{"title":"Value at Risk","authors":"A. Vries","doi":"10.1002/9781119595663.ch44","DOIUrl":"https://doi.org/10.1002/9781119595663.ch44","url":null,"abstract":"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","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"28 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84623604","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}
{"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}
{"title":"Pricing Fixed Income Options","authors":"","doi":"10.1002/9781119595663.ch40","DOIUrl":"https://doi.org/10.1002/9781119595663.ch40","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"5 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77967675","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}
{"title":"Interest Rate Swaps","authors":"R. Jarrow, Arkadev Chatterjea","doi":"10.1002/9781119595663.ch33","DOIUrl":"https://doi.org/10.1002/9781119595663.ch33","url":null,"abstract":"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","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"22 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77589613","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}
{"title":"Pricing Fixed Income Derivatives","authors":"","doi":"10.1002/9781119595663.ch41","DOIUrl":"https://doi.org/10.1002/9781119595663.ch41","url":null,"abstract":"","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"495 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86803961","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}
{"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}
{"title":"Interest Rate Futures","authors":"","doi":"10.1002/9781119595663.ch11","DOIUrl":"https://doi.org/10.1002/9781119595663.ch11","url":null,"abstract":"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.","PeriodicalId":40006,"journal":{"name":"Journal of Derivatives","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81736645","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}
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