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Call Option (call + option)
Kinds of Call Option Selected AbstractsNonconvergence in the Variation of the Hedging Strategy of a European Call OptionMATHEMATICAL FINANCE, Issue 4 2003R. Th. In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order. [source] A Reexamination of the Tradeoff between the Future Benefit and Riskiness of R&D IncreasesJOURNAL OF ACCOUNTING RESEARCH, Issue 1 2008ALLAN EBERHART ABSTRACT Many previous studies document a positive relation between research and development (R&D) and equity value. Though R&D can increase equity value by increasing firm value, it can also increase equity value at the expense of bondholder wealth through an increase in firm risk because equity is analogous to a call option on the underlying firm value. Shi [2003] tests this hypothesis by examining the relation between a firm's R&D intensity and its bond ratings and risk premiums at issuance. His results show that the net effect of R&D is negative for bondholders. We reexamine Shi's [2003] findings and in so doing make three contributions to the literature. First, we find that Shi's [2003] results are sensitive to the method of measuring R&D intensity. When we use what we argue is a better measure of R&D intensity, we find that the net effect of R&D is positive for bondholders. Second, when we use tests that Shi [2003] recognizes are even better than the ones that he uses, we find even stronger evidence of the positive effect of R&D on bondholders. Third, we examine cross-sectional differences in the effect of R&D on debtholders. Consistent with our main finding, we document a negative relation between R&D increases and default risk. The default risk reduction is also more pronounced for firms with higher initial default scores (where the debtholders have more to gain from an R&D increase) and for firms with more bank debt (where the debtholders have greater covenant protection from the possible detriments associated with R&D increases). [source] THE COST OF ILLIQUIDITY AND ITS EFFECTS ON HEDGINGMATHEMATICAL FINANCE, Issue 4 2010L. C. G. Rogers Though liquidity is commonly believed to be a major effect in financial markets, there appears to be no consensus definition of what it is or how it is to be measured. In this paper, we understand liquidity as a nonlinear transaction cost incurred as a function of rate of change of portfolio. Using this definition, we obtain the optimal hedging policy for the hedging of a call option in a Black-Scholes model. This is a more challenging question than the more common studies of optimal strategy for liquidating an initial position, because our goal requires us to match a random final value. The solution we obtain reduces in the case of quadratic loss to the solution of three partial differential equations of Black-Scholes type, one of them nonlinear. [source] OPTIMAL CONTINUOUS-TIME HEDGING WITH LEPTOKURTIC RETURNSMATHEMATICAL FINANCE, Issue 2 2007We examine the behavior of optimal mean,variance hedging strategies at high rebalancing frequencies in a model where stock prices follow a discretely sampled exponential Lévy process and one hedges a European call option to maturity. Using elementary methods we show that all the attributes of a discretely rebalanced optimal hedge, i.e., the mean value, the hedge ratio, and the expected squared hedging error, converge pointwise in the state space as the rebalancing interval goes to zero. The limiting formulae represent 1-D and 2-D generalized Fourier transforms, which can be evaluated much faster than backward recursion schemes, with the same degree of accuracy. In the special case of a compound Poisson process we demonstrate that the convergence results hold true if instead of using an infinitely divisible distribution from the outset one models log returns by multinomial approximations thereof. This result represents an important extension of Cox, Ross, and Rubinstein to markets with leptokurtic returns. [source] Nonconvergence in the Variation of the Hedging Strategy of a European Call OptionMATHEMATICAL FINANCE, Issue 4 2003R. Th. In this paper we consider the variation of the hedging strategy of a European call option when the underlying asset follows a binomial tree. In a binomial tree model the hedging strategy of a European call option converges to a continuous process when the number of time points increases so that the price process of the underlying asset converges to a Brownian motion, the Bachelier model. However, the variation of the hedging strategy need not converge to the variation of the limit process. In fact, it is shown that the asymptotic variation of the hedging strategy may be of any order. [source] Capacity expansion under a service-level constraint for uncertain demand with lead timesNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2009Rahul R. Marathe Abstract For a service provider facing stochastic demand growth, expansion lead times and economies of scale complicate the expansion timing and sizing decisions. We formulate a model to minimize the infinite horizon expected discounted expansion cost under a service-level constraint. The service level is defined as the proportion of demand over an expansion cycle that is satisfied by available capacity. For demand that follows a geometric Brownian motion process, we impose a stationary policy under which expansions are triggered by a fixed ratio of demand to the capacity position, i.e., the capacity that will be available when any current expansion project is completed, and each expansion increases capacity by the same proportion. The risk of capacity shortage during a cycle is estimated analytically using the value of an up-and-out partial barrier call option. A cutting plane procedure identifies the optimal values of the two expansion policy parameters simultaneously. Numerical instances illustrate that if demand grows slowly with low volatility and the expansion lead times are short, then it is optimal to delay the start of expansion beyond when demand exceeds the capacity position. Delays in initiating expansions are coupled with larger expansion sizes. