higher the jump intensity, the later the option to invest is exercised, but its effect on the option value is ambiguous; (ii) the option value increases with the belief in a boom economy; (iii) if investors are more uncertain about the economic environment, information is more valuable; (iv) the more likely the transition from boom to recession, the lower the value of the option; (v) the bigger the dispersion of the expected return, the higher the information value; (vi) a higher cash flow volatility induces a lower information value.     

A Fuzzy Set Approach for Generalized CRR Model: An Empirical Analysis of S&;P 500 Index Options

This paper applies fuzzy set theory to the Cox, Ross and Rubinstein (CRR) model to set up the fuzzy binomial option pricing model (OPM). The model can provide reasonable ranges of option prices, which many investors can use it for arbitrage or hedge. Because of the CRR model can provide only theoretical reference values for a generalized CRR model in this article we use fuzzy volatility and fuzzy riskless interest rate to replace the corresponding crisp values. In the fuzzy binomial OPM, investors can correct their portfolio strategy according to the right and left value of triangular fuzzy number and they can interpret the optimal difference, according to their individual risk preferences. Finally, in this study an empirical analysis of S&P 500 index options is used to find that the fuzzy binomial OPM is much closer to the reality than the generalized CRR model.This project has been supported by NSC 93-2416-H-009-024.JEL Classification:     

Growth through rigidity: An explanation for the rise in CEO pay

The dramatic rise in CEO compensation during the 1990s and early 2000s is a longstanding puzzle. In this paper, we show that much of the rise can be explained by a tendency of firms to grant the same number of options each year. Number-rigidity implies that the grant-date value of option awards will grow with firm equity returns, which were very high on average during the tech boom. Further, other forms of CEO compensation did not adjust to offset the dramatic growth in the value of option pay. Number-rigidity in options can also explain the increased dispersion in pay, the difference in growth between the US and other countries, and the increased correlation between pay and firm-specific equity returns. We present evidence that number-rigidity arose from a lack of sophistication about option valuation that is akin to money illusion. We show that regulatory changes requiring transparent expensing of the grant-date value of options led to a decline in number-rigidity and helps explain why executive pay increased less with equity returns during the housing boom in the mid-2000s.     

Option Replication in Discrete Time with Transaction Costs

Option replication is discussed in a discrete-time framework with transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option pricing model to cover the case of proportional transaction costs. The method proceeds by constructing the appropriate replicating portfolio at each trading interval. Numerical values of these prices are presented for a range of parameter values. The paper derives a simple Black-Scholes type approximation for the option prices with transaction costs and demonstrates numerically that it is quite accurate for plausible parameter values.     

A simple efficient approximation to price basket stock options with volatility smile

This paper develops a new approach to obtain the price and risk sensitivities of basket options which have a volatility smile. Using this approach, the Black–Scholes model and the Stochastic Volatility Inspired model have been used to obtain an approximate analytical pricing formula for basket options with a volatility smile. It is found that our approximate formula is quite accurate by comparing it with Monte Carlo simulations. It is also proved the option value of our approach is consistent with the option value generated by Levy’s and Gentle’s approaches for typical ranges of volatility. Further, we give a theoretical proof that the option values from Levy’s and Gentle’s works are the upper bound and the lower bound, respectively, for our option value. The calibration procedure and a practical example are provided. The main advantage of our approach is that it provides accurate and easily implemented basket option prices with volatility smile and hedge parameters and avoids the need to use time-consuming numerical procedures such as Monte Carlo simulation.     

Impact of volatility estimation method on theoretical option values

The volatility of an asset price measures how uncertain we are about future asset price movements. It is one of the factors affecting option price and the only input into the Black–Scholes model that cannot be directly observed. Thus, estimating volatility properly is vital. Two approaches to calculating volatility are historical and implied volatilities. Using index options listed on the Chicago Board of Options Exchange, this paper focuses on historical volatility. Since numerous methods of estimating volatility may provide different results, this paper assesses the impact of volatility estimation method on theoretical option values.     

The dynamics of mergers and acquisitions

This paper presents a dynamic model of takeovers based on the stock market valuations of merging firms. The model incorporates competition and imperfect information and determines the terms and timing of takeovers by solving option exercise games between bidding and target shareholders. The implications of the model for returns to stockholders are consistent with the available evidence. In addition, the model generates new predictions relating these returns to the drift, volatility and correlation coefficient of the bidder and the target stock returns and to the dispersion of beliefs regarding the benefits of the takeover.     

Pricing and Hedging Discount Bond Options in the Presence of Model Risk

This paper focuses on pricing and hedging options on a zero-coupon bond in a Heath–Jarrow–Morton (1992) framework when the value and/or functional form of forward interest rates volatility is unknown, but is assumed to lie between two fixed values. Due to the link existing between the drift and the diffusion coefficients of the forward rates in the Heath, Jarrow and Morton framework, this is equivalent to hedging and pricing the option when the underlying interest rate model is unknown. We show that a continuous rangeof option prices consistent with no arbitrage exist. This range is bounded by the smallest upper-hedging strategy and the largest lower-hedging strategy prices, which are characterized as the solutions of two non-linear partial differential equations. We also discuss several pricing and hedging illustrations.     

BLACK-SCHOLES vs. KASSOUF OPTION PRICING: AN EMPIRICAL COMPARISON

This paper presents a comparison of the Black-Scholes and Kassouf models for the pricing of options. Graphical presentations of simulated call option prices show the effects of changing the different variables on the prices of options. An empirical study using observed option prices shows that there is little practical difference between the values given by the two models, and that an investment strategy based upon using either of the two models would yield about the same return.     

Dispersion of Financial Analysts' Earnings Forecasts and the (Option Model) Implied Standard Deviations of Stock Returns

This study examines whether the information implied by simultaneous levels of option and stock prices (specifically, the implied standard deviation of returns) reflects other contemporaneously available information. The independent contemporaneous measure considered is the observed dispersion (across several financial analysts), at a point in time, in the forecasts of earnings per share for a given firm. The results indicate that implied standard deviations clearly reflect the contemporaneous dispersion in analysts' forecasts incrementally, i.e., beyond the information contained in the historical time series of returns.