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Strike Prices (strike + price)
Selected AbstractsCRITICAL PRICE NEAR MATURITY FOR AN AMERICAN OPTION ON A DIVIDEND-PAYING STOCK IN A LOCAL VOLATILITY MODELMATHEMATICAL FINANCE, Issue 3 2005Etienne ChevalierArticle first published online: 10 JUN 200 We consider an American put option on a dividend-paying stock whose volatility is a function of the stock value. Near the maturity of this option, an expansion of the critical stock price is given. If the stock dividend rate is greater than the market interest rate, the payoff function is smooth near the limit of the critical price. We deduce an expansion of the critical price near maturity from an expansion of the value function of an optimal stopping problem. It turns out that the behavior of the critical price is parabolic. In the other case, we are in a less regular situation and an extra logarithmic factor appears. To prove this result, we show that the American and European critical prices have the same first-order behavior near maturity. Finally, in order to get an expansion of the European critical price, we use a parity formula for exchanging the strike price and the spot price in the value functions of European puts. [source] American options on assets with dividends near expiryMATHEMATICAL FINANCE, Issue 3 2002J. D. Evans Explicit expressions valid near expiry are derived for the values and the optimal exercise boundaries of American put and call options on assets with dividends. The results depend sensitively on the ratio of the dividend yield rate D to the interest rate r. For D>r the put boundary near expiry tends parabolically to the value rK/D where K is the strike price, while for D,r the boundary tends to K in the parabolic-logarithmic form found for the case D=0 by Barles et al. (1995) and by Kuske and Keller (1998). For the call, these two behaviors are interchanged: parabolic and tending to rK/D for D A generalization of Rubinstein's "Pay now, choose later"THE JOURNAL OF FUTURES MARKETS, Issue 5 2008Jia-Hau Guo This article provides quasi-analytic pricing formulae for forward-start options under stochastic volatility, double jumps, and stochastic interest rates. Our methodology is a generalization of the Rubinstein approach and can be applied to several existing option models. Properties of a forward-start option may be very different from those of a plain vanilla option because the entire uncertainty of evolution of its price is cut off by the strike price at the time of determination. For instance, in contrast to the plain vanilla option, the value of a forward-start option may not always increase as the maturity increases. It depends on the current term structure of interest rates. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:488,515, 2008 [source] Optimal approximations of nonlinear payoffs in static replication,THE JOURNAL OF FUTURES MARKETS, Issue 11 2010Qiang Liu Static replication of nonlinear payoffs by line segments (or equivalently vanilla options) is an important hedging method, which unfortunately is only an approximation. If the strike prices of options are adjustable (for OTC options), two optimal approximations can be defined for replication by piecewise chords. The first is a naive minimum area approach, which seeks a set of strike prices to minimize the area enclosed by the payoff curve and the chords. The second improves on the first by taking the conditional distribution of the underlying into consideration, and minimizes the expected area instead. When the strike prices are fixed (for exchange-traded options), a third or the approach of least expected squares locates the minimum for the expected sum of squared differences between the payoff and the replicating portfolio, by varying the weights or quantities of the options used in the replication. For a payoff of variance swap, minimum expected area and least expected squares are found to produce the best numerical results in terms of cost of replication. Finally, piecewise tangents can also be utilized in static replication, which together with replication by chords, forms a pair of lower or upper bound to a nonlinear payoff. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source] Box-spread arbitrage efficiency of Nifty index options: The Indian evidenceTHE JOURNAL OF FUTURES MARKETS, Issue 6 2009VipulArticle first published online: 1 APR 200 This study examines the market efficiency for the European style Nifty index options using the box-spread strategy. Time-stamped transactions data are used to identify the mispricing and arbitrage opportunities for options with this modelfree approach. Profit opportunities, after accounting for the transaction costs, are quite frequent, but do not persist even for two minutes. The mispricing is higher for the contracts with higher liquidity (immediacy) risk captured by the moneyness (the difference between the strike prices and the spot price) and the volatility of the underlying. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:544,562, 2009 [source] Multifactor implied volatility functions for HJM modelsTHE JOURNAL OF FUTURES MARKETS, Issue 8 2006I-Doun Kuo This study evaluates two one-factor, two two-factor, and two three-factor implied volatility functions in the HJM class, with the use of eurodollar futures options across both strike prices and maturities. The primary contributions of this article are (a) to propose and test three implied volatility multifactor functions not considered by K. I. Amin and A. J. Morton (1994), (b) to evaluate models using the AIC criteria as well as other standard criteria neglected by S. Y. M. Zeto (2002), and (c) to .nd that multifactor models incorporating the exponential decaying implied volatility functions generally outperform other models in .tting and prediction, in sharp contrast to K. I. Amin and A. J. Morton, who find the constantvolatility model superior. Correctly specified and calibrated simple constant and square-root factor models may be superior to inappropriate multifactor models in option trading and hedging strategies. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:809,833, 2006 [source] Hedging in Futures and Options Markets with Basis RiskTHE JOURNAL OF FUTURES MARKETS, Issue 1 2002Olivier Mahul This paper analyzes the hedging decisions for firms facing price and basis risk. Two conditions assumed in most models on optimal hedging are relaxed. Hence, (i) the spot price is not necessarily linear in both the settlement price and the basis risk and (ii) futures contracts and options on futures at different strike prices are available. The design of the first-best hedging instrument is first derived and then it is used to examine the optimal hedging strategy in futures and options markets. The role of options as useful hedging tools is highlighted from the shape of the first-best solution. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:59,72, 2002 [source]
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