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source] Portfolio theory and how parent birds manage investment riskOIKOS, Issue 10 2009Scott Forbes Investment theory is founded on the premise that higher returns are generally associated with greater risk, and that portfolio diversification reduces risk. Here I examine parental investment decisions in birds from this perspective, using data from a model system, a 16-year study of breeding red-winged blackbirds Agelaius phoeniceus. Like many altricial birds, blackbirds structure their brood into core (first-hatched) and marginal (later-hatched) elements that differ in risk profile. I measured risk in two ways: as the coefficient of variation in growth and survival of core and marginal offspring from a given brood structure; and using financial beta derived from the capital asset pricing model of modern portfolio theory. Financial beta correlates changes in asset value with changes in the value of a broader market, defined here as individual reproductive success vs. population reproductive success. Both measures of risk increased with larger core (but not marginal) brood size; and variation in growth and survival was significantly greater during ecologically adverse conditions. Core offspring showed low beta values relative to marginal progeny. The most common brood structures in the population exhibited the highest beta values for both core and marginal offspring: many parent blackbirds embraced rather than avoided risk. But they did so prudently with an investment strategy that resembled a financial instrument, the call option. A call option is a contingent claim on the future value of the asset, and is exercised only if asset value increases beyond a point fixed in advance. Otherwise the option lapses and the investor loses only the initial option price. Parents created high risk marginal progeny that were forfeited during ecological adversity (the option lapses) but raised otherwise (the option called); at the same time parents maintained a constant investment and return in low risk core progeny that varied little with changes in brood size or ecological conditions. [source] Implied Mortgage Refinancing ThresholdsREAL ESTATE ECONOMICS, Issue 3 2000Paul Bennett The optimal prepayment model asserts that rational homeowners will refinance if they can reduce the current value of their liabilities by an amount greater than the refinancing threshold, defined as the cost of carrying the transaction plus the time value of the embedded call option. To compute the notional value of the refinancing threshold, researchers have traditionally relied on discrete- or continuous-time option-pricing models. Using a unique loan level database that links homeowner attributes with property and loan characteristics, this study proposes an alternative approach for estimating the implied value of the refinancing threshold. This empirical method enables us to measure the minimum interest-rate differential needed to justify refinancing conditional on the borrower's creditworthiness, loan-to-value ratio and other observable characteristics. [source] A modified static hedging method for continuous barrier options,THE JOURNAL OF FUTURES MARKETS, Issue 12 2010San-Lin Chung This study modifies the static replication approach of Derman, E., Ergener, D., and Kani, I. (1995, DEK) to hedge continuous barrier options under the Black, F. and Scholes, M. (1973) model. In the DEK method, the value of the static replication portfolio, consisting of standard options with varying maturities, matches the zero value of the barrier option at n evenly spaced time points when the stock price equals the barrier. In contrast, our modified DEK method constructs a portfolio of standard options and binary options with varying maturities to match not only the zero value but also zero theta on the barrier. Our numerical results indicate that the modified DEK approach improves performance of static hedges significantly for an up-and-out call option under the BS model even if the bid,ask spreads are considered. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark [source] Pricing Reinsurance Contracts on FDIC LossesFINANCIAL MARKETS, INSTITUTIONS & INSTRUMENTS, Issue 3 2008Dilip B. Madan This paper proposes a pricing model for the FDIC's reinsurance risk. We derive a closed-form Weibull call option pricing model to price a call-spread a reinsurer might sell to the FDIC. To obtain the risk-neutral loss-density necessary to price this call spread we risk-neutralize a Weibull distributed FDIC annual losses by a tilting coefficient estimated from the traded call options on the BKX index. An application of the proposed approach yield reasonable reinsurance prices. [source] A neural network versus Black,Scholes: a comparison of pricing and hedging performancesJOURNAL OF FORECASTING, Issue 4 2003Henrik Amilon Abstract An Erratum has been published for this article in Journal of Forecasting 22(6-7) 2003, 551 The Black,Scholes formula is a well-known model for pricing and hedging derivative securities. It relies, however, on several highly questionable assumptions. This paper examines whether a neural network (MLP) can be used to find a call option pricing formula better corresponding to