Real world exposure and CVA simulation
The risk-neutral approach assumes that asset prices follow stochastic process with drift coinciding with the short rate r(t) being risk-free interest rate. dS(t)=S(t)[rdt+σ(S(t),t) 〖dW〗^Q (t)]
Instead, in real-world measure they follow more complex process, which embodies time and risk aversion of investors, namely: dS(t)=S(t)[μ(S(t),t)dt+σ(S(t),t) 〖dW〗^R (t)] or, equivalently, a process with real-world stochastic discount factors which depend on risk-free interest rates but also on asset prices itself.
The form of this process with almost arbitrary process’s drift term complicates the implementation; for example, makes it difficult in practice to simulate asset prices through standard analytic or quasi-analytic approaches of measure transformation via Girsanov theorem. Let alone the case of imperfect replication with infinite number of no-arbitrage consistent measures, the absence of the unambiguous common real-world measure, as opposed to risk-neutral ones, make real-world simulation much more difficult to implement that risk-neutral one.
Having a limited supply of analytic or quasi-analytic shortcuts and unique no-arbitrage consistent measure, practitioners often choose a brute force approach for risk management purposes such as real-world PFE and CVA simulations, which both require full simulation of exposure distributions for any other-than-vanilla instrument. This brute force approach, known as nested Monte Carlo on Monte Carlo, comprises the following two steps repeated in a loop: drawing real-world yield curves and other relevant market factors at all forward model steps using explicit model assumptions (equivalently, assumptions on drift terms) for a subset of stochastic paths,
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...k-neutral market models.
Nested Monte Carlo schema requires calculation of instrument
There are a few shortcuts for vanilla instruments. One can omit next nested Monte Carlo step and just price vanilla instruments off the forward curves at each model step t_i. Similarly, one can reduce the pricing of vanilla caps or swaptions to interpolation mechanism of forward volatilities/prices, which is an effective but valid way to avoid building nested evolution model.
For weak path-dependent instruments such as Bermudan callable instruments, which permit representation of conditional exposures as nonlinear function of some market states or non-callable underlying exposures, there is a way to avoid by reusing standard risk-neutral American Monte Carlo results.
Works Cited
Solvency II and Nested Simulations - a Least-Squares Monte Carlo Approach
Staum
Riccardo Rebonato
Also, the usage of high yield bonds securities for financing became popular during the 1990s in foreign markets such as Latin America, Asia, and Europe showing the rise in international appeal for these kinds of securities. However, outside of the U.S the high yield market has taken a longer time to become popular and thus there is still room for the development of high yield bonds within financial markets in emerging countries. It is safe to determine that the market for high-yield bonds will always be in existence since it is a viable alternative for many fast growing firms to acquire financing and is a rewarding option for investors. The key to the still growing, strong market demand for high yield bonds is based on linking the [U.S.] economy’s constant desire for capital with investors’ desire for higher returns on their investment.
The aim of this paper is to cover how each area of the simulation relates to what we have discussed in the class. We are going to discuss target market, 4p’s of marketing, performance metrics and research data.
Banc One uses the following investment to manage interest rate exposure. In the early 1980s, Esty, Tufano and Headley (1998) mentioned that it managed its exposure to interest rate risk by adding balancing assets to its investment portfolio until it felt it had enough fixed-rate investments to offset its fixed-rate liabilities. In 1983, Banc One began to use interest rate swaps to manage interest rate exposure. Swaps will be discussed in the later paragraphs. In 1986, Mortgage-Backed Securities (MBSs) was introduced.
Even though most of us may not realized it, interest rate actually play an important role in our everyday lives due to its great effect on the buying power. For instances, if the interest rate is higher, people tend to reduce their spending and rather save it in the deposit account due to the large interest that they can gained. However, if the interest rate is lower, they rather spend it than keeping it in the deposit account. The reason for this is because the ups and down of the interest rates have a significant impact on their personal income. Furthermore, since interest rate have a major impact on investment it is important for the investors to keep track on these interest rate’s trend before making any decision.
