Wiener Process and Ito's lemma process
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The document discusses stochastic processes for modeling stock prices, including Wiener processes, generalized Wiener processes, and Ito processes. It explains that Ito processes are continuous-time, continuous-variable processes best suited for modeling stock prices, with the stock price following a process where the return and volatility are functions of the stock price and time. The document also summarizes Ito's lemma, which describes the stochastic process followed by functions of variables that themselves follow stochastic processes.
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- Key factors like strike price, expiration date, and underlying assets.
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This document discusses options on financial futures contracts. It defines call and put options, explaining that a call option gives the buyer the right to buy the underlying asset and a put option gives the buyer the right to sell. It describes how option value is determined from intrinsic value and time value. The document provides examples of how buying and selling options can be used by commercial banks to hedge their interest rate risk exposures from rising or falling rates. In general, options limit potential losses compared to futures but also cap potential gains.
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This document describes a stock price model based on the voter model from statistical physics. The model represents stock investors on a lattice who can be in a buying, selling, or neutral position based on interactions with neighboring investors. The stock price is then derived from the positions of investors. Computer simulations of the 1D model are presented, showing the fluctuations of generated stock prices and returns. The document also discusses properties found in real stock market data, such as power law distributions and volatility clustering, that the model aims to replicate.
Black scholes pricing consept
This document discusses the Black-Scholes pricing concept for options. It summarizes two popular derivations of the Black-Scholes equation, the original derivation and an alternative presented in other literature. It also discusses ambiguities that have been noted in the derivation of the Black-Scholes equation and proposes corrections to the derivation using modern stochastic calculus. Specifically, it introduces a hedged portfolio function defined over two variables to accurately represent the value and dynamics of the hedged portfolio. The document concludes that the Black-Scholes pricing concept only guarantees a risk-free return at a single point in time and does not necessarily reflect market prices.
Black scholes pricing concept
This document discusses the Black-Scholes pricing concept for options. It summarizes two common derivations of the Black-Scholes equation, the original by Black and Scholes which uses a hedged position consisting of a long stock position and short option position. An alternative derivation presented in some textbooks uses a hedged position consisting of a long option position and short stock position. The document also notes that while the Black-Scholes price guarantees a risk-free return at a single moment in time, it does not necessarily reflect market prices and there is no guarantee the market will use the Black-Scholes price.
Black scholes pricing consept
This document discusses the Black-Scholes pricing concept for options. It summarizes two common derivations of the Black-Scholes equation, the original by Black and Scholes which uses a hedged position consisting of a long stock position and short option position. An alternative derivation presented in some textbooks uses a hedged position consisting of a long option position and short stock position. The document also notes that while the Black-Scholes price guarantees a risk-free return at a single point in time, it does not necessarily reflect market prices and there is market risk for the option seller at future times.
Black scholes pricing concept
. In some papers it have been remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular in [2,3 ] there are two problems which can be raise by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and other the pricing definition of the option.
In this paper, we show how the ambiguities in derivation of the BSE can be eliminated.
We pay attention to option as a hedging instrument and present definition of the option price based on market risk weighting. In such approach, we define random market price for each market scenario. The spot price then is interpreted as a one that reflects balance between profit-loss expectations of the market participants.
Ch01HullOFOD8thEdition.pptx
1. Derivatives are financial instruments whose value is based on an underlying asset such as a stock, currency, or commodity. Examples include futures, forwards, swaps, and options.
2. Derivatives play a key role in transferring risk between parties. They are traded both over-the-counter between private parties and on exchanges.
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1. Derivatives are financial instruments whose value is based on an underlying asset such as a stock, currency, or commodity. Examples include futures, forwards, swaps, and options.
2. Derivatives play a key role in transferring risk between parties. They are traded both over-the-counter between private parties and on exchanges.
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In this paper, we show how the ambiguities in derivation of the BSE can be eliminated.
We pay attention to option as a hedging instrument and present definition of the option price based on market risk weighting. In such approach, we define random market price for each market scenario. The spot price then is interpreted as a one that reflects balance between profit-loss expectations of the market participants.
Black scholes pricing concept
In this paper, we show how the ambiguities in derivation of the BSE can be eliminated.
We pay attention to option as a hedging instrument and present definition of the option price based on market risk weighting. In such approach, we define random market price for each market scenario. The spot price then is interpreted as a one that reflects balance between profit-loss expectations of the market participants.
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Wiener Process and Ito's lemma process
- 1. Wiener Processes and Itô’s Lemma Chapter 12 Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008
- 21. Monte Carlo Simulation – One Path (See Table 12.1, page 268) Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
- 24. Ignoring Terms of Higher Order Than t Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
- 25. Substituting for x Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
- 26. The 2 t Term Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
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