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Derivative (finance)
Derivative (finance)

Derivative (finance)
Derivative (finance)

... In finance, a derivative is a financial instrument derived from some other asset; rather than trade or exchange of the asset itself, market participants enter into an agreement to exchange money, assets or some other value at some future date based on the underlying asset. A simple example is a futu ...
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... Barrier options are a generic name given to derivative securities with payoffs which are contingent on the spot price reaching a certain level, or barrier over the life time of the option. A number of different types of barrier option regularly trade over the counter (OTC) market. They attractive to ...
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... • A new concept is elicitability, that means that there exists a function such that one can measure whether a measure is better then another. • In other words, a measure is elicitable if it results from the optimization of a function. For example, minimizing a quadratic function yields the mean, whi ...
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... European Installment options (Davis, Schachermayer, and Tompkins (2001)) ...
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Note présentée au Collège

Option Value = 162 - 145 = $17 mil
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... project are shown. The project costs $180 million, either now or later. The figures in parentheses show payoffs from the option to wait and to invest later if the project is positive-NPV at year 1. Waiting means loss of the first year’s cash flows. The problem is to figure out the current value of t ...
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Pricing and Hedging under the Black-Merton

... discount back with riskfree rate, we do not really care about the actual probability of each scenario happening. We just care about what all the possible scenarios are and whether our hedging works under all scenarios. Q is not about getting close to the actual probability, but about being fair wrt ...
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... Employees of economic and foreign departments of large enterprises do not usually use these instruments because they do not know them very well, and they are afraid of these processes. They have not understood importance and significance of financial derivatives. Before 1989, these instruments used ...
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... Futures contracts are mark-to-market, which means that gains and losses are settled at the close of trading each day, not at the end of the contract. The reporting of financial futures differs from that of spot markets. The prices listed are points of 100 percent, not percentages of face value. Bris ...
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... The initial focus of the dissertation is to analyze the current pricing models of financial derivatives, including the effects of volatility risk and uncertainty. Most option pricing schemes formulated to date have been based on the classical Black-Scholes theory (1973). Black and Scholes have model ...
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... arbitrage in the market. These restrictions can be difficult to enforce, however, when we are “bumping” or “stressing” the volatility surface, a task that is commonly performed for risk management purposes. Why is there a Skew? For stocks and stock indices the shape of the volatility surface is alwa ...
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... •  See Figure 17.3 or 18.3 (call) and 17.4 or 18.4 (put) • Delta of call always between zero and 1. • Delta of put always between -1 and 0. ...
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... The parameter /3 is a discount factor; changing /3 affects the interest rate. The function m(V, y) is a differentiable function of the asset price and a "risk aversion" parameter y.1 The important economic content of equation (2) is that M does not depend on the probability density parameter 0. In w ...
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... The purpose of this paper is to derive the prices of yield options in the ECIR( δ ( t ) ) model by assuming that the market is complete and arbitrage-free. Nowadays, both European and American options on yields are incorporated in different interest-rate derivatives like e.g. interest-rate caps, flo ...
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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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