The Mark-to-Market Value of a Forward Contract
A forward contract is an agreement between two parties to trade one currency for another on a specified future date and at a pre-determined rate. In other words, it is an exchange rate transaction whose settlement timeline exceeds T+2. The…
Spot Rate, Forward Rate, and Forward Premium/Discount
A spot exchange rate is the general price level in the market used to directly trade one currency for another, with the exchange occurring at the earliest possible time. The standard delivery time for spot currency transactions is no longer…
The Bid-offer Spread
An exchange rate is the price of the base currency expressed in terms of the price currency. For example, assume that the USD/CAD rate is 0.7625. This implies that the Canadian dollar, the base currency, costs 0.7625 US dollars (One…
Risk Governance
After completing this reading, you should be able to: Explain Basel regulatory expectations for an operational risk management framework’s governance. Describe and compare the roles of different committees and the board of directors in operational risk governance. Describe the…
Machine Learning and AI for Risk Management
After completing this reading, you should be able to: Explain the distinctions between the two broad categories of machine learning and describe the techniques used within each category. Analyze and discuss the application of AI and machine learning techniques in…
General Cash Flows, Portfolios, and Asset Liability Management
After completing this chapter, the candidate will be able to: Define and recognize the definitions of the following terms: yield rate/rate of return, current value, duration and convexity (Macaulay and modified), portfolio, spot rate, forward rate, yield curve, cash flow…
Apply the Central Limit Theorem to calculate probabilities for linear combinations of independent and identically distributed random variables
One of the most important results in probability theory is the central limit theorem. According to the theory, the sum of a large number of independent random variables has an approximately normal distribution. The theory provides a simple method of…
Calculate moments for linear combinations of independent random variables
In the previous reading, we defined \(Y=c_1X_1+c_2X_2+\ldots+c_pX_p\) to be a linear combination of the independent random variables \(X_1, X_2,\ldots, X_p\) where \(c_1,,\ c_2,\ldots,\ c_p\) are constants. We also proved that if \(X_1, X_2,\ldots,X_n\) are independent normal random variables with means…
Calculate probabilities for linear combinations of independent normal random variables
Definition: Let \(X_{1}, X_{2}, \ldots, X_{n}\) be random variables and let \(c_{1}, c_{2}, \ldots, c_{n}\) be constants. Then, $$ \text{Y}=\text{c}_{1} \text{X}_{1}+\text{c}_{2} \text{X}_{2}+\cdots+\text{c}_{\text{n}} \text{X}_{\text{n}} $$ is a linear combination of \(X_{1}, X_{2}, \ldots, X_{n}\). In this reading, however, we will only…
Determine the distribution of order statistics from a set of independent random variables
Order Statistics Order Statistics are distributions obtained when we look at test scores from a random sample arranged in ascending order, i.e., from the smallest to the largest. In recent years, the importance of order statistics has increased because of…
