Implied Stock Prices Research Articles

Monotonic transformation and recovering the implied stock price process

AbstractThe paper demonstrates the construction of a stock price stochastic process that aligns with observed option prices, drawing inspiration from a manuscript by Professor Erio Castagnoli that employs the concept of a non-linear monotonic transformation of a standard Brownian motion. The paper includes a detailed numerical example that illustrates the implementation of this straightforward and ingenious idea.

ConAgra Foods: valuing a potential recipe for success

In the fall of 2012, ConAgra Foods had the opportunity to become the largest private-label packaged food producer in North America. ConAgra was considering the purchase of Ralcorp, a large private brands manufacturer. This could be a strategic step for ConAgra, since the potential acquisition seemed aligned to the firm’s strategy for growth. Ralcorp, with revenue and assets representing about one third of ConAgra’s, was large enough to impact ConAgra’s business strategy and financial structure. This case study provides both firm level and private brands industry data to assess the potential acquisition. Ranges of implied stock prices could be estimated by using Discounted Cash Flow Valuation, Comparable Multiples, and Comparable Merger and Acquisitions Transaction analysis. A comparison of implied stock prices and actual stock price by the time of the case leads to the topic of control premium paid during acquisitions and to potential enterprise synergies.

Long memory and the relation between options and stock prices

This study investigates the long-memory property and the fractionally cointegration between absolute changes in observed stock prices and implied stock prices from option pricing model. We find a stylized fact that absolute price movements in stock and option markets are characterized by long memory and they present a fractionally cointegrated relation. The option prices appear to be valuable for the stock prices based on an appropriate econometric methodology, which captures the persistence of both price series. Our empirical results also support the presence of information effect in call option, but the volume effect is absent for all cases.

Contingent Capital: Pricing and Risks

This paper shows how the credit risk of CoCos materially differs from the credit risk of other defaultable securities, allowing us to replicate them with a portfolio of risk-free bonds and equity derivatives. We use a stochastic volatility model with jumps (SVJ) calibrated on credit and volatility data to compute the value of a traded CoCo. Using this model, we show how to extract new information-content about a bank from CoCo prices, computing an implied stock price trigger. From this perspective, we price a real-world CoCo and observe a potential mispricing. We analyse CoCos’ payoff profile, explaining why they carry significant endogenous risk. Finally, we discuss why they might not be suitable for many traditional fixed-income investors.

Tick Size, Microstructure Noise, Informed Trading and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price, as well as on the statistical technique used to estimate these metrics. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics, all statistical techniques used for their estimation, and all inversion methods. In addition, we document systematic differences in option market information shares between equities and exchange traded funds both before and after the tick size change, and we present strong event-type empirical evidence of informed trading in the equity option market after the tick size change, with extreme values of the IS and CS metrics in that market producing similar abnormal underlying asset returns.

Use of Bayesian Estimates to determine the Volatility Parameter Input in the Black-Scholes and Binomial Option Pricing Models

The valuation of options and many other derivative instruments requires an estimation of exante or forward looking volatility. This paper adopts a Bayesian approach to estimate stock price volatility. We find evidence that overall Bayesian volatility estimates more closely approximate the implied volatility of stocks derived from traded call and put options prices compared to historical volatility estimates sourced from IVolatility.com (“IVolatility”). Our evidence suggests use of the Bayesian approach to estimate volatility can provide a more accurate measure of ex-ante stock price volatility and will be useful in the pricing of derivative securities where the implied stock price volatility cannot be observed.

Tick Size, Microstructure Noise and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Tick Size Reduction and Price Discovery in Option Markets: An Empirical Investigation

We examine the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. We first document a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the inversion method of the option value to find the implied stock price. We then introduce a more accurate inversion method that results in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. In all cases, however, we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Tick Size, Microstructure Noise and Volatility Inversion Effects on Price Discovery in Option Markets: Theory and Empirical Evidence

We document both theoretically and empirically a major dependence in both the Information Shares (IS) and Component Shares (CS) approaches to the estimation of the price discovery metrics on the errors arising out of the inversion method of the option value to find the implied stock price. We then introduce accurate inversion methods that result in a major increase in the information shares of option markets for both IS and CS metrics compared to the dominant Lagged Implied Volatility (LIV) inversion method. We apply these insights by examining the impact of the tick size reduction introduced by the CBOE in 2007 in its second pilot program on the simultaneous price discovery process in the markets for options and their underlying securities. In all cases we document a major impact of the tick size reduction in the option market that increases the option market information shares for all metrics and all inversion methods.

Examining the interrelation dynamics between option and stock markets using the Markov-switching vector error correction model

This study examines the dynamics of the interrelation between option and stock markets using the Markov-switching vector error correction model. Specifically, we calculate the implied stock prices from the Black–Scholes 6 model and establish a statistic framework in which the parameter of the price discrepancy between the observed and implied prices switches according to the phase of the volatility regime. The model is tested in the US S&P 500 stock market. The empirical findings of this work are consistent with the following notions. First, while option markets react more quickly to the newest stock–option disequilibrium shocks than spot markets, as found by earlier studies, we further indicate that the price adjustment process occurring in option markets is pronounced when the high variance condition is concerned, but less so during the stable period. Second, the degree of the co-movement between the observed and implied prices is significantly reduced during the high variance state. Last, the lagged price deviation between the observed and implied prices functions as an indicator of the variance-turning process.

