Real Options Premia Implied from Recent Transactions in the Greek Real Estate Market

This research is the first to examine the empirical predictions of a real option-pricing model on market values from the realty market of a Euro area country, namely Greece. Using a manually collected sample of land and property transaction prices, we demonstrate that, a model which incorporates the option to wait to develop land has explanatory power on observed prices over and above the intrinsic value from a simple discounted cash flow (DCF) approach. Recent land transactions in our sample seem to reflect a premium for the option to wait (‘real option premium’) that can be as high as 26.66%–52.38%, especially in the west and north suburbs of Athens. Estimates of annual volatility for specific properties, as implied by transaction prices, are found to range from 15% to 21%.     

The value of risk in real estate markets

In this article we test the urban asset pricing model of Capozza and Sick (1988) and focus on the empirical dimensions of the effects of risk on urban land prices. The effects of systematic and unsystematic risk are distinguished in the model which incorporates the value of the option to convert land to urban uses into the pricing of urban real estate. We find the value of systematic risk in our Canadian urban areas to be negative and highly statistically significant. We find that approximately 2.5 percent of the value of houses in our sample arises from systematic risk. In our sample, unsystematic risk is a larger proportion of total risk than systematic risk. Therefore, most of the effect of total risk may be ascribed to unsystematic risk. The effect of total risk on land prices is illustrated through the irreversibility premia estimates. These premia vary greatly in size and statistical significance. Thus, the effect of unsystematic risk is highly city specific. In the two regions where the irreversibility premia are statistically significant, it accounts for 22 percent and 53 percent of the average housing price; thus, unsystematic risk can be a very important determinant of housing prices.These results highlight the importance of risk in determining urban land prices. The value of the option to convert land to urban uses imparts considerable value to developed land and must be considered when evaluating interurban area price differences.     

Estimation and pricing under long-memory stochastic volatility

We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein–Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, the reality is that observations can only be collected in discrete time. Using historical stock price information we adapt an interacting particle stochastic filtering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the long-memory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.     

Monitoring Financial Distress in a High-Stress Financial World: The Role of Option Prices as Bank Risk Metrics

The current financial crisis offers a unique opportunity to investigate the leading properties of market indicators in a stressed environment and their usefulness from a banking supervision perspective. One pool of relevant information that has been little explored in the empirical literature is the market for bank’s exchange-traded option contracts. In this paper, we first extract implied volatility indicators from the prices of option contracts on financial firms’ equity. We then examine empirically their ability to predict financial distress by applying survival analysis techniques to a sample of large US financial firms. We find that market indicators extracted from option prices significantly explain the survival time of troubled financial firms and do a better job in predicting financial distress than other time-varying covariates typically included in bank failure models. Overall, both accounting information and option prices contain useful information of subsequent financial problems and, more importantly, their combination produces good forecasts in a high-stress financial world.     

A MULTIFACTOR MODEL OF THE QUALITY OPTION IN TREASURY FUTURES CONTRACTS

The values of quality options in Treasury futures contracts are set relative to the prices of all coupon bonds in their respective deliverable sets. As a result, any model used to value the quality option should set its price relative to the set of observed bond prices. This requirement rules out the use of most simple equilibrium models that represent all bond prices in terms of a finite number of state variables. We use the two-factor Heath-Jarrow-Morton model, which permits claims to be priced relative to observable bond prices, to investigate the potential value of the quality option in Treasury bond and note futures. We show that the quality option has significantly more value in a two-factor interest rate economy than in a single-factor economy, and that ignoring it could lead to significant mispricing.     

On Jumps in Common Stock Prices and Their Impact on Call Option Pricing

The Black-Scholes call option pricing model exhibits systematic empirical biases. The Merton call option pricing model, which explicitly admits jumps in the underlying security return process, may potentially eliminate these biases. We provide statistical evidence consistent with the existence of lognormally distributed jumps in a majority of the daily returns of a sample of NYSE listed common stocks. However, we find no operationally significant differences between the Black-Scholes and Merton model prices of the call options written on the sampled common stocks.     

