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Martingales and arbitrage in multiperiod securities.


In finance , the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options . The binomial model was first proposed by Cox , Ross and Rubinstein in 1979. [1] Essentially, the model uses a "discrete-time" ( lattice based ) model of the varying price over time of the underlying financial instrument. In general, Christoforou showed that binomial options pricing models do not have closed-form solutions . [2]

The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time. Being relatively simple, the model is readily implementable in computer software (including a spreadsheet ).

Although computationally slower than the Black–Scholes formula, it is more accurate, particularly for longer-dated options on securities with dividend payments. For these reasons, various versions of the binomial model are widely used by practitioners in the options markets. [ citation needed ]

The binomial pricing model traces the evolution of the option's key underlying variables in discrete-time. This is done by means of a binomial lattice (tree), for a number of time steps between the valuation and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time.

Valuation is performed iteratively, starting at each of the final nodes (those that may be reached at the time of expiration), and then working backwards through the tree towards the first node (valuation date). The value computed at each stage is the value of the option at that point in time.

The up and down factors are calculated using the underlying volatility , σ {\displaystyle \sigma } , and the time duration of a step, t {\displaystyle t} , measured in years (using the day count convention of the underlying instrument). From the condition that the variance of the log of the price is σ 2 t {\displaystyle \sigma ^{2}t} , we have:

In finance , the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options . The binomial model was first proposed by Cox , Ross and Rubinstein in 1979. [1] Essentially, the model uses a "discrete-time" ( lattice based ) model of the varying price over time of the underlying financial instrument. In general, Christoforou showed that binomial options pricing models do not have closed-form solutions . [2]

The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time. Being relatively simple, the model is readily implementable in computer software (including a spreadsheet ).

Although computationally slower than the Black–Scholes formula, it is more accurate, particularly for longer-dated options on securities with dividend payments. For these reasons, various versions of the binomial model are widely used by practitioners in the options markets. [ citation needed ]

The binomial pricing model traces the evolution of the option's key underlying variables in discrete-time. This is done by means of a binomial lattice (tree), for a number of time steps between the valuation and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time.

Valuation is performed iteratively, starting at each of the final nodes (those that may be reached at the time of expiration), and then working backwards through the tree towards the first node (valuation date). The value computed at each stage is the value of the option at that point in time.

The up and down factors are calculated using the underlying volatility , σ {\displaystyle \sigma } , and the time duration of a step, t {\displaystyle t} , measured in years (using the day count convention of the underlying instrument). From the condition that the variance of the log of the price is σ 2 t {\displaystyle \sigma ^{2}t} , we have:

,./<b5v-35/9s3 workingpaper alfredp.sloanschoolofmanagement multiperiodsecuritiesmarkets withdifferentialinformation: martingalesandresolutiontimes* by

JOURNAL OF ECONOMIC THEORY 20, 381-408 (1979) Martingales and Arbitrage in Multiperiod Securities Markets J. MICHAEL HARRISON AND DAVID M. KREPS Graduate School of ...

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational ...

6: MULTI-PERIOD MARKET MODELS MarekRutkowski School ofMathematics andStatistics UniversityofSydney Semester 2, 2016 M. …

JOURNAL OF ECONOMIC THEORY 20, 381-408 (1979) Martingales and Arbitrage in Multiperiod Securities Markets J. MICHAEL HARRISON AND DAVID M. KREPS

Price, Trade Size, and Information Revelation in Multi-Period Securities Markets Han N. Ozsoylev Sa¨ıd Business School and Linacre College University of Oxford

In finance , the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options . The binomial model was first proposed by Cox , Ross and Rubinstein in 1979. [1] Essentially, the model uses a "discrete-time" ( lattice based ) model of the varying price over time of the underlying financial instrument. In general, Christoforou showed that binomial options pricing models do not have closed-form solutions . [2]

The Binomial options pricing model approach has been widely used since it is able to handle a variety of conditions for which other models cannot easily be applied. This is largely because the BOPM is based on the description of an underlying instrument over a period of time rather than a single point. As a consequence, it is used to value American options that are exercisable at any time in a given interval as well as Bermudan options that are exercisable at specific instances of time. Being relatively simple, the model is readily implementable in computer software (including a spreadsheet ).

Although computationally slower than the Black–Scholes formula, it is more accurate, particularly for longer-dated options on securities with dividend payments. For these reasons, various versions of the binomial model are widely used by practitioners in the options markets. [ citation needed ]

The binomial pricing model traces the evolution of the option's key underlying variables in discrete-time. This is done by means of a binomial lattice (tree), for a number of time steps between the valuation and expiration dates. Each node in the lattice represents a possible price of the underlying at a given point in time.

Valuation is performed iteratively, starting at each of the final nodes (those that may be reached at the time of expiration), and then working backwards through the tree towards the first node (valuation date). The value computed at each stage is the value of the option at that point in time.

The up and down factors are calculated using the underlying volatility , σ {\displaystyle \sigma } , and the time duration of a step, t {\displaystyle t} , measured in years (using the day count convention of the underlying instrument). From the condition that the variance of the log of the price is σ 2 t {\displaystyle \sigma ^{2}t} , we have:

,./<b5v-35/9s3 workingpaper alfredp.sloanschoolofmanagement multiperiodsecuritiesmarkets withdifferentialinformation: martingalesandresolutiontimes* by

JOURNAL OF ECONOMIC THEORY 20, 381-408 (1979) Martingales and Arbitrage in Multiperiod Securities Markets J. MICHAEL HARRISON AND DAVID M. KREPS Graduate School of ...

We model multiperiod securities markets with differential information. A price system that admits no free lunches is related to martingales when agents have rational ...

6: MULTI-PERIOD MARKET MODELS MarekRutkowski School ofMathematics andStatistics UniversityofSydney Semester 2, 2016 M. …

JOURNAL OF ECONOMIC THEORY 20, 381-408 (1979) Martingales and Arbitrage in Multiperiod Securities Markets J. MICHAEL HARRISON AND DAVID M. KREPS

Price, Trade Size, and Information Revelation in Multi-Period Securities Markets Han N. Ozsoylev Sa¨ıd Business School and Linacre College University of Oxford

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