Time-homogeneous diffusion processes are widely applied in finance and economics to model the values of assets. Two classic examples can be referred to in Black and Scholes (1973) and Cox et al. ...(1985). The applications include investment decisions and pricing derivatives. Due to mathematical tractability, approximation methods such as the Monte Carlo simulation and the lattice approximation are required in the applications. In this paper, we present a simple method to construct a recombining trinomial tree to approximate a time-homogeneous diffusion process in distribution. As an important application of lattice approximation is pricing derivatives, we also offer several numerical examples of pricing derivatives to examine our method of constructing recombining trinomial trees.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•The classical Cox–Ross–Rubinstein binomial model is extended in two ways.•Show that CRR-model can be extended to a new version with time-dependent parameters.•Develop a new trinomial model in the ...natural (historical) world.•Derive a hedging strategy for hedging at any node of the trinomial pricing tree.
We extend the classical Cox–Ross–Rubinstein binomial model in two ways. We first develop a binomial model with time-dependent parameters that equate all moments of the pricing tree increments with the corresponding moments of the increments of the limiting Itô price process. Second, we introduce a new trinomial model in the natural (historical) world, again fitting all moments of the pricing tree increments to the corresponding geometric Brownian motion. We introduce the risk-neutral trinomial tree and derive a hedging strategy based on an additional perpetual derivative used as a second asset for hedging at any node of the trinomial pricing tree.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A European option is a financial contract which gives its holder a right (but not an obligation) to buy or sell an underlying asset from writer at the time of expiry for a pre-determined price. The ...continuous European options pricing model is given by the Black-Scholes. The discrete model can be priced using the lattice models ih here we use trinomial model. We define the error simply as the difference between the trinomial approximation and the value computed by the Black-Scholes formula. An interesting characteristic about error is how to realize convergence of trinomial model option pricing to Black-Scholes option pricing. In this case we observe the convergence of Boyle trinomial model and trinomial model that built with Cox Ross Rubenstein theory.
We study insider trading in a jump-binomial model of the financial market that is based on a marked binomial process and that serves as a suitable alternative to some classical trinomial models. Our ...investigations focus on the two main questions: measuring the advantage of the insider’s additional information and stating a closed form for her hedging strategy. Our approach is based on the results of enlargement of filtration in a discrete-time setting stated by Blanchet-Scalliet and Jeanblanc (in: From probability to finance, Springer, Berlin, 2020) and on a stochastic analysis for marked binomial processes developed in the companion paper (Halconruy in Electron J Probab 27:1–39, 2022). Our work provides in a discrete-time and an incomplete market setting the analogues of some results of Amendinger et al. (Stoch Process Appl 89(1):101–116, 2000; Finance Stoch 7(1):29–46, 2003), Imkeller et al. (1998, 2006) and extends in an insider framework some utility maximization results stated in Delbaen and Schachermayer (The mathematics of arbitrage, Springer, Berlin, 2006) and in Runggaldier et al. (in: Seminar on stochastic analysis, random fields and applications III, Springer, Berlin, 2002).
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
A European option is a financial contract which gives its holder a right (but not an obligation) to buy or sell an underlying asset from writer at the time of expiry for a pre-determined price. The ...continuous European options pricing model is given by the Black-Scholes. The discrete model can be priced using the lattice models ih here we use trinomial model. We define the error simply as the difference between the trinomial approximation and the value computed by the Black-Scholes formula. An interesting characteristic about error is how to realize convergence of trinomial model option pricing to Black-Scholes option pricing. In this case we observe the convergence of Boyle trinomial model and trinomial model that built with Cox Ross Rubenstein theory.
Summary Time varying, individual covariates are problematic in experiments with marked animals because the covariate can typically only be observed when each animal is captured. We examine three ...methods to incorporate time varying, individual covariates of the survival probabilities into the analysis of data from mark-recapture-recovery experiments: deterministic imputation, a Bayesian imputation approach based on modeling the joint distribution of the covariate and the capture history, and a conditional approach considering only the events for which the associated covariate data are completely observed (the trinomial model). After describing the three methods, we compare results from their application to the analysis of the effect of body mass on the survival of Soay sheep (Ovis aries) on the Isle of Hirta, Scotland. Simulations based on these results are then used to make further comparisons. We conclude that both the trinomial model and Bayesian imputation method perform best in different situations. If the capture and recovery probabilities are all high, then the trinomial model produces precise, unbiased estimators that do not depend on any assumptions regarding the distribution of the covariate. In contrast, the Bayesian imputation method performs substantially better when capture and recovery probabilities are low, provided that the specified model of the covariate is a good approximation to the true data-generating mechanism.
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BFBNIB, DOBA, FSPLJ, FZAB, GIS, IJS, INZLJ, IZUM, KILJ, NLZOH, NMLJ, NUK, OILJ, PILJ, PNG, SAZU, SBCE, SBMB, UILJ, UKNU, UL, UM, UPUK, ZRSKP
In this paper, we analyze offshore outsourcing contracts using the trinomial model, which is very useful in analyzing real options associated with offshoring projects. Earlier studies by Grenadier ...(1995) and Pashley, Krishnaswamy and Gilbert (1997) used the option pricing model to analyze lease contracts and debt contracts respectively. So far, however, no studies address offshore outsourcing contracts. Gopal, Mukhopadhyay, Krishnan, and Sivaramakrishnan (2003), Ethiraj, Kale, Krishnan, and Singh, (2004), Gopal and Koka (2010), and Gopal and Koka (2012) found through empirical studies a significant relationship between profits and type of contracts, and price and types of contracts respectively. But they do not provide a theoretical basis for their findings. In this paper we provide a theoretical basis for such a relationship employing the real options analysis using trinomial option pricing model.
Summary
Time‐varying individual covariates present a challenge in modelling data from mark–recapture–recovery (MRR) experiments of wild animals. Many values of the covariate will be unknown because ...they can be observed only when an individual is captured, and the missing values cannot be ignored.
Catchpole et al. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 70, 445–460, 2008 presents one solution to this problem by constructing a conditional likelihood depending only on the observed covariate information – the so‐called trinomial model.
This paper describes the link between the trinomial model and the mark–recapture–recovery model of Burnham (Marked Individuals in the Study of Bird Population, 199–213, 1993) and shows how the trinomial model can be implemented in the software package program mark. This provides the user with access to all of the features of program mark including the facilities for model building and model selection without having to write custom code.
I provide details on the analysis of a simulated data set and discuss an r package developed to help users format their data and to implement the model through the existing rmark package.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
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