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When t=T
When t=T

...  Since each risky asset in the portfolio pays dividend at a certain rate at certain times, the number of dividend payments for the portfolio would be large, and we can approximate it as continuous payment (dividend rate can be timedependent). ...
Options and Risk Measurement
Options and Risk Measurement

... option is the right but not the obligation to sell 100 shares of the stock at a stated exercise price on or before a stated expiration date.  The price of the option is not the exercise price. ...
1 The Greek Letters
1 The Greek Letters

Modeling Asset Prices in Continuous Time
Modeling Asset Prices in Continuous Time

... •  This involves initially SELLING enough of the portfolio (or of index futures) to match the Δ of the put option ...
Institute of Actuaries of India  INDICATIVE SOLUTION
Institute of Actuaries of India INDICATIVE SOLUTION

... for the portfolio and then to hedge the guarantee risk they need to buy a put option. Since derivative markets may not be deep, the fund manager may synthesize the option contract by regularly buying the stocks and lending/borrowing money. At times the manager may use futures in place of stocks beca ...
Chpt 6 - Glen Rose FFA
Chpt 6 - Glen Rose FFA

...  Buyer of a corn put pays $1,000 ($.20 x 5,000) to the seller of the put  If the option is worthless at the time he is ready to sell his corn, let it expire, and lose ...
Having Your Options and Eating Them Too
Having Your Options and Eating Them Too

... If, at the end of the two-year period, the market price of the company’s shares is below $10.00, both the ESOP and the covered call options will expire worthless, but the executive will retain the premium paid by the holder of the covered call options. If, however, the market price is $20.00, both s ...
A EXTENDED WITH ROBUST OPTION REPLICATION FOR BLACK-
A EXTENDED WITH ROBUST OPTION REPLICATION FOR BLACK-

... effects and B h is fBm with Hurst index h E It is known that B h for h E 1[ is a process of unbounded variation and square variation zero. See [8, 10]. From this it follows that B h is not a semi-martingale and the use of fractional Brownian motion B h or a more general process Z with zero quadratic ...
The cost of preferred stock is equal to the preferred
The cost of preferred stock is equal to the preferred

... people consider preferred stock to be more like debt than equity. ...
Greeks- Theory and Illustrations
Greeks- Theory and Illustrations

... many Euro dollar futures contracts are needed to hedge the portfolio? A Eurodollar contract has a face value of $ 1 million and a maturity of 3 months. If rates change by 1 basis point, the value changes by (1,000,000) (.0001)/4= $ 25. So the number of futures contracts needed = 1100/25=44 ...
FINANCIAL DERIVATIVES FOR BEGINNERS
FINANCIAL DERIVATIVES FOR BEGINNERS

9 Complete and Incomplete Market Models
9 Complete and Incomplete Market Models

... Under a stochastic volatility model, the market is incomplete. No unique price. More random sources than traded assets. It is not always possible to hedge a generic contingent claim. Captures more empirical characteristics. ...
International Banking - Module A Part II
International Banking - Module A Part II

... which one grants the other the right to buy (‘call’ option) or sell (‘put’ option) an asset under specified conditions (price, time) and assumes the obligation to sell or buy it. • The party who has the right but not the obligation is the ‘buyer’ of the option and pays a fee or premium to the ‘write ...
(Module A) – Part II
(Module A) – Part II

... which one grants the other the right to buy (‘call’ option) or sell (‘put’ option) an asset under specified conditions (price, time) and assumes the obligation to sell or buy it. • The party who has the right but not the obligation is the ‘buyer’ of the option and pays a fee or premium to the ‘write ...
Appendix C Taxation - Inquiry report
Appendix C Taxation - Inquiry report

RMTF - The Greeks - Society of Actuaries
RMTF - The Greeks - Society of Actuaries

... Strengths and Weaknesses of the Greeks The concept of using partial derivatives in pricing and hedging options and other financial instruments is well known and mathematically correct. It is necessary to evaluate some of these derivatives to understand the risk in a portfolio. However, the partial d ...
an investor`s guide to index futures
an investor`s guide to index futures

... sale of a particular asset at a specific future date. The price at which the asset would change hands in the future is agreed upon at the time of entering into the contract. The actual purchase or sale of the underlying involving payment of cash and delivery of the instrument does not take place unt ...
24. Portfolio Insurance and Synthetic Options
24. Portfolio Insurance and Synthetic Options