Mean Reversion and Momentum: Another Look at the Price-Volume Correlation in the Real Estate Market

Based on behavioral finance and economics literature, we construct a theoretical framework in which consumers of newly constructed housing units perceive prices to follow a stochastic mean reversion pattern. Given this belief and the high carrying cost maintained by real estate developers, potential buyers opt to either exercise immediately or defer the purchase. We simulate the model within a real option framework by which we show that the optimal time to wait before exercising a purchase is positively related to the price level; hence, a negative (positive) correlation between transaction volume and price level (yield) emerges. Observing data on housing prices and new construction sales in Israel for the years 1998–2007, we apply an adaptive expectation regression model to test consumers’ belief in both mean reversion and momentum price patterns. The empirical evidence shows that while consumers’ demand pattern is simultaneously consistent with the belief in both momentum and mean reversion processes, the effect of the latter generally dominates. Moreover, while the data does not allow for testing the volume and price-level correlation, it does provide support to the positive volume-price yield correlation.     

On Valuing American Call Options with the Black-Scholes European Formula

Empirical papers on option pricing have uncovered systematic differences between market prices and values produced by the Black-Scholes European formula. Such “biases” have been found related to the exercise price, the time to maturity, and the variance. We argue here that the American option variant of the Black-Scholes formula has the potential to explain the first two biases and may partly explain the third. It can also be used to understand the empirical finding that the striking price bias reverses itself in different sample periods. The expected form of the striking price bias is explained in detail and is shown to be closely related to past empirical findings.     

Continuous rainbow options on commodity outputs: what is the real value of switching facilities?

We develop real rainbow option models to value an operating asset with the flexibility to choose between two commodity outputs. We provide a quasi-analytical solution and a numerical lattice solution to a model with continuous switching opportunities between two commodity outputs, taking into account operating and switching costs. The models are applied to an illustrative case, demonstrating that the quasi-analytical solution and the lattice approach provide near identical results for the asset valuation and optimal switching boundaries. We find that the switching boundaries generally narrow as prices decline. In the presence of operating costs and temporary suspension, however, the thresholds diverge for low enough prices. A fertilizer plant with flexibility between selling ammonia and urea is valued in an empirical section using our real option models. Despite the high correlation between the two alternative commodities, ammonia and urea, there is significant value in the flexibility to choose between the two. Both strategic and policy implications for stakeholders in flexible assets are discussed, with some generalisations outside the fertilizer industry.     

A general closed form option pricing formula

A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram–Charlier series expansion, known as the Gauss–Hermite expansion. This expansion converges for fat-tailed distributions commonly encountered in the study of financial returns. The expansion coefficients can be calibrated from observed option prices and can also be computed, for example, in models with the probability density function or the characteristic function known in closed form. We investigate the properties of the new option pricing model by calibrating it to both real-world and simulated option prices and find that the resulting implied volatility curves provide an accurate approximation for a wide range of strike prices. Based on an extensive empirical study, we conclude that the new approximation method outperforms other methods both in-sample and out-of-sample.

     

The Intraday Relation between NYSE and CBOE Prices

I extend the literature regarding price discovery across stock and option markets through an empirical model that allows information to flow through an error‐correction term and volatility. NYSE prices tend to lead CBOE prices by at least thirty minutes over the entire six‐year sample period. In addition, informed trading in the options market is revealed more strongly through persistence in volatility and the spillover of volatility to the stock market than it is through returns.     

Option Volume and Stock Prices: Evidence on Where Informed Traders Trade

This paper investigates the informational role of transactions volume in options markets. We develop an asymmetric information model in which informed traders may trade in option or equity markets. We show conditions under which informed traders trade options, and we investigate the implications of this for the linkage between markets. Our model predicts an important informational role for the volume of particular types of option trades. We empirically test our model's hypotheses with intraday option data. Our main empirical result is that negative and positive option volumes contain information about future stock prices.     

American option pricing with discrete and continuous time models: An empirical comparison

This paper considers discrete time GARCH and continuous time SV models and uses these for American option pricing. We first of all show that with a particular choice of framework the parameters of the SV models can be estimated using simple maximum likelihood techniques. We then perform a Monte Carlo study to examine their differences in terms of option pricing, and we study the convergence of the discrete time option prices to their implied continuous time values. Finally, a large scale empirical analysis using individual stock options and options on an index is performed comparing the estimated prices from discrete time models to the corresponding continuous time model prices. The results show that, while the overall differences in performance are small, for the in the money put options on individual stocks the continuous time SV models do generally perform better than the discrete time GARCH specifications.     