...al portfolio based on risk preferences, personal constraints and investment objectives following the Mean-Variance Theory. We have applied a CPPI strategy to allocate assets dynamically over-time and highlighted its superiority compared to the Market and Benchmark Portfolios. We have used both classical (e.g. Sharpe Ratio) and advanced performance measures (e.g. T2, Omega Ratio). We have identified that much of the portfolio’s performance can be attributed to the Selection Effect. The significant MoM indicates the presence of Momentum Effect in the portfolio’s returns. We have highlighted the contribution of Omega Ratio in modern portfolio management because of its ability to capture Higher Moments. Overall, we conclude that insurance strategies, such as CPPI, can be quite useful when investors seek insurance against rapid falls in the market and crash in equities.
6. Data Download Program, The Federal Reserve Board, 5 Aug 2009, web. 6Dec. 2009 www.federalreserve.gov/datadownload,
Answer: Monte Carlo simulation is a very flexible technique and could easily be adapted or extended. Usually, when it is difficult or, sometimes, even impossible to obtain a closed-form expression of certain results or attributes, it becomes very useful [1]. Because, through repeated random sampling, we might be able to obtain approximate values of our desired results or attributes.
The higher the index value, the higher the excess returns received by the unit system risk. Is the return indicator of each unit market risk, more than possible in the risk-free investment to obtain the return indicators. It is used to measure the return for risk
The concept of beta has gained prominence due to the pioneering works of Sharpe (1963), Lintner (1965) and Mossin (1966). There are many studies that examine the behaviour and nature of beta. These studies include the impact of the length of the estimation interval, the stability of individual security beta as compared to portfolio beta, factors influencing the beta as well as the stability of beta in various market conditions.
Investment theory is based upon some simple concepts. Investors should want to maximize their return while minimizing their risk at the same time. In order to accomplish this goal investors should diversify their portfolios based upon expected returns and standard deviations of individual securities. Investment theory assumes that investors are risk averse, which means that they will choose a portfolio with a smaller standard deviation. (Alexander, Sharpe, and Bailey, 1998). It is also assumed that wealth has marginal utility, which basically means that a dollar potentially lost has more perceived value than a dollar potentially gained. An indifference curve is a term that represents a combination of risk and expected return that has an equal amount of utility to an investor. A two dimensional figure that provides us with return measurements on the vertical axis and risk measurements (std. deviation) on the horizontal axis will show indifference curves starting at a point and moving higher up the vertical axis the further along the horizontal axis it moves. Therefore a risk averse investor will choose an indifference curve that lies the furthest to the northwest because this would r...
see, foreign exchange hedging was an area of key importance for AIFS given the level of currency
Ravi, Sreenivasan. "Statistical And Probabilistic Methods In Actuarial Science." Journal Of The Royal Statistical Society: Series A (Statistics In Society) 172.2 (2009): 530. Business Source Premier. Web. 25 Oct. 2013.
Chapter 11 closes our discussion with several insights into the efficient market theory. There have been many attempts to discredit the random walk theory, but none of the theories hold against empirical evidence. Any pattern that is noticed by investors will disappear as investors try to exploit it and the valuation methods of growth rate are far too difficult to predict. As we said before the random walk concludes that no patterns exist in the market, pricing is accurate and all information available is already incorporated into the stock price. Therefore the market is efficient. Even if errors do occur in short-run pricing, they will correct themselves in the long run. The random walk suggest that short-term prices cannot be predicted and to buy stocks for the long run. Malkiel concludes the best way to consistently be profitable is to buy and hold a broad based market index fund. As the market rises so will the investors returns since historically the market continues to rise as a whole.
Asset prices instantly and completely reflect all information of the previous prices. This means future price variations can’t be foreseen by using preceding prices.
The Modern portfolio theory {MPT}, "proposes how rational investors will use diversification to optimize their portfolios, and how an asset should be priced given its risk relative to the market as a whole. The basic concepts of the theory are the efficient frontier, Capital Asset Pricing Model and beta coefficient, the Capital Market Line and the Securities Market Line. MPT models the return of an asset as a random variable and a portfolio as a weighted combination of assets; the return of a portfolio is thus also a random variable and consequently has an expected value and a variance.