Asian option

About: Asian option is a research topic. Over the lifetime, 2717 publications have been published within this topic receiving 87919 citations. The topic is also known as: average value option.

Theory of rational option pricing

Abstract: The long history of the theory of option pricing began in 1900 when the French mathematician Louis Bachelier deduced an option pricing formula based on the assumption that stock prices follow a Brownian motion with zero drift. Since that time, numerous researchers have contributed to the theory. The present paper begins by deducing a set of restrictions on option pricing formulas from the assumption that investors prefer more to less. These restrictions are necessary conditions for a formula to be consistent with a rational pricing theory. Attention is given to the problems created when dividends are paid on the underlying common stock and when the terms of the option contract can be changed explicitly by a change in exercise price or implicitly by a shift in the investment or capital structure policy of the firm. Since the deduced restrictions are not sufficient to uniquely determine an option pricing formula, additional assumptions are introduced to examine and extend the seminal Black-Scholes theory of option pricing. Explicit formulas for pricing both call and put options as well as for warrants and the new "down-and-out" option are derived. The effects of dividends and call provisions on the warrant price are examined. The possibilities for further extension of the theory to the pricing of corporate liabilities are discussed.

The value of an option to exchange one asset for another

Abstract: SOME COMMON FINANCIAL ARRANGEMENTS are equivalent to options to exchange one risky asset for another: the investment adviser's performance incentive fee, the general margin account, the exchange offer, and the standby commitment. Yet the literature does not discuss the theory of such an option.' In this paper, I develop an equation for the value of the option to exchange one risky asset for another. My theory grows out of the brilliant Black-Scholes (1973) solution to the longstanding call option pricing problem-which assumes that the price of a riskless discount bond grew exponentially at the riskless interest rate-and Merton's (1973) extension-in which the discount bond's value is stochastic until maturity. In section II, I develop the pricing equation for a European-type option to exchange one asset for another. In section III, I show that such an option is worth more alive than dead, which implies that its owner will not exercise it until the last possible moment. Thus, the formula for the European option is also valid for its American counterpart. Since such an option is not only a call, but also a put, the formula is a closed-form expression for the value of a special sort of American put option. I derive the put-call parity theorem for American options of this sort. Section IV contains applications of the model to financial arrangements commonplace in the real world: the investment adviser's performance incentive fee, the general margin account, the exchange offer, and the standby commitment. In the last section, I summarize the findings.

Recovering Probability Distributions from Option Prices

Abstract: This article derives underlying asset risk-neutral probability distributions of European options on the S&P 500 index. Nonparametric methods are used to choose probabilities that minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices. Alternative optimization specifications produce approximately the same implied distributions. A new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed. Since the crash, the risk-neutral probability of a three (four) standard deviation decline in the index (about -36 percent (-46 percent) over a year) is about 10 (100) times more likely than under the assumption of lognormality. RECENTLY, THE INCREASING POPULARITY of derivatives and some highly publicized failures to control risk have led to increased efforts to find reasonable methods to measure the sensitivity of large institutional derivatives portfolios to extreme events. Merely because such events are rare is not sufficient to ignore them, since on the few occasions when they do occur, significant amounts of money can change hands, potentially wiping out profits accumulated over long prior periods. A key assumption behind methods of estimation is the joint probability distribution of constituent underlying asset returns. This has long been a concern of financial economists, since probability assumptions are critical to much of their research during the last quarter century. Heretofore, probability distributions of stock market returns have typically been estimated from historical time series. Unfortunately, common hypotheses may not capture the probability of extreme events, and the events of interest are rare or may not be present in the historical record, even though they are clearly possible.