Reference no: EM132360750

Economics of Finance Assignment Questions -

Q1. Options - BHP Billiton (BHP), the leading Australian iron ore mining giant, is also listed on New York Stock Exchange. The iron ore prices have almost doubled from $67.87 last year to $123.16 on 3 July 2019. The following table shows the BHP's stock prices in USD and the annualised historical volatility of BHP on NYSE, VIX Index, the iron ore prices in USD at given dates below.

A European call option with underlying stock BHP's strike price of $65 is traded at $1.46 on 3 July 2019, expiring on 17 Jan 2020. A European put option with underlying stock BHP's strike price of $65 is traded at $8.55 on 3 July 2019, expiring on 17 Jan 2020. The risk-free rate of interest is 2.15%.

Your may use Matlab function and/or Excel functions. You are expected not to exceed 500 words for this Q1(i) to (iii).

(i) Determine the implied volatility of both put and call options using the Black-Scholes Options. You are also expected to provide an economic rationale justifying any differences between the implied volatilities of call and put options.

(ii) Provide an economic rationale in your comparative analysis of implied volatilities of the options with your historical volatility trends to identify any arbitrage opportunity. If so, please devise an optimising strategy using the option(s).

(iii) Evaluate the vega of the call option for the period based on the period 3 June 2019 to 3 July 2019. Comment on your results.

Q2. Duration - Consider a 5-year bond with annual coupon payments. The bond that has a face value of $100 and sells for $95. The coupon rate is X% where X is the last digit in your student number. If the last digit in your student number is zero then the coupon rate is 3.5%. Coupon rate determines the coupon payment as a percentage of the face value. The face value is paid at the maturity year in addition to the coupon payment.

i) Calculate the bond's duration.

Now, suppose that one can establish a relationship between the 5-year bond's own yield-to-maturity, y and some market rate of interest, y^. Assume that y = 0.9y^ + .02, where y^ is the interest rate on 1-year zero coupon government bonds (T-bills).

ii) Use the bond's duration to determine the percentage change in the 5-year bond's value if the interest rate on 1-year T-bills falls by one basis point, that is, by 0.01%.

Q3. Arrow-Debreu Economy - Consider a world in which there are only two dates: 0 and 1. At date 1 there are three possible states of nature: a good weather state (GW), a fair weather state (FW), and a bad weather state (BW). Denote S₁ as the set of these states, i.e., s₁ ∈ S₁ = {GW, FW, BW}. The state at date zero is known: call it s₀. Denote probability of the three states as π (·),π (S₁) = (0.4, 0.3, 0.3).

There is one non-storable consumption good - say apples. There are three consumers in this economy. Their preferences over apples are exactly the same and are given by the following expected utility function

c₀ⁱ (s₀) + β∑_{s_1∈S_1}π(s₁)u(c₁ⁱ(s₁)),

where subscript i = 1, 2, 3 denotes consumers. In period 0, all agents have a linear utility while in period 1, the three consumers have the same CRRA instantaneous utility function: u (c) = c^1-γ/1-γ, where the coefficient of RRA is γ = 0:2. The consumers' time discount factor, β, is 0.98.

The consumers differ in their endowments which are given in the table below:

i) Write down the consumers' budget constraints for all times and states.

ii) Define a Sequential Market Equilibrium in this economy. Is there any trade of Arrow-Debreu securities possible in this economy?

iii) Write down the Lagrangian for the consumers' optimisation problem and find the first order necessary conditions.

iv) Characterise the equilibrium (i.e., find the allocations and prices defined in the equilibrium).

v) At the equilibrium, calculate the forward price and risk premium for each atomic security. What do your results suggest about the consumers' preference? Prove your intuition, and comment on your results.

Suppose that instead of Arrow-Debreu securities there are two other securities, a (risky) bond and a stock, available for trade in this economy. The bond pays 1 apple in GW and FW, but 0 in BW, while the stock pays 2, 1 and 0 apples in GW, FW and BW, respectively. There is no other dealers in the market, but each trader in the financial market need to make credible claim (there is no default risk in this economy).

vi) What is the competitive equilibrium now?

Suppose in addition to bond and stock, there exists an option based on the stock price which only pays at one state. This option completes the market.

vii) What is the type of this option (call or put)? What is the range of the strike price of this option? Design such an option and show how it completes the market.

viii) Characterise the competitive equilibrium with bond, stock and the security you designed.

ix) Explain how financial innovation affects the social desirability of the allocations in the economy. (max. 200 words).

Q4. CAPM - Suppose the risk-free rate of return is 0.03. There are three stocks available on the market, their returns are all normally distributed, and their variance-covariance and returns are given as the Table below:

There are two investors in the economy. Their instantaneous utility functions are given by:

u(r) = 1 - e^-c_ir, for i = 1, 2,

where c₁ = 2 and c₂ = 3.

i) Derive the market portfolio and Sharpe ratio. Are they related to the individual investors' preference?

ii) Derive the two individual investors' portfolios. What are the expected return of each individual investor's choice?

iii) Compare the two investors' choice. What does your results suggest? Comment on your observations. (max. 200 words).

Attachment:- Economics of Finance Assignment File.rar