I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.

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A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options

https://pages.stern.nyu.edu/~lpederse/courses/LAP/papers/Information,Fundamental/GlostenMilgrom85.pdf

Bid, ask and transaction prices in a specialist market with heterogeneously informed traders

https://w4.stern.nyu.edu/finance/docs/WP/2000/pdf/wpa00041.pdf

Illiquidity and stock returns: cross-section and time-series effects $

New tests are presented on the effects of stock illiquidity on stock return. Over time, expected market illiquidity positively affects ex ante stock excess return (usually called â¬Srisk premiumâ¬?). This complements the positive cross-sectional return-illiquidity relationship. The illiquidity measure here is the average daily ratio of absolute stock return to dollar volume, which is easily obtained from daily stock data for long time series in most stock markets. Illiquidity affects more strongly small firms stocks, suggesting an explanation for the changes â¬Ssmall firm effectâ¬? over time. The impact of market illiquidity on stock excess return suggests the existence of illiquidity premium and helps explain the equity premium puzzle.

Illiquidity and Stock Returns: Cross-Section and Time-Series Effects

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

This paper provides simple, analytic approximations for pricing exchange-traded American call and put options written on commodities and commodity futures contracts. These approximations are accurate and considerably more computationally efficient than finite-difference, binomial, or compound-option pricing methods. OPTIONS WRITTEN ON A wide variety of commodities and commodity futures contracts' now trade in the U.S. and Canada. Nearly all these options are American style2 and thus have early exercise premiums implicitly embedded in their prices. Unlike the European-style option-pricing problems, however, analytic solutions for the American option-pricing problems have not been found, and the pricing of American options has usually resorted to finite-difference, binomial, or, more recently, compound-option approximation methods. While these approximation methods yield accurate American option values, they are cumbersome and expensive to use. The purpose of this paper is to provide an accurate, inexpensive method for pricing American call and put options written on commodities and commodity futures contracts. The development of the "quadratic" approximation method is contained in Section I. Commodity option and commodity futures option contracts are defined, the underpinnings of commodity option valuation are discussed, and the solutions to the European call and put option-pricing problems are presented. Unlike the non-dividend-paying stock option case, it is shown that the American call option written on a commodity, as well as the American put option, may optimally be exercised prior to expiration. The approximation methods for the American call and put option values are then derived in the

Efficient Analytic Approximation of American Option Values

Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) hypothesize that asset return volatility is a deterministic function of asset price and time, and develop a deterministic volatility function (DVF) option valuation model that has the potential of fitting the observed cross section of option prices exactly. Using S&P 500 options from June 1988 through December 1993, we examine the predictive and hedging performance of the DVF option valuation model and find it is no better than an ad hoc procedure that merely smooths Black–Scholes (1973) implied volatilities across exercise prices and times to expiration.

/pdf/implied-volatility-functions-empirical-tests-1gsn2dxgxv.pdf

Implied Volatility Functions: Empirical Tests

The Chicago Board Options Exchange9s Market Volatility Index (VIX) is called the “investor fear gauge.” To understand why, it is necessary to understand the index9s construction. To understand how VIX performs its role, it is necessary to examine its history and its relation to stock market returns. In this article, the author describes the construction of the volatility index and examines in movements over the past fourteen years.

The Investor Fear Gauge

In rational, efficiently functioning markets, the returns on stock index and stock index futures contracts should be perfectly, contemporaneously correlated. This study investigates the time series properties of 5-minute, intraday returns of stock index and stock index futures contracts, and finds that SP however, the effect is not completely unidirectional, with lagged stock index returns having a mild positive predictive impact on futures returns.

The Dynamics of Stock Index and Stock Index Futures Returns

This paper examines the relation between net buying pressure and the shape of the implied volatility function (IVF) of S&P 500 index options and options on twenty individual stocks. We find that time variation in the implied volatility of an option series is directly related to net buying pressure from public order flow. We also find that movements in implied volatility in the index option market are most strongly affected by buying pressure for index puts, while call options tend to dominate in stock option markets. Simulated delta-neutral trading strategies that sell options generate abnormal returns that match the deviations of the IVFs from historical volatility levels. Index option abnormal returns decrease monotonically across exercise prices and are significant, while stock option abnormal returns are symmetric, smaller, and insignificant. When vega risk is also hedged in the simulations using index options, however, the abnormal returns go from positive to negative, indicating that the steeply sloped IVF for index options does not present a profitable arbitrage opportunity once the costs of hedging have been considered.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID319261_code020808500.pdf?abstractid=319261

Robert E. Whaley

Papers

Efficient Analytic Approximation of American Option Values

Implied Volatility Functions: Empirical Tests

The Investor Fear Gauge

The Dynamics of Stock Index and Stock Index Futures Returns

Does Net Buying Pressure Affect the Shape of Implied Volatility Functions