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The Put-in-Bay road races, 1952-1963
\"A sports car race took place on an island in Lake Erie. The cars they raced were those they drove as daily transportation: MGs, Porsches, Triumphs, Alfas and others. In this illustrated history, drivers, officials, mechanics and spectators share their stories. The text paints a vivid picture of the sports car racing scene in post-war America\"--Provided by publisher.
Book
The Joint Cross Section of Stocks and Options
Stocks with large increases in call (put) implied volatilities over the previous month tend to have high (low) future returns. Sorting stocks ranked into decile portfolios by past call implied volatilities produces spreads in average returns of approximately 1% per month, and the return differences persist up to six months. The cross section of stock returns also predicts option implied volatilities, with stocks with high past returns tending to have call and put option contracts that exhibit increases in implied volatility over the next month, but with decreasing realized volatility. These predictability patterns are consistent with rational models of informed trading.
Journal Article
Deviations from Put-Call Parity and Stock Return Predictability
Deviations from put-call parity contain information about future stock returns. Using the difference in implied volatility between pairs of call and put options to measure these deviations, we find that stocks with relatively expensive calls outperform stocks with relatively expensive puts by 50 basis points per week. We find both positive abnormal performance in stocks with relatively expensive calls and negative abnormal performance in stocks with relatively expensive puts, which cannot be explained by short sale constraints. Rebate rates from the stock lending market directly confirm that our findings are not driven by stocks that are hard to borrow. The degree of predictability is larger when option liquidity is high and stock liquidity low, while there is little predictability when the opposite is true. Controlling for size, option prices are more likely to deviate from strict put-call parity when underlying stocks face more information risk. The degree of predictability decreases over the sample period. Our results are consistent with mispricing during the earlier years of the study, with a gradual reduction of the mispricing over time.
Journal Article
Haunted Put-In-Bay
\"Tells the stories of more than fifteen locations on South Bass Island in Lake Erie that are attached to some rather hair-raising ghostly tales.\" -- Visit Put-in-Bay Behind Put-in-Bay's breathtaking scenery and wild nightlife is a side of the island that will make your hair stand on end.
eBook
Solving high-dimensional optimal stopping problems using deep learning
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number of underlying assets. High-dimensional optimal stopping problems are, however, notoriously difficult to solve due to the well-known curse of dimensionality. In this work, we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option. The proposed algorithm can also be applied to optimal stopping problems that arise in other areas where the underlying stochastic process can be efficiently simulated. We present numerical results for a large number of example problems, which include the pricing of many high-dimensional American and Bermudan options, such as Bermudan max-call options in up to 5000 dimensions. Most of the obtained results are compared to reference values computed by exploiting the specific problem design or, where available, to reference values from the literature. These numerical results suggest that the proposed algorithm is highly effective in the case of many underlyings, in terms of both accuracy and speed.
Journal Article
Short-Sale Constraints and Options Trading: Evidence from Reg SHO
We examine the effects of a temporary suspension of short-sale price tests on the options market. Consistent with the notion that put option trading substitutes for short selling, we find a significant reduction in put option volume. In addition, pressure on put option prices significantly declines, violations of the put-call parity become significantly less frequent, and option volume becomes less informed. Our findings add clarity to a long-standing debate on whether investors use options to circumvent equity short-selling restrictions.
Journal Article
Expected Option Returns
This paper examines expected option returns in the context of mainstream asset-pricing theory. Under mild assumptions, expected call returns exceed those of the underlying security and increase with the strike price. Likewise, expected put returns are below the risk-free rate and increase with the strike price. S&P index option returns consistently exhibit these characteristics. Under stronger assumptions, expected option returns vary linearly with option betas. However, zero-beta, at-the-money straddle positions produce average losses of approximately three percent per week. This suggests that some additional factor, such as systematic stochastic volatility, is priced in option returns.
Journal Article
A note on options and bubbles under the CEV model: implications for pricing and hedging
The discounted price process under the constant elasticity of variance (CEV) model is not a martingale (wrt the risk-neutral measure) for options markets with upward sloping implied volatility smiles. The loss of the martingale property implies the existence of (at least) two option prices for the call option: the price for which the put-call parity holds and the (risk-neutral) price representing the lowest cost of replicating the call payoff. This article derives closed-form solutions for the Greeks of the risk-neutral call option pricing solution that are valid for any CEV process exhibiting forward skew volatility smile patterns. Using an extensive numerical analysis, we conclude that the differences between the call prices and Greeks of both solutions are substantial, which might yield significant errors of analysis for pricing and hedging purposes.
Journal Article
An Implicit Scheme for American Put Options
In this paper, an implicit scheme is proposed to solve a parabolic variational inequality arising from the American put options. The discretization leads to a class of discrete elliptic variational inequalities. Well-posedness, including existence, uniqueness, comparison principle, and stability of the discrete elliptic variational inequality is established. A simple and efficient algorithm to solve the implicit discretized variational inequality is discovered. The novelty here is an explicit formula for the optimal exercise boundary. An improved algorithm is also presented to eliminate the singularity near the time to expiry. Numerical examples are carried out to show the accuracy and efficiency of the proposed algorithms.
Journal Article
Option-Implied Zero-Coupon Yields: Unifying Bond and Equity Markets
This paper addresses a critical inconsistency in models of the term structure of interest rates (TSIR), where zero-coupon bonds are priced under risk-neutral measures distinct from those used in equity markets. We consider a unified TSIR framework that treats zero-coupon bonds as European options with deterministic payoffs, ensuring that they are priced under the same risk-neutral measure that governs equity derivatives. Using put–call parity, we extract zero-coupon bond implied yield curves from S&P 500 index options and compare them with the US daily treasury par yield curves. As the implied yield curves contain maturity time T and strike price K as independent variables, we investigate the K—dependence of the implied yield curve. Our findings, that at-the-money option-implied yield curves provide the closest match to treasury par yield curves, support the view that the equity options market contains information that is highly relevant for the TSIR. By insisting that the risk-neutral measure used for bond valuation is the same as that revealed by equity derivatives, we offer a new organizing principle for future TSIR research.
Journal Article