# Risk

Paper, Order, or Assignment Requirements

MODULE TITLE: Risk and Derivative Markets
Question 1

Instructions: This section contains 10 short questions. Answer each question succinctly and briefly. All questions contain equal marks.

Explain the difference between writing a call option and buying a put option. Use graphs to describe the payoff profiles.

A stock index currently stands at 1150. The risk free interest rate is 4% per annum (with continuous compounding) and the dividend yield on the index is 2% per annum. What should the forward price for a 4-month contact be?

What is meant by the delta of an option?

A 3-month forward contract on a non-dividend paying stock is valued at \$45. The underlying stock price is \$44.50 and the constant risk free rate of interest is 2%. Does an arbitrage opportunity exist and how would you exploit it?
Note the 1-step binomial model below.

What is the value of C0 in a risk neutral world?
The strike price, K = 24.75 and the risk free rate is 2%

Why is backtesting of the Value at risk (VaR) or Expected Shortfall (ES) models performed on daily data even when the risk horizon is defined as 10-day?
Describe the process of calculating MC VaR.
Describe the problem of nonlinear dependence in financial time series.
Describe Vasicek’s default intensity credit model.
Describe how a stressed covariance matrix can be applied to historical VaR.

Question 2
Bloomberg A.

Bloomberg B
(i)         Explain in detail what is hedging and speculation? Also explain what is the difference between hedging and speculation?
(ii)       As an options trader, discuss the information given by Cecile Vannucci and NikolajGammeltoft in Bloomberg A. Your discussion can be generalist in nature but should include;

Strategy ideas that you can use to potentially make money
Risks that your strategy might encounter

(iii)       Explain what line (1) and line (41) of the image Bloomberg B tells the trader?

(iv)       Suppose that a European call option to buy a share for \$100.00 cost \$5.00 and is held to maturity.

(a)Under what circumstances does the investor make a profit?
(b) Under what circumstances will the option be exercised?
(c) Draw a diagram showing the variation of the investors profit with the stock price at the maturity of the option.

Question 3

Name the six factors that affect the price of a stock option.

The Black Scholes equation wasn’t the real problem. It was useful, it was precise, and its limitations were clearly stated. It provided an industry-standard method to assess the likely value of a financial derivative. So derivatives could be traded before they matured. The formula was fine if you used it sensibly and abandoned it when market conditions weren’t appropriate. The trouble was its potential for abuse. It allowed derivatives to become commodities that could be traded in their own right. The financial sector called it the Midas Formula and saw it as a recipe for making everything turn to gold. But the markets forgot how the story of King Midas ended.

Discuss this statement in particular:

list and discuss the limitations of the Black-Scholes equation.
list and discuss the market conditions for which the Black Scholes equation is not an adequate model

Given the following information,
Constant risk free rate of interest = 5%
Time to maturity = 2 months
Current Stock price = \$32.00
Strike Price = \$32
Up movement (u) = 1.05
Down movement (d) = 1/u

What is the price of an American Put Option on the stock using a 2-step binomial tree? You are asked to complete the boxes in the figure below.

Question 4

The h-day expected tail loss (conditional VaR) can be expressed:

Where
α is the significance level and σh is the h-day volatility and μh is the h-day mean, Φ and φ are the standard normal distribution and density functions respectively and φ(Φ-1(α)) is the height of the standard normal density at this point.

A portfolio’s returns have volatility of 35%, assuming zero excess return and that the returns are independent, identically distributed (i.i.d.), find the 1% 10-day and ETL expressed as a percentage.

The appropriate values can be selected from the following table:

Describe what is meant by the term endogenous risk.

Discuss the procyclical nature of Value at Risk (VaR). Include in your discussion:
The role of leverage and capital adequacy requirements in the 2007-2009 financial crisis.
The advantages and disadvantages of the expected tail loss (also known as expected shortfall or conditional VaR) risk measure.
The amendments included under Basel III that attempt to

mitigate the problems caused by procyclicality of capital adequacy requirements.

Question 5

Engle (1982) proposed the Autoregressive Conditional Heteroskedasticity (ARCH) model which was designed to capture volatility clusters. It can be expressed:

Explain how this statement can be read and derive the ARCH(1).
What is the key weakness of this volatility model?

Describe two concepts of liquidity risk.
Discuss the amendments included in Basel III to address liquidity risk.

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