Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch44
A. Vries
The main business of banks and insurance companies is risk. Banks and financial institutions lend money, running the risk of losing the lended amount, and they borrow “short money” having less risk but higher expected rates of return. Insurance companies on the other hand earn a risk premium for guaranteeing indemnifification for a negative outcome of a certain event. The evaluation of risk is essential for both kinds of business. During the 1990’s there has been established a measure for risk in finance theory as well as in practice, the Value at Risk, VaR. It was mainly popularized by J.P. Morgan’s RiskMetrics, a database supplying the essential statistical data to calculate the VaR of derivatives. In the context of finance Value at Risk is an estimate, with a given degree of confidence, of how much one can lose from a portfolio over a given time horizon. The portfolio can be that of a single trader, or it can be the portfolio of the whole bank. As a downside risk measure, Value at Risk concentrates on low probability events that occur in the lower tail of a distribution. In establishing a theoretical construct for VaR, Jorion [10] first defines the critical end of period portfolio value as the worst possible end-of-period portfolio value with a pre-determined confidence level “1− α” (e.g., 99%) These worst values should not be encountered more than α percent of the time. For example, a Value at Risk estimate of 1 million dollars at the 99% level of confidence implies that portfolio losses should not exceed 1 million dollars more than 1% of the time over the given holding period [10]. Currently, Value at Risk is being embraced by corporate risk managers as an important tool in the overall risk management process. Initial interest in VaR, however, stemmed from its potential applications as a regulatory tool. In the wake of several financial disasters involving the trading of derivatives products, such as the Barrings Bank collapse (see [10], regulatory agencies such as
银行和保险公司的主要业务是风险。银行和金融机构借钱，冒着失去贷款金额的风险，他们借“短期资金”，风险较小，但预期回报率较高。另一方面，保险公司通过保证对某一事件的负面结果进行赔偿而获得风险溢价。风险评估对这两种业务都是必不可少的。20世纪90年代，在金融理论和实践中都建立了一种衡量风险的方法，即风险价值(Value at risk, VaR)。它主要是由摩根大通的RiskMetrics推广开来的，该数据库提供了计算衍生品VaR的必要统计数据。在金融的背景下，风险价值是在给定的信心程度下，对一个投资组合在给定的时间范围内可能损失多少的估计。投资组合可以是单个交易员的投资组合，也可以是整个银行的投资组合。作为一种下行风险度量，风险值集中于发生在分布下尾的低概率事件。在建立VaR的理论结构时，Jorion[10]首先将关键期末投资组合价值定义为具有预先确定的置信水平“1 - α”(例如，99%)的最差可能期末投资组合价值，这些最差值不应超过α %的时间。例如，在99%的置信水平下，风险价值估计为100万美元，这意味着在给定的持有期间，投资组合损失不应超过1%的时间超过100万美元[10]。目前，风险价值作为整体风险管理过程中的一个重要工具被企业风险管理人员所接受。然而，最初对风险价值的兴趣源于其作为监管工具的潜在应用。在几次涉及衍生产品交易的金融灾难之后，如巴林银行的崩溃(见[10])，监管机构如
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Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch24
{"title":"Analysis of Black–Scholes","authors":"","doi":"10.1002/9781119595663.ch24","DOIUrl":"https://doi.org/10.1002/9781119595663.ch24","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"305 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86446130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch40
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Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch33
R. Jarrow, Arkadev Chatterjea
The following sections are included:IntroductionA Brief HistoryThe Introduction of Swap ContractsFrom a Brokerage to a Dealership MarketISDA and Standardization of ContractsInstitutional FeaturesEntering a Swap ContractDocumentationClosing a Swap PositionValuationVariations of Interest Rate SwapsSwaps and FRAsSynthesizing Swaps with Eurodollars and FRAsThe Yield and Swap CurveEXTENSION 22.1: Computing Forward Rates from Swap RatesSummaryCasesQuestions and Problems
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Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch41
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Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch48
The question is can we derive an equation for v(t, x)? The answer is yes, and the equation is a Partial Differential Equation (PDE): an equation connecting the partial derivatives of v in t and x, hence the name. This equation is of interest because if we can solve it, then to decide Vt we only need to plug in St for x. Of course we can decide Vt by taking Expectation via the Independence Lemma, which leads to the Black-Scholes formula. Numerically, this would lead to the pricing by simulation method: we simulate the paths of St and summing over the paths as way to approximate the expectation. The pricing of Vt by by figuring out v(t, x) would like to the numerical solution of PDE approach. This provides us with an alternative (and sometimes possibly more powerful) approach to the simulation method described above.
{"title":"Black–Scholes\u0000 PDE","authors":"","doi":"10.1002/9781119595663.ch48","DOIUrl":"https://doi.org/10.1002/9781119595663.ch48","url":null,"abstract":"The question is can we derive an equation for v(t, x)? The answer is yes, and the equation is a Partial Differential Equation (PDE): an equation connecting the partial derivatives of v in t and x, hence the name. This equation is of interest because if we can solve it, then to decide Vt we only need to plug in St for x. Of course we can decide Vt by taking Expectation via the Independence Lemma, which leads to the Black-Scholes formula. Numerically, this would lead to the pricing by simulation method: we simulate the paths of St and summing over the paths as way to approximate the expectation. The pricing of Vt by by figuring out v(t, x) would like to the numerical solution of PDE approach. This provides us with an alternative (and sometimes possibly more powerful) approach to the simulation method described above.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"19 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89662941","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-10-07DOI: 10.1002/9781119595663.ch11
a forward market. Whereas futures contracts are traded on federally designated contract markets, forward contracts are not. Each commodities exchange maintains a clearinghouse that reconciles all trades executed on the floor of the exchange. The clearinghouse interposes itself in the middle of each transaction, becoming the buyer to every seller, and the seller to every buyer. The contractual obligation of each market participant, therefore, is to the clearinghouse, eliminating the need for market participants to concern themselves with the identity or credit standing of the other party to the transaction. Members of the clearinghouse post margins on their contracts, similar to performance bonds, to ensure the financial integrity of the market. Each day the accounts of the clearing members are adjusted as to gain or loss. Losses posted to an account must be eliminated by the deposit of cash prior to the opening of trading the following day. In contrast, forward markets generally do not require margin deposits or daily settlement is the sale of a futures contract today as a temporary substitute for the sale of the actual instrument in the future. By using a short hedge, the loss on the actual instrument would be offset by a gain in the futures market when the holder buys back (offsets his short position) at an anticipated lower price. Financial institutions that own fixedincome securities or create them for sale to investors could use a short hedge to protect themselves against a rise in interest rates. For example, mortgage bankers holding a pool of mortgages for later resale to permanent investors would be vulnerable to losses on their holdings during periods of rising interest rates. By initiating a short hedge, a mortgage banker could protect himself against the price consequences of rising interest rates. The second objective-to lock in the interest cost of debt to be issued at a future time-also would entail the initiation of a short hedge in the futures market. A short hedge thus could be used by a bank in its asset/liability management. Banks especially of accounts. Parties to a forward contract are vulnerable to changes in the level of must, therefore, assess the credit worthiness of the other party to the transaction. For this reason, forward contracts may entail a greater risk of default.
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