Tight bounds on American option prices

In contrast to the constant exercise boundary assumed by Broadie and Detemple (1996) [Broadie, M., Detemple, J., 1996. American option valuation: New bounds, approximations, and comparison of existing methods. Review of Financial Studies 9, 1211–1250], we use an exponential function to approximate the early exercise boundary. Then, we obtain lower bounds for American option prices and the optimal exercise boundary which improve the bounds of Broadie and Detemple (1996). With the tight lower bound for the optimal exercise boundary, we further derive a tight upper bound for the American option price using the early exercise premium integral of Kim (1990) [Kim, I.J., 1990. The analytic valuation of American options. Review of Financial Studies 3, 547–572]. The numerical results show that our lower and upper bounds are very tight and can improve the pricing errors of the lower bound and upper bound of Broadie and Detemple (1996) by 83.0% and 87.5%, respectively. The tightness of our upper bounds is comparable to some best accurate/efficient methods in the literature for pricing American options. Moreover, the results also indicate that the hedge ratios (deltas and gammas) of our bounds are close to the accurate values of American options.     

The early exercise premia of America put options on stocks

Using the put-call parity, this paper finds that early exercise premia of short-lived American put options on stocks account for a significant portion of put prices. This finding holds even for out-of-the-money put options. The magnitude of the early exercise premia of American put options with no dividend is positvely related to the degree of moneyness, time to maturity of the put option, and the volatility. The magnitude of the early exercise premia of American put options with dividend is positvely related to the degree of moneyness and the risk-free interest rates.     

The information frown in option prices

In the S&P 500 options market, the information content of implied volatilities differs by strike in a frown pattern that is a rough mirror image of the implied volatility smile. Implied volatilities calculated from moderately high strike price options are both unbiased and efficient predictors of future volatility. Implied volatilities calculated from low and at-the-money strikes are biased and less efficient. This bias cannot be explained by market imperfections but is consistent with the hedging pressure argument of Bollen and Whaley [J. Finan. 59 (2004) 711] and Ederington and Guan [J. Derivat. 10 (2002) (Winter) 9]. We also find that a serious estimation bias results when the relations are estimated using panel data.     

The early exercise of American puts

This paper shows that American puts on dividend paying stocks are most likely to be exercised either just after an ex-dividend date or just prior to expiration. At any other time the option to exercise an American put early may have less value. Thus, put writers and converters can predict when protection against premature exercise will be most valuable. The probability of early exercise is shown to be sensitive to managerial policy regarding the suspension of dividend payments, transaction costs, and interest rates. However, dividend payments are demonstrated to be the primary deterrent to early exercise.     

Pricing by American option by approximating its early exercise boundary as a multipiece exponential function

This article proposes to price an American option by approximatingits early exercise boundary as a multipiece exponential function.Closed form formulas are obtained in terms of the bases andexponents of the multipiece exponential function. It is demonstratedthat a three-point extrapolation scheme has the accuracy ofan 800-time-step binomial tree, but is about 130 times faster.An intuitive argument is given to indicate why this seeminglycrude approximation works so well. Our method is very simpleand easy to implement. Comparisons with other leading competingmethods are also included.     

Default risk premium and asset prices

We estimate a standard structural model of credit risk to draw insights about the premium demanded by investors for bearing default risk, using data on credit default swaps and market capitalization. We pin down the daily market value of assets for a set of non-financial firms and uncover cross-sectional heterogeneity in terms of the magnitude and time variation of the premium. By exploring the link between asset and default risk premia, we show that this heterogeneity closely depends on the relationship between the firm-specific market value of the assets and the business cycle.     

Factorization of European and American option prices under complete and incomplete markets

In a standard option-pricing model, with continuous-trading and diffusion processes, this paper shows that the price of one European-style option can be factorized into two intuitive components: One robust, X₀, which is priced by arbitrage, and a second, Π₀, which depends on a risk orthogonal to the traded securities. This result implies the following: (1) In an incomplete market, these parts represent the price of a hedging portfolio, which is unique, and a premium, which depends only on the risk premiums associated with the residual risk, respectively. (2) In a complete market, it allows factoring the contribution of the different sources of risk to the final option price. For example, in a stochastic volatility model, we can quantify the impact on the option price of volatility risk relative to market risk, Π₀ and X₀, respectively. Hence, certain misspricings in option markets can be directly related to the premium, Π₀. (3) Moreover, these results extend to American securities, which have a third component – an additional early-exercise premium.     

