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Jamshidian's Trick
Jamshidian's trick is a technique for one-factor asset price models, which re-expresses an option Option or Options may refer to: Computing *Option key, a key on Apple computer keyboards *Option type, a polymorphic data type in programming languages *Command-line option, an optional parameter to a command *OPTIONS, an HTTP request method ... on a portfolio of assets as a portfolio of options. It was developed by Farshid Jamshidian in 1989. The trick relies on the following simple, but very useful mathematical observation. Consider a sequence of monotone (increasing) functions f_i of one real variable (which map onto strike of the option on the portfolio of assets. We can therefore express the payoff of an option on a portfolio of assets in terms of a portfolio of options on the individual assets f_i(W) with corresponding strikes f_i(w). References *Jamshidian, F. (1989). "An exact bond option pricing formula," Journal of Finance, Vol 44, pp 205-209 Mathematical fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asset Pricing
In financial economics, asset pricing refers to a formal treatment and development of two main pricing principles, outlined below, together with the resultant models. There have been many models developed for different situations, but correspondingly, these stem from either general equilibrium asset pricing or rational asset pricing, the latter corresponding to risk neutral pricing. Investment theory, which is near synonymous, encompasses the body of knowledge used to support the decision-making process of choosing investments, and the asset pricing models are then applied in determining the asset-specific required rate of return on the investment in question, or in pricing derivatives on these, for trading or hedging. (See also .) General Equilibrium Asset Pricing Under General equilibrium theory prices are determined through market pricing by supply and demand. Here asset prices jointly satisfy the requirement that the quantities of each asset supplied and the qua ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Option (finance)
In finance, an option is a contract which conveys to its owner, the ''holder'', the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or financial instrument, instrument at a specified strike price on or before a specified expiration (options), date, depending on the Option style, style of the option. Options are typically acquired by purchase, as a form of compensation, or as part of a complex financial transaction. Thus, they are also a form of asset and have a Valuation of options, valuation that may depend on a complex relationship between underlying asset price, time until expiration, market volatility, the risk-free rate of interest, and the strike price of the option. Options may be traded between private parties in ''Over-the-counter (finance), over-the-counter'' (OTC) transactions, or they may be exchange-traded in live, public markets in the form of standardized contracts. Definition and application An option is a contract that all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Portfolio (finance)
In finance, a portfolio is a collection of investments. Definition The term “portfolio” refers to any combination of financial assets such as stocks, bonds and cash. Portfolios may be held by individual investors or managed by financial professionals, hedge funds, banks and other financial institutions. It is a generally accepted principle that a portfolio is designed according to the investor's risk tolerance, time frame and investment objectives. The monetary value of each asset may influence the risk/reward ratio of the portfolio. When determining asset allocation, the aim is to maximise the expected return and minimise the risk. This is an example of a multi-objective optimization problem: many efficient solutions are available and the preferred solution must be selected by considering a tradeoff between risk and return. In particular, a portfolio A is dominated by another portfolio A' if A' has a greater expected gain and a lesser risk than A. If no portfolio domina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Farshid Jamshidian
Farshid Jamshidian is a finance researcher, academic and practitioner. His experience covers both fixed-income and equity research and trading. Dr. Jamshidian has made important contributions to the theory of derivatives pricing, and has published extensively, especially on interest rate modelling, amongst other contributions, developing the use of the forward measure, and " Jamshidian's trick", widely applied in the pricing of bond options. He is professor of Applied Mathematics at the University of Twente, and is at NIBC Bank. He is a member of the Editorial Board of ''The Journal of Fixed Income''. Previously he was managing director of NetAnalytic, a risk management products and services company he founded in 1999; Managing Director of New Products and Equity Derivatives at Sakura Global Capital; Executive Director of Technical Trading at Fuji International Finance; and head of quantitative fixed-income research at Merrill Lynch. As an academic, he was an associate edito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonic Function
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus and analysis In calculus, a function f defined on a subset of the real numbers with real values is called ''monotonic'' if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called ''monotonically increasing'' (also ''increasing'' or ''non-decreasing'') if for all x and y such that x \leq y one has f\!\left(x\right) \leq f\!\left(y\right), so f preserves the order (see Figure 1). Likewise, a function is called ''monotonically decreasing'' (also ''decreasing'' or ''non-increasing'') if, whenever x \leq y, then f\!\left(x\right) \geq f\!\left(y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads H and tails T) in a sample space (e.g., the set \) to a measurable space, often the real numbers (e.g., \ in which 1 corresponding to H and -1 corresponding to T). Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a rando ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strike Price
In finance, the strike price (or exercise price) of an option is a fixed price at which the owner of the option can buy (in the case of a call), or sell (in the case of a put), the underlying security or commodity. The strike price may be set by reference to the spot price, which is the market price of the underlying security or commodity on the day an option is taken out. Alternatively, the strike price may be fixed at a discount or premium. The strike price is a key variable in a derivatives contract between two parties. Where the contract requires delivery of the underlying instrument, the trade will be at the strike price, regardless of the market price of the underlying instrument at that time. Moneyness Moneyness is the value of a financial contract if the contract settlement is financial. More specifically, it is the difference between the strike price of the option and the current trading price of its underlying security. In options trading, terms such as ''in-the-m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Finance
''The Journal of Finance'' is a peer-reviewed academic journal published by Wiley-Blackwell on behalf of the American Finance Association. It was established in 1946 and is considered to be one of the premier finance journals. The editor-in-chief is Antoinette Schoar. According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 7.544. It is listed as one of the 50 journals used by the ''Financial Times'' to compile its business-school research ranking and ''Bloomberg Businessweek''s Top 20 Journals. Editors The editorial board of the journal of finance consists of the editor, co-editors and associate editors. The executive editor is Antoinette Schoar (MIT), the first female in the position. The following persons are or have been editor-in-chief of the journal: Awards Each year the associate editors vote for the best papers published in the journal. The Smith Breeden Prize is awarded for the best finance papers and the Brattle Prize for the best corporat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios. French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fixed Income Analysis
Fixed income analysis is the process of determining the value of a debt security based on an assessment of its risk profile, which can include interest rate risk, risk of the issuer failing to repay the debt, market supply and demand for the security, call provisions and macroeconomic considerations affecting its value in the future. It also addresses the likely price behavior in hedging portfolios. Based on such an analysis, a fixed income analyst tries to reach a conclusion as to whether to buy, sell, hold, hedge or avoid the particular security. Fixed income products are generally bonds: debt instruments requiring the issuer (i.e. the debtor or borrower) to repay the lender the amount borrowed (principal) plus interest over a specified period of time (coupon payments) until maturity. They are issued by government treasuries, government agencies, companies or international organizations. Calculating Value To determine the value of a fixed income security, the analyst must ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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