market prices and the properties of the underlying asset than the Black,Scholes formula. The neural network method is applied to the out-of-sample pricing and delta-hedging of daily Swedish stock index call options from 1997 to 1999. The relevance of a hedge-analysis is stressed further in this paper. As benchmarks, the Black,Scholes model with historical and implied volatility estimates are used. Comparisons reveal that the neural network models outperform the benchmarks both in pricing and hedging performances. A moving block bootstrap is used to test the statistical significance of the results. Although the neural networks are superior, the results are sometimes insignificant at the 5% level.,Copyright © 2003 John Wiley & Sons, Ltd. [source] Robust Hedging of Barrier OptionsMATHEMATICAL FINANCE, Issue 3 2001Haydyn Brown This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion. We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight. [source] Alternative tilts for nonparametric option pricingTHE JOURNAL OF FUTURES MARKETS, Issue 10 2010M. Ryan Haley This study generalizes the nonparametric approach to option pricing of Stutzer, M. (1996) by demonstrating that the canonical valuation methodology introduced therein is one member of the Cressie,Read family of divergence measures. Alhough the limiting distribution of the alternative measures is identical to the canonical measure, the finite sample properties are quite different. We assess the ability of the alternative divergence measures to price European call options by approximating the risk-neutral, equivalent martingale measure from an empirical distribution of the underlying asset. A simulation study of the finite sample properties of the alternative measure changes reveals that the optimal divergence measure depends upon how accurately the empirical distribution of the underlying asset is estimated. In a simple Black,Scholes model, the optimal measure change is contingent upon the number of outliers observed, whereas the optimal measure change is a function of time to expiration in the stochastic volatility model of Heston, S. L. (1993). Our extension of Stutzer's technique preserves the clean analytic structure of imposing moment restrictions to price options, yet demonstrates that the nonparametric approach is even more general in pricing options than originally believed. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:983,1006, 2010 [source] Cross-market efficiency in the Indian derivatives market: A test of put,call parityTHE JOURNAL OF FUTURES MARKETS, Issue 9 2008VipulArticle first published online: 30 JUL 200 This study examines the cross-market efficiency of the Indian options and futures market using model-free tests. The put,call,futures and put,call,index parity conditions are tested for European style Nifty Index options. Thirty-five-month time-stamped transactions data are used to identify mispricing. Frequent violations of both forms of put,call parity are observed. The restriction on short sales largely accounts for the put,call,index parity violations. There are numerous put,call,futures arbitrage profit opportunities even after accounting for transaction costs, which vanish quickly. Put options are overpriced more often than call options. The mispricing shows specific patterns with respect to time of the day, moneyness, volatility, and days to expiry. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:889,910, 2008 [source] Valuing credit derivatives using Gaussian quadrature: A stochastic volatility frameworkTHE JOURNAL OF FUTURES MARKETS, Issue 1 2004Nabil Tahani This article proposes semi-closed-form solutions to value derivatives on mean reverting assets. A very general mean reverting process for the state variable and two stochastic volatility processes, the square-root process and the Ornstein-Uhlenbeck process, are considered. For both models, semi-closed-form solutions for characteristic functions are derived and then inverted using the Gauss-Laguerre quadrature rule to recover the cumulative probabilities. As benchmarks, European call options are valued within the following frameworks: Black and Scholes (1973) (represents constant volatility and no mean reversion), Longstaff and Schwartz (1995) (represents constant volatility and mean reversion), and Heston (1993) and Zhu (2000) (represent stochastic volatility and no mean reversion). These comparisons show that numerical prices converge rapidly to the exact price. When applied to the general models proposed (represent stochastic volatility and mean reversion), the Gauss-Laguerre rule proves very efficient and very accurate. As applications, pricing formulas for credit spread options, caps, floors, and swaps are derived. It also is shown that even weak mean reversion can have a major impact on option prices. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:3,35, 2004 [source] A note on rational call option exerciseTHE JOURNAL OF FUTURES MARKETS, Issue 5 2002Malin Engström Using Swedish equity option data, the rationality in the exercise of American call options is analyzed to see how well it complies with the theoretical exercise rules. Although the exercise behavior appears to be rational overall, several cases of both faulty exercise and failure to exercise are found. Almost a third of the early exercised calls are exercised at other times than predicted by theory. Several of these exercise decisions could potentially be explained by transaction costs, indicating that market frictions do affect the exercise behavior. However, over two thirds of the faulty exercises cannot be explained at all. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:471,482, 2002 [source] | ||||||||||