The saga of the American put

The American put is one of the oldest problems in mathematical finance. We review the development of the relevant literature over the last 40 years. Today the mainstream computational problems have been solved satisfactorily and the target of research is shifting towards the development of further insights into the value of timing investment decisions.     

Risk-neutral compatibility with option prices

A common problem is to choose a “risk-neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of “compatibility” between X and the prices of our options, and this poses some significant mathematical difficulties.     

The value of corporate voting rights embedded in option prices

This paper proposes and tests a new method to extract the value of corporate voting rights from market prices of American-style single-stock options. The method models voting-right values as non-cash dividends and backs them out via numerical optimization from prices of equity options. Simulation experiments show that the method is accurate and outperforms existing option-based approaches by reducing their measurement error from 17.2% to 1.57% in terms of root mean squared errors and almost eliminates their bias.The paper also contributes an empirical analysis of corporate voting-right values in European companies in the time period between 2003 and 2010. Voting rights have an annualized average value of 0.37% of the share price and are significantly worth more in months in which either ordinary or extraordinary general meetings take place but no single shareholder holds a majority stake in the company. Finally, voting values are higher in companies incorporated in French-civil-law countries (France and the Netherlands) than in German-civil-law countries (Germany and Switzerland).     

Computing American option prices in the lognormal jump–diffusion framework with a Markov chain

This note examines a numerical approach for computing American option prices in the lognormal jump–diffusion context. The approach uses the known transition density of the process to build a discrete-time, homogenous Markov chain to approximate the target jump–diffusion process. Numerical results showing the performance of the proposed method are examined.     

Optimal exercise of American put options near maturity: A new economic perspective

Review of Derivatives Research - The critical price $$S^{*}\left( t\right) $$ of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide...     

On the modelling of option prices

Dilip B Madan discusses how even good financial models often fail to perform when applied to real economic data. To overcome market volatility, he suggests, the right model must successfully reduce dimension.     

Biases in option prices : Evidence from the foreign currency option market

This paper examines a European call model of option pricing over a data set which does not suffer from the early exercise problems that have plagued earlier studies of call options on common stocks. We specifically examine a data set of American call prices on spot foreign exchange for which it is plausible to apply an adjusted version of the Garman-Kohlhagen (1983) and Grabbe (1983) European call option model. We make adjustments for interest rate risk and find that the model is nearly unbiased in the valuation of foreign currency options. We conclude that the Geske-Roll (1984) conjecture about dividend uncertainty creating biases in stock option prices holds analogously in the foreign currency option market. Interest rate differential risk (analogous to risky dividends) thus appears to be an important element in the valuation of foreign currency options.     

Anticipated information releases reflected in call option prices

This study captures the ex ante information content of a financial reporting event (the annual earnings announcement) by examining the behavior of call option prices on dates leading up to and passing through the disclosure date. This approach differs from most previous empirical security price research which has been ex post in nature. The hypothesis that investors anticipate that the future release of annual earnings numbers will affect security prices is empirically confirmed. In particular, systematic changes in variance rates implied by the Black-Scholes option pricing model are demonstrated.     

Term structure movements implicit in Asian option prices

In this paper we implement dynamic term structure models that adopt bonds and Asian options in the estimation process. The goal is to analyse the pricing and hedging implications of term structure movements when options are (or are not) included in the estimation process. We investigate how options affect the shape, risk premium and hedging structure of the dynamic factors. We find that the inclusion of options affects the loadings of the slope and curvature factors, and considerably changes the risk premium and hedging structure of all dynamic factors.     

Assessing models of individual equity option prices

Review of Quantitative Finance and Accounting - This study sheds light on risk exposures of cooperative banks in Austria, Germany and Italy. We investigate how major risk elements of banks in these...