... Stop Loss Order - a conditional market order which indicates that the investor wishes to sell his holdings when the market price (asset price) drops to a predefined level. ...
Option Pricing - Department of Mathematics, Indian Institute of Science
Option Pricing - Department of Mathematics, Indian Institute of Science

... We have thus far analyzed the value of the option CT (or PT ) at the expiration date. At any time t between 0 to T , the option has a value Ct (or Pt ). We say that a call option at time t is in the money, at the money, or out of the money depending on whether St > K, St = K, or St < K, respectively ...
Why We Have Never Used the Black-Scholes
Why We Have Never Used the Black-Scholes

Currency derivatives Currency derivatives are a contract between
Currency derivatives Currency derivatives are a contract between

... agreements, foreign currency swaps, foreign currency-rupee swaps, foreign currency options, foreign currency-rupee options or such other instruments as may be specified by RBI from time to time. 2.2 Derivative products Though derivatives can be classified based on the underlying asset class (such as ...
Why We Have Never Used the Black-Scholes
Why We Have Never Used the Black-Scholes

... known—formula. The argument, we will see, is extremely fragile to assumptions. The foundations of option hedging and pricing were already far more firmly laid down before them. The Black-Scholes-Merton argument, simply, is that an option can be hedged using a certain methodology called “dynamic hedg ...
The Greek Letters
The Greek Letters

... Hedging in Practice • Traders usually ensure that their portfolios are delta-neutral at least once a day • Whenever the opportunity arises, they improve gamma and vega • As portfolio becomes larger hedging becomes less expensive Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. ...
Chapter 19 | You Will Learn... 1. To detail recent changes in
Chapter 19 | You Will Learn... 1. To detail recent changes in

FROM NAVIER-STOKES TO BLACK-SCHOLES
FROM NAVIER-STOKES TO BLACK-SCHOLES

< 1 ... 12 13 14 15 16 17 18 19 20 >

Employee stock option

An employee stock option (ESO) is commonly viewed as a complex call option on the common stock of a company, granted by the company to an employee as part of the employee's remuneration package. Regulators and economists have since specified that ""employee stock options"" is a label that refers to compensation contracts between an employer and an employee that carries some characteristics of financial options but are not in and of themselves options (that is they are ""compensation contracts"").As described in the AICPA's Financial Reporting Alert on this topic, for the employer who uses ESO contracts as compensation, the contracts amount to a ""short"" position in the employer's equity, unless the contract is tied to some other attribute of the employer's balance sheet. To the extent the employer's position can be modeled as a type of option, it is most often modeled as a ""short position in a call."" From the employee's point of view, the compensation contract provides a conditional right to buy the equity of the employer and when modeled as an option, the employee's perspective is that of a ""long position in a call option."" Employee Stock Options are non standard contracts with the employer whereby the employer has the liability of delivering a certain number of shares of the employer stock, when and if the employee stock options are exercised by the employee. Traditional employee stock options have structural problems, in that when exercised followed by an immediate sale of stock, the alignment between employee/shareholders is eliminated. Early exercises also have substantial penalties to the exercising employee. Those penalties are a) part of the ""fair value"" of the options, called ""time value"" is forfeited back to the company and b) an early tax liability occurs. These two penalties overcome the merits of ""diversifying"" in most cases.Stock option expensing was a controversy well before the most recent set of controversies in the early 2000s. The earliest attempts by accounting regulators to expense stock options in the early 1990s were unsuccessful and resulted in the promulgation of FAS123 by the Financial Accounting Standards Board which required disclosure of stock option positions but no income statement expensing, per se. The controversy continued and in 2005, at the insistence of the SEC, the FASB modified the FAS123 rule to provide a rule that the options should be expensed as of the grant date. One misunderstanding is that the expense is at the fair value of the options. This is not true. The expense is indeed based on the fair value of the options but that fair value measure does not follow the fair value rules for other items which are governed by a separate set of rules under ASC Topic 820. In addition the fair value measure must be modified for forfeiture estimates and may be modified for other factors such as liquidity before expensing can occur. Finally the expense of the resulting number is rarely made on the grant date but in some cases must be deferred and in other cases may be deferred over time as set forth in the revised accounting rules for these contracts known as FAS123(revised).
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