Option pricing with discrete rebalancing

Prigent, Jean‐Luc; Renault, Olivier; Scaillet, Olivier

doi:10.1016/j.jempfin.2003.09.001

Cited by 9 publications

(3 citation statements)

References 36 publications

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“…Mello and Neuhaus [20] research the accumulated hedging error due to discrete rebalancing, extending the work by Figlewski [12] to imperfect markets. The idea of allowing hedging at the time when fixed relative changes in the stock price occur is explored in [25], where the price dynamic (in an incomplete market) is a marked point process.…”

Section: Introductionmentioning

confidence: 99%

Optimal Hedging of a Perpetual American Put with a Single Trade

Cai¹,

Angelis²,

Palczewski³

2021

SIAM J. Finan. Math.

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It is well-known that using delta hedging to hedge financial options is not feasible in practice. Traders often rely on discrete-time hedging strategies based on fixed trading times or fixed trading prices (i.e., trades only occur if the underlying asset's price reaches some predetermined values). Motivated by this insight and with the aim of obtaining explicit solutions, we consider the seller of a perpetual American put option who can hedge her portfolio once until the underlying stock price leaves a certain range of values (a, b). We determine optimal trading boundaries as functions of the initial stock holding, and an optimal hedging strategy for a bond/stock portfolio. Optimality here refers to the variance of the hedging error at the (random) time when the stock leaves the interval (a, b). Our study leads to analytical expressions for both the optimal boundaries and the optimal stock holding, which can be evaluated numerically with no effort.

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Section: Introductionmentioning

confidence: 99%

Optimal Hedging of a Perpetual American Put with a Single Trade

Cai¹,

Angelis²,

Palczewski³

2021

SIAM J. Finan. Math.

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“…There, the Authors approach the filtering problem (after time discretization in intervals of equal length) using a particle filter on the counting observations, based on a sampling importance resampling algorithm. Other works dealing with MPP but more concerned with option pricing and hedging can be found in Kirch and Runggaldier [18], Prigent [20] and Prigent et al [21]. In Kirch and Runggaldier [18], assuming a model in which the asset price follows a geometric Poisson process with unknown constant intensity, the optimal hedging strategy is constructed using stochastic control techniques.…”

Section: Introductionmentioning

confidence: 99%

“…In Kirch and Runggaldier [18], assuming a model in which the asset price follows a geometric Poisson process with unknown constant intensity, the optimal hedging strategy is constructed using stochastic control techniques. On the other hand, in Prigent [20], in a very general context, the equivalent martingale measures are characterized by their Radon-Nykodim derivatives with respect to the natural probability, whereas in Prigent et al [21] the problem of option pricing is considered in the case in which the (dynamic) portfolios are adjusted only after fixed relative changes in the stock prices.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo Derivative Pricing With Partial Information in a Class of Doubly Stochastic Poisson Processes With Marks

Centanni

Minozzo

2012

Int. J. Theor. Appl. Finan.

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To model intraday stock price movements we propose a class of marked doubly stochastic Poisson processes, whose intensity process can be interpreted in terms of the effect of information release on market activity. Assuming a partial information setting in which market agents are restricted to observe only the price process, a filtering algorithm is applied to compute, by Monte Carlo approximation, contingent claim prices, when the dynamics of the price process is given under a martingale measure. In particular, conditions for the existence of the minimal martingale measure Q are derived, and properties of the model under Q are studied.Keywords: Minimal martingale measure; news arrival; marked point process; nonlinear filtering; reversible jump Markov chain Monte Carlo; ultra-high frequency data. † Corresponding author. 1250018-1 Int. J. Theor. Appl. Finan. 2012.15. Downloaded from www.worldscientific.com by THE UNIVERSITY OF WESTERN ONTARIO on 04/12/15. For personal use only. 1250018-2 Int. J. Theor. Appl. Finan. 2012.15. Downloaded from www.worldscientific.com by THE UNIVERSITY OF WESTERN ONTARIO on 04/12/15. For personal use only. Monte Carlo Derivative Pricing in a Class of Marked DSPPtrajectory of the price process in any bounded time interval is characterized by a finite (although random) number of changes.An interesting feature of the framework proposed is that it can be interpreted to account for the link between the information release and the changes in price volatility and trading activity, whose existence has been many times suggested in the economic literature (see, among others, Engle and Ng [9] and Kalev et al. [17]). In our model, this link is embodied by the intensity process δ governing the speed of price changes. In particular, if δ is a shot noise process, its sudden increases can be interpreted as perturbations in market activity caused by pieces of news reaching the market, being the size of each increase due to the importance and unexpectedness of the news, and its consequent exponential decays can be interpreted as progressive normalizations due to the absorption of the effect of the news by the market.As far as the problem of pricing a contingent claim is concerned, a basic result of mathematical finance states that for a stochastic process S, representing the discounted stock price, the existence of an equivalent martingale measure, that is, of a measure equivalent to the "natural" probability P, such that S is a local martingale, is essentially equivalent to the absence of arbitrage opportunities (see, for example, Harrison and Kreps [15], Delbaen and Schachermayer [7]). If the price of the risky asset follows a marked point process, the market model is in general incomplete and it can be shown that there exist more then one of such equivalent measures. Thus, the problem of pricing a contingent claim, under the no arbitrage assumption, is reduced to taking expected values under the "right" measure among all existing equivalent martingale measures. One possibility is to choose the so cal...

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Bioactive Sheath/Core nanofibers containing olive leaf extract

Doğan

Başal

Bayraktar

et al. 2015

Microsc. Res. Tech.

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This study aimed at producing silk fibroin (SF)/hyaluronic acid (HA) and olive leaf extract (OLE) nanofibers with sheath/core morphology by coaxial electrospinning method, determining their antimicrobial properties, and examining release profiles of OLE from these coaxial nanofibers. Optimum electrospinning process and solution parameters were determined to obtain uniform and bead-free coaxial nanofibers. Scanning electron microscopy and transmission electron microscopy (TEM) were used to characterize the morphology of the nanofibers. The antimicrobial activities of nanofibers were tested according to AATCC test method 100. Total phenolic content and total antioxidant activity were tested using in vitro batch release system. The quality and quantity of released components of OLE were determined by high-performance liquid chromatography. The changes in nanofibers were examined by Fourier-transform infrared spectroscopy. Uniform and bead-free nanofibers were produced successfully. TEM images confirmed the coaxial structure. OLE-loaded nanofibers demonstrated almost perfect antibacterial activities against both of gram-negative and gram-positive bacteria. Antifungal activity against C. albicans was rather poor. After a release period of 1 month, it was observed that $70-95% of the OLE was released from nanofibers and it was still bioactive. Overall results indicate that the resultant shell/core nanofibers have a great potential to be used as biomaterials. Microsc.

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Option pricing with discrete rebalancing

Cited by 9 publications

References 36 publications

Optimal Hedging of a Perpetual American Put with a Single Trade

Optimal Hedging of a Perpetual American Put with a Single Trade

Monte Carlo Derivative Pricing With Partial Information in a Class of Doubly Stochastic Poisson Processes With Marks

Bioactive Sheath/Core nanofibers containing olive leaf extract

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