Potential Biases from Using Only Trade Prices of Related Securities on Different Exchanges: A Comment

equilibrium prices of the underlying stocks using daily (trade) prices. This paper points out that a bias associated with the bid-ask spread and nonsynchronous trading may create the impression that option prices contain information not reflected in the contemporaneous stock prices even during times when the two prices are in equilibrium. The MR methodology is described in Section I, and the potential biases arising due to the bid-ask bounce and the non-synchroneity of stock and option prices are illustrated in Section II. Following an observation in their paper that the stock prices implied by the option prices are smaller than the corresponding stock prices only thirty-seven percent of the time, Section III looks at the distribution of trade prices relative to the last quoted bid-ask prices for both stocks and options. Many more during-the-day option trades occur at the ask than at the bid, whereas the distribution is approximately symmetric for stocks. A likely implication is that the option trade prices, and therefore the implied stock prices, are upward-biased estimates of the corresponding true prices.' This bias increases at day end for both stocks and options.

Stock splits and implied stock price volatility

T his study addresses the issue of stock splits, their effect on the volatility of stock prices, and the prospect of using this change in volatility to make trading profits in the market. We ask the questions: Do option prices following a stock split reflect higher stock volatilities? Can an option trader use this information to make profits in the market? Our findings show that post-split option prices do imply higher stock volatilities, but that the increase is insufficient to allow option traders to profit after considering transactions costs. Our analysis proceeds from earlier research into the price behavior of lower-priced securities. Studies of returns on these securities usually examine stocks of companies that fall into one of two areas: 1) small-capitalization companies whose stocks are lowpriced and generally riskier than higher-priced stocks, and 2) companies whose stocks are lower-priced because the company has recently had a stock split. Studies in the first group' generally show that returns are greater for the lower-priced stocks, even after adjusting for the higher levels of risk of lower-priced stocks. Studies falling into the second group' generally conclude that the volatility of stock returns (risk) appears to increase after the split, although there is no significant change in the level of stock returns after a split. In their study of the possibility of profits from stock splits, Reilly and Drzycimski [14] found that the

Some Comments on the CBOE Call Option Index

The Chicago Board Options Exchange (CBOE) Call Option Index provides an estimate of the average value of standardized, six-month, at-the-money call options, expressed as a percentage of the price of the underlying stocks. The CBOE index does not attempt to eliminate the effects of changing interest rates and changes in the pattern and timing of dividends. The Gastineau-Madansky index, on the other hand, eliminates these effects and focuses on changes in the market's expectation for the volatility of the underlying stocks. One can gain some appreciation of the effect of interest rates and dividends on the CBOE index by looking at the level of and the net difference between the shortterm interest rate and the average dividend yield. Since 1978, when short-term rates began to rise relative to dividend yields, the CBOE and the GastineauMadansky indexes have diverged materially. The high short-term rates of 1979 caused the CBOE index to exceed the levels that prevailed during most of 1977; the Gastineau-Madansky index, in contrast, showed that expected stock price volatility was at a historical low in the second quarter of 1979. Most investors who use an option premium index in their analyses use it as a measure of expected or implied stock price volatility. But the CBOE Call Option Index is too dependent on the dividend-interest rate differential to be a meaningful indicator of the market's expectations for future stock price volatility.

Stock Market Efficiency and Price Predictions Implicit in Option Trading

The Black-Scholes option pricing model (with approximate adjustments for dividends and exercise price changes) was used to generate stock prices which are “implied” by the model. If the stock market is efficient, these implied prices should not be capable of being used profitably by traders. This hypothesis is tested using prices established in the Australian Options Market and the Sydney Stock Exchange over the period February 1976 to December 1980. A close correspondence is found between implied stock prices and actual stock prices. Tests of the predictive power of the implied prices were unable to discover evidence of market inefficiency. However, a simulated trading strategy executed over one trading day and based on the largest discrepancies between actual and implied prices did meet with some success.

Option Prices as Predictors of Equilibrium Stock Prices

ABSTRACTThe Black‐Scholes option pricing model, modified for dividend payments, is used to calculate jointly implied stock prices and implied standard deviations. A comparison of the implied stock prices with observed stock prices reveals that the implied prices contain information regarding equilibrium stock prices that is not fully reflected in observed stock prices. The implications of this finding are discussed.

Why Simulations Are an Unreliable Test of Option Strategies

* Since the start of listed options trading in 1973, computer simulations have become increasingly popular as a method for testing and comparing option strategies. Simulations can typically answer the question, Given the actual history of security prices, what return on investment would a given options strategy have produced? But they cannot reveal whether a specific option strategy is good, bad or indifferent. To do this, a test must maintain between the options strategies compared. The key to stock equivalence is the neutral hedge ratio the rate at which option prices change with changes in underlying stock prices. The neutral hedge ratio changes with changes in the ratio of striking price to market price, in the time remaining to expiration and in the volatility of the underlying stock. Such well known simulations as those of Kassouf and Merton, Scholes and Gladstein rely on test portfolios with fixed positions, neglecting the fact that the stock equivalence of those positions will vary over time. The sophisticated investor is less interested in the hypothetical return on investment from a particular option strategy than with its probable impact on the risk-reward structure of his current portfolio. The authors propose an index approach that is specifically designed to answer the latter question. It assesses option strategies by comparing actual and implied stock price volatilities. If the volatility implied by the option price as traded exceeds the stock's actual volatility, the price of the option has exceeded its value. >