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How to Model a Financial Bubble Mathematically Lecture 1 April 12, 2013
How to Model a Financial Bubble Mathematically Lecture 1 April 12, 2013

Stock option contract adjustments The case of special dividends
Stock option contract adjustments The case of special dividends

... any adjustment, based on its judgment as to what is appropriate for the protection of investors and the public interest, taking into account such factors as fairness to holder and writers (or purchasers and sellers) of affected contracts,y1 The purpose of this paper is to analyze the fairness of con ...
NBER WORKING PAPER SERIES DEMAND-BASED OPTION PRICING Nicolae Garleanu Lasse Heje Pedersen
NBER WORKING PAPER SERIES DEMAND-BASED OPTION PRICING Nicolae Garleanu Lasse Heje Pedersen

... impossibility of trading continuously, stochastic volatility, jumps in the underlying, and transaction costs (Figlewski (1989)).1 To capture this effect, we depart from the standard no-arbitrage literature that follows Black-Scholes-Merton by considering explicitly how options are priced by competit ...
Price functionals with bid-ask spreads : an axiomatic
Price functionals with bid-ask spreads : an axiomatic

How volatile are East Asian stocks during high volatility periods?*
How volatile are East Asian stocks during high volatility periods?*

Equity Quantitative Study - International Swaps and Derivatives
Equity Quantitative Study - International Swaps and Derivatives

... to MarkitServ in OTC equity options and variance swaps. Table 1 provides an overview of the transactions that were analyzed in the study in terms of sample size. For simplicity, we restricted ourselves to the three major currencies where OTC equity derivatives are traded: JPY, EUR and USD. As the re ...
PDF
PDF

Chapter 10
Chapter 10

... the analysis of derivatives. • Note that the Black–Scholes–Merton differential equation does not involve any variable that is affected by the risk preferences of investors. • The only variables are S0, T, s, and r. • So any set of risk preferences can be used when evaluating f. Let’s use risk neutra ...
The New Risk Management: The Good, the Bad
The New Risk Management: The Good, the Bad

... percent of the shares and whose holdings are undiversified): expending resources to reduce risk may benefit the large shareholders at the expense of the rest of the shareholders. Management may have a similar conflict, since risk threatens their jobs and they may have a significant proportion of the ...
DETERMINING THE FAIR PRICE OF WEATHER HEDGING
DETERMINING THE FAIR PRICE OF WEATHER HEDGING

... Weather derivatives are relatively new a la Arrow Debreu financial instruments that allow companies to limit their exposure to financial risks such as unusually high or low temperatures, the amount and duration of rainfall, the wind speed and power, etc. The dependence on the financial performance o ...
Does Option Trading Impact Underlying Stock Prices
Does Option Trading Impact Underlying Stock Prices

... theoretical models imply that this trading due to hedge rebalancing will either increase or decrease the volatility of the underlying asset, depending upon the nature (positive or negative gamma) of the option positions that are being hedged. This section develops the main testable prediction about ...
Demand-Based Option Pricing - Faculty Directory | Berkeley-Haas
Demand-Based Option Pricing - Faculty Directory | Berkeley-Haas

... denote the agents who have a fundamental need for option exposure as “end users.” Intermediaries such as market makers provide liquidity to end users by taking the other side of the end-user net demand. If competitive intermediaries can hedge perfectly — as in a Black-Scholes-Merton economy — then o ...
The Link between Real Options and finance
The Link between Real Options and finance

The nature of Jumps in Brazil`s stock market
The nature of Jumps in Brazil`s stock market

Derivatives Digest
Derivatives Digest

... Paisewallah: Is there a theoretical way of pricing futures? Sharekhan: The theoretical price of a futures contract is spot price of the underlying plus the cost of carry. Please note that futures are not about predicting future prices of the underlying assets. In general, Futures Price = Spot Price ...
Basket Options on Heterogeneous Underlying Assets
Basket Options on Heterogeneous Underlying Assets

Forecasting Stock Market Volatility and the Informational Efficiency
Forecasting Stock Market Volatility and the Informational Efficiency

... of an asset or portfolio, with risk being related to the volatility of the returns. The volatility of returns plays also a central role in the valuation of financial derivatives such as options and futures, and can, in fact, have a greater influence on the value of derivative securities than price mov ...
Failure is an Option: Impediments to Short Selling and
Failure is an Option: Impediments to Short Selling and

manual - IME-USP
manual - IME-USP

A Fully-Dynamic Closed-Form Solution for ∆-Hedging
A Fully-Dynamic Closed-Form Solution for ∆-Hedging

Chapter 8 - FBE Moodle
Chapter 8 - FBE Moodle

... • The intrinsic value is the financial gain if the option is exercised immediately (at-the-money) – This value will reach zero when the option is out-of-themoney – When the spot rate rises above the strike price, the option will be in-the-money – At maturity date, the option will have a value equal ...
An Option Pricing Model with Regime
An Option Pricing Model with Regime

(n).
(n).

Pricing Swing Options and other Electricity Derivatives
Pricing Swing Options and other Electricity Derivatives

... In this thesis we propose and examine in detail a simple mean-reverting process exhibiting price spikes. A distinct feature of electricity markets is the formation of price spikes and are caused by events where the maximum supply is approached by current demand. The occurrence of spikes has far reac ...
DaveGThesis4
DaveGThesis4

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Black–Scholes model

The Black–Scholes /ˌblæk ˈʃoʊlz/ or Black–Scholes–Merton model is a mathematical model of a financial market containing derivative investment instruments. From the model, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-style options. The formula led to a boom in options trading and legitimised scientifically the activities of the Chicago Board Options Exchange and other options markets around the world. lt is widely used, although often with adjustments and corrections, by options market participants. Many empirical tests have shown that the Black–Scholes price is ""fairly close"" to the observed prices, although there are well-known discrepancies such as the ""option smile"".The Black–Scholes model was first published by Fischer Black and Myron Scholes in their 1973 paper, ""The Pricing of Options and Corporate Liabilities"", published in the Journal of Political Economy. They derived a partial differential equation, now called the Black–Scholes equation, which estimates the price of the option over time. The key idea behind the model is to hedge the option by buying and selling the underlying asset in just the right way and, as a consequence, to eliminate risk. This type of hedging is called delta hedging and is the basis of more complicated hedging strategies such as those engaged in by investment banks and hedge funds.Robert C. Merton was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term ""Black–Scholes options pricing model"". Merton and Scholes received the 1997 Nobel Memorial Prize in Economic Sciences for their work. Though ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the Swedish Academy.The model's assumptions have been relaxed and generalized in many directions, leading to a plethora of models that are currently used in derivative pricing and risk management. It is the insights of the model, as exemplified in the Black-Scholes formula, that are frequently used by market participants, as distinguished from the actual prices. These insights include no-arbitrage bounds and risk-neutral pricing. The Black-Scholes equation, a partial differential equation that governs the price of the option, is also important as it enables pricing when an explicit formula is not possible.The Black–Scholes formula has only one parameter that cannot be observed in the market: the average future volatility of the underlying asset. Since the formula is increasing in this parameter, it can be inverted to produce a ""volatility surface"" that is then used to calibrate other models, e.g. for OTC derivatives.
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