• Study Resource
  • Explore Categories
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
Valuing a European option with the Heston model
Valuing a European option with the Heston model

... In modern financial analysis, due to some limitations of Black-Scholes equation, stochastic process theories are prevalent for asset pricing, especially in option pricing. Lots of mathematicians and statisticians are focusing on determining the behavior of the underlying assets in both academic and ...
Share options
Share options

50 The LC Gupta Committee Report: Some Observations
50 The LC Gupta Committee Report: Some Observations

... India has seen significant improvements during the nineties with the introduction of screen-based trading, creation of depositories, and dematerialisation of some of the shares; the participants in equity trading have had long exposures to this activity and hence have a fairly good understanding of ...
Lecture Notes on Optimal Control
Lecture Notes on Optimal Control

... Applications of Dynamic Programming The versatility of the dynamic programming method is really only appreciated by exposure to a wide variety of applications. In this chapter we look at applications of the method organized under four distinct rubrics. In Section 1, we consider problems in which the ...
Term Structure Lattice Models
Term Structure Lattice Models

... It is very easy to hedge in a binomial-lattice model. For example, if we wish to hedge a payoff that occurs at t = s, then we can use any two securities (that do not expire before t = s) to do this. In particular, we could use the cash account and a zero-coupon bond with maturity t > s as our hedgin ...
Derivatives - Karvy Fortune
Derivatives - Karvy Fortune

...  Expiry date: It is the date specified in the futures contract. This is the last day on which the contract will be traded, at the end of which it will cease to exist.  Contract size: The amount of asset that has to be delivered under one contract. Also called as lot size.  Basis: In the context o ...
Risk Measures Guide - The Albridge Resource Center
Risk Measures Guide - The Albridge Resource Center

... Up-Market Capture Ratio - The Up-Market capture ratio is a measure of a manager's performance in up markets relative to the index during the same period. A ratio value of 115 indicates that the manager has outperformed the market index by 15% in periods when the index has risen (higher is better). D ...
full text
full text

... density with market observed spot prices. Strong and Xu (1999) repeat similar tests as in Longstaff (1995) but use the S&P 500 index options instead of the S&P 100 options. They claim that the martingale restriction cannot be rejected for the S&P 500 index calls and puts over the period from 1990 to ...
УДК 336.7 JEL Code G10 С.М. ДЕНЬГА (Полтавський університет
УДК 336.7 JEL Code G10 С.М. ДЕНЬГА (Полтавський університет

... implementation of certain operations. The market agent exposed every minute some risk because of their dependence on market factors such as interest rates, exchange rates and prices of goods. To avoid losses from foreign currency transactions, which expect a break in time of shipment and payment or ...
Mid-term 1 solution
Mid-term 1 solution

Answers to Concepts Review and Critical Thinking Questions
Answers to Concepts Review and Critical Thinking Questions

... to occur forever, that is, the stock provides dividends in perpetuity, and (ii) if a constant growth rate of dividends occurs forever. A violation of the first assumption might be a company that is expected to cease operations and dissolve itself some finite number of years from now. The stock of su ...
In segregating responsibilities, this office reconciles payments with
In segregating responsibilities, this office reconciles payments with

... derivatives EOY(end of year)of 2010? (A) Commodity contracts (B) Foreign exhange contracts (C) Credit default swaps (D) Interest rate contracts 46. What are the contract months available for trading? (A) the 4 nearest serial months (B) the quarterly months of March, June, September and December (C) ...
American Options
American Options

Options on Energy Portfolios in an HJM Framework
Options on Energy Portfolios in an HJM Framework

... approach in Munk(1999), and we find that this numerical method produces results quite close to the “true” prices found through Monte Carlo simulation. Key words: Stochastic exchange rates, forward and futures prices, convenience yields, options, portfolios of single-delivery contracts, flow forwards ...
Equity Compensation Seminar Slides
Equity Compensation Seminar Slides

... Black-Scholes is the most broadly used and practical model for valuing employee stock options for decision support because the assumptions used are less complicated than alternatives The Binomial model is an alternative to BlackScholes that financial experts believe can produce lower values for expe ...
Finance Math Refresher
Finance Math Refresher

... fraction) of integers, and a denominator of non-zero. Formally, Q = p / q where p, q ϵ Z (reads: p and q are elements of the Integer number set Z) and q ≠ 0. As a consequence, rational numbers have finite decimals. d) Irrational numbers are numbers that cannot be expressed as quotient of integers wi ...
Pricing Bermudan Style Swaptions Using the Calibrated Hull White
Pricing Bermudan Style Swaptions Using the Calibrated Hull White

... When choosing models for valuing interest rate derivatives, the derivatives can be divided into two major groups. The first group consists the European style derivatives. These can be valued using Black’s model, which is a generalization of the Black-Scholes model. A full description of how to use t ...
FIN 472 Fixed-Income Analysis Term
FIN 472 Fixed-Income Analysis Term

... of (riskfree) option-free coupon bonds up to maturity T – can be priced directly from the zero rates (or zero discount YC) by bootstrapping the original set of coupon bonds (t=1,…,T). – One intuition from the above is that therefore the calibration will not affect such option-free bond prices. ...
OPTIONS HEDGING AS A MEAN OF PRICE RISK ELIMINATION
OPTIONS HEDGING AS A MEAN OF PRICE RISK ELIMINATION

Las Vegas Callable Debt Workshop Jim Zucco – Director
Las Vegas Callable Debt Workshop Jim Zucco – Director

... Fannie Mae issues callable debt instruments with a variety of maturity dates along the yield curve. ...
Expected Dividend Growth and Valuation Ratios
Expected Dividend Growth and Valuation Ratios

Solutions to Questions and Problems
Solutions to Questions and Problems

Contract Specifications for Option Contract on EURUSD
Contract Specifications for Option Contract on EURUSD

... Deep-out-of-the-money short options may show zero or minimal Scan Risk given the price and volatility moves in the 16 market scenarios, yet still present risk in the event that these options move closer-to-the-money or in-the-money, thereby generating potentially large losses. Hence a Short Option M ...
PowerPoint for Chapter 3
PowerPoint for Chapter 3

... From Table 3-1, the arithmetic mean of J&J stock HPYs over a 10-year period, 1999–2009, can be calculated as: ...
LEV
LEV

... 1. Alternate Rate of Return (ARR): The rate an investor can earn in his/her best comparable alternative investment. (Note: An alternative investment must be comparable in terms of risk, liquidity; taxes, transaction costs and time period) ...
< 1 ... 10 11 12 13 14 15 16 17 18 ... 35 >

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.
  • studyres.com © 2026
  • DMCA
  • Privacy
  • Terms
  • Report