Expansions and Contractions of Major US Shopping Centers

We analyze the determinants of expansions and contractions of shopping centers using a unique dataset of property level data for shopping centers in eleven metropolitan areas over the period from 1995 through 2005. We find that shopping centers with large operating costs are less likely to expand and are more likely to contract. Higher expected revenue per square foot increases the likelihood of expansion and decreases the likelihood of contraction. For small shopping centers the decision to change gross leasable area (GLA) is largely driven by potential revenue, while the decision to change the number of stores is largely a function of cost. We find some support for Grenadier’s theory that a larger number of competitors reduces the value of option to wait and increases the likelihood of both expansion and contraction. The market share of competitors reduces the likelihood of increasing the number of stores as suggested by the theory of strategic positioning. Our hypotheses best explain contraction decisions of large shopping centers and expansion decisions of small shopping centers. We find that both expansions and contractions of GLA are less likely for large shopping centers in MSAs with greater uncertainty about real estate prices, indicating that the option to delay has value. Moreover, small centers are significantly less sensitive to cost and revenue; since small centers are likely to have greater idiosyncratic risk than large; this provides indirect evidence for a significant delay option.     

Pricing Warrants: An Empirical Study of the Black-Scholes Model and Its Alternatives

This paper uses a sample of over 25,000 daily warrant prices to empirically investigate potential problems with the commonly used warrant pricing model proposed by Black and Scholes as an extension of their call option model. One problem seems to be especially important: the constant variance assumption of the dilution adjusted Black-Scholes model appears to cause biases in model prices for almost all warrants and over the entire sample period. We show that more accurate price forecasts are obtained with a specific form of the constant elasticity of variance model.     

Model Uncertainty and Option Markets with Heterogeneous Beliefs

This paper provides option pricing and volume implications for an economy with heterogeneous agents who face model uncertainty and have different beliefs on expected returns. Market incompleteness makes options nonredundant, while heterogeneity creates a link between differences in beliefs and option volumes. We solve for both option prices and volumes and test the joint empirical implications using S&P500 index option data. Specifically, we use survey data to build an Index of Dispersion in Beliefs and find that a model that takes information heterogeneity into account can explain the dynamics of option volume and the smile better than can reduced‐form models with stochastic volatility.     

Equilibrium Forward Curves for Commodities

We develop an equilibrium model of the term structure of forward prices for storable commodities. As a consequence of a nonnegativity constraint on inventory, the spot commodity has an embedded timing option that is absent in forward contracts. This option's value changes over time due to both endogenous inventory and exogenous transitory shocks to supply and demand. Our model makes predictions about volatilities of forward prices at different horizons and shows how conditional violations of the 'Samuelson effect' occur. We extend the model to incorporate a permanent second factor and calibrate the model to crude oil futures data.     

Cross-sectional tests of deterministic volatility functions

We study the cross-sectional performance of option pricing models in which the volatility of the underlying stock is a deterministic function of the stock price and time. For each date in our sample of FTSE 100 index option prices, we fit an implied binomial tree to the panel of all European style options with different strike prices and maturities and then examine how well this model prices a corresponding panel of American style options. We find that the implied binomial tree model performs no better than an ad-hoc procedure of smoothing Black–Scholes implied volatilities across strike prices and maturities. Our cross-sectional results complement the time-series findings of Dumas et al. [J. Finance 53 (1998) 2059].     

Dynamic copula models for the spark spread

We propose a non-symmetric copula to model the evolution of electricity and gas prices by a bivariate non-Gaussian autoregressive process. We identify the marginal dynamics as driven by normal inverse Gaussian processes, estimating them from a series of observed UK electricity and gas spot data. We estimate the copula by modeling the difference between the empirical copula and the independent copula. We then simulate the joint process and price options written on the spark spread. We find that option prices are significantly influenced by the copula and the marginal distributions, along with the seasonality of the underlying prices.     

Employee Stock Option Exercise and Firm Cost

We develop an empirical model of employee stock option exercise that is suitable for valuation and allows for behavioral channels. We estimate exercise rates as functions of option, stock, and employee characteristics using all employee exercises at 88 public firms, 27 of them in the S&P 500. Increasing vesting frequency from annual to monthly reduces option value by 11% to 16%. Men exercise faster, reducing value by 2% to 4%, while top employees exercise slower, increasing value by 2% to 7%. Finally, we develop an analytic valuation approximation that is more accurate than methods used in practice.