CM2 Financial Engineering & Loss Reserving

WHAT ARE THE DIFFERENT FORMS OF EFFICIENT MARKETS?
Efficient market consists of: weak form market where market prices reflect all of the information contained in historical price data, semi-strong form is one where market prices reflect all publicly available information & strong form is where market prices reflect all information, whether or not it is publicly available.

WHAT IS MEANT BY UTILITY?
In economics, ‘utility’ is the satisfaction that an individual obtains from a particular course of action.

WHAT IS THE SHAPE OF UTILITY CURVE FOR A RISK-AVERSE INVESTOR?
for a risk-averse investor, utility is a (strictly) concave function of wealth which reflects that the marginal utility of wealth (strictly) decreases with the level of wealth and consequently each additional dollar, say, adds less satisfaction to the investor than the previous one.

WHAT IS ABSOLUTE AND RELATIVE RISK AVERSION?
if the absolute value of the certainty equivalent decreases (increases) with increasing (decreasing) wealth, the investor is said to exhibit declining absolute risk aversion. If the absolute value of the certainty equivalent decreases (increases) as a proportion of total wealth as wealth increases the investor is said to exhibit declining (increasing) relative risk aversion.

WHAT IS VARIANCE OF RETURN?
Variance of return refers to change in the market value of the asset about the mean value.

WHAT IS DOWN-SIDE VARIANCE? WHY IS IT IMPORTANT?
Downside semi variance helps to calculate the possibility of low returns. It is the risk of actual values being less than expected values.

WHAT DO YOU UNDERSTAND BY VALUE AT RISK?
VaR represents the maximum potential loss on a portfolio over a given future time period with a given degree of confidence. It calculates the likelihood of underperforming.

WHAT IS PORTFOLIO THEORY?
Mean-variance portfolio theory leads to optimum portfolios where investors can be assumed to have quadratic utility functions & if returns are assumed to be normally distributed.

DESCRIBE DIFFERENT TYPES OF MULTI-FACTOR MODELS?
macroeconomic, fundamental and statistical factor models.

WHAT ARE THE BASIC ASSUMPTIONS OF CAPITAL ASSET PRICING METHOD?
The basic assumptions of CAPM are investors are risk-averse and non-satiated, no transact

WHAT DOES CAPM DEPICT?
The capital asset pricing model (CAPM) tells us about the relationship between risk and return for security markets as a whole.

WHAT IS A MARTINGALE?
A martingale is a process whose current value is the best estimate of its future values. So, the expected future value is the current value or that the process has ‘no drift’.

STATE SOME PROPERTIES OF A STANDARD BROWNIAN MOTION.
A Wiener process is a stochastic process with independent and stationary increments, also  it has normally distributed increments, along with continuous sample paths.

ARE STOCHASTIC PROCESSES GOOD MODELS FOR ASSET PRICES?
No, since asset prices do not start at zero, are not continuous and they certainly don’t exhibit normally distributed increments.

STATE WHAT IS MEANT BY ARBITRAGE?
An arbitrage opportunity is a situation where we can make a certain profit with no risk.

OUTLINE THE FACTORS THAT AFFECT OPTION PRICES.
There are usually 5 factors affecting option prices: the underlying share price, the strike price, the time to expiry, the volatility of the underlying share and the risk-free interest rate.

EXPLAIN WHAT IS MEANT BY PUT-CALL PARITY.
In an arbitrage free market, two portfolios which  have the same value at expiry, for example, A: consisting of a European call plus cash, B: consisting of the underlying share plus a European put with the same expiry date and exercise price as the call, and since the options cannot be exercised before then they should have the same value at any time.

NAME DIFFERENT TYPES OF OPTION GREEKS.
The Greeks are a group of mathematical derivatives that can be used to help us to manage or understand the risks in our portfolio. Greeks are: delta, gamma, theta, rho and vega.

IS THERE ANY DIFFERENCE BETWEEN EUROPEAN AND AMERICAN OPTION?
A European option is an option that can only be exercised at expiry. An American option is one that can be exercised on any date before its expiry.

EXPLAIN THE DIFFERENCE BETWEEN THE REAL-WORLD MEASURE AND THE RISK-NEUTRAL MEASURE.
Risk-neutral measure is the probability measure with respect to which any asset, whether risky or risk-free, offers the same expected return to investors, namely, the risk-free rate of return. However, in the real-world, investors do need extra return for the amount of risk undertaken.

WHAT ARE RUN-OFF TRIANGLES?
Run-off triangles are two-dimensional matrices that help in estimating the ultimate cost of claims under general insurance business.

STATE HOW RUN-OFF TRIANGLES ARE USED FOR RESERVE CALCULATIONS?
The method is based on an accident-year basis where claims development is clustered by the year an accident has occurred. The task is to decide the amounts yet to be paid in respect of the given accident years by calculating respective development factors and accumulating the claims already paid and finally, finding the incremental claims to be paid.