Question

1. Answer three parts of the question. Your answer for each part should be no more than two pages long. (a) Describe how a Collateralized Debt Obligation (CDO) distributes payments to its investors. (b) ‘American call options should never be exercised before the maturity date’. Evaluate this statement, providing proofs where necessary. (c) Explain how you would create a Box spread and show its payoff at maturity. (d) Holding all other factors constant, what effect does a change in the ‘time to maturity’ have in the price of European options? Fully explain your answer. (e) In a one-step Binomial option pricing model, we can compute the price of the option as: f= e-rT [p fu + (1-p) fd] what is p and how is it computed? If you can solve D, B and C that would be great!

Answer 1

a) Here is the description of how the Collateralized Debt Obligation (CDO) distributes payments to its Investors :

Collateralized Debt Obligation is a product in finance which is in complex structure.It is backed up with loans and other assets which are sold to its investors. These assets will become Colletral if the loans default. The usual investors here in CDO are Investment Banks , Pension funds, Insurance Companies , Banks and Hedge Funds. They usually buy CDO's to outperform treasury yields which there by mimimizes the exposure of risk. The stratergy here is that when the economy is in boom then adding more risk can yield better returns.

The payments to the investors are distributed by first pooling the assets which provides diversified portfolio option with an aggregation of various debt assets , susch as loans issued corporates and individuals . Then they form the trenches and thereby distribute them to investors . Depending upon various risks involved these trenches are distributed to the investors . The most senior trench is sold to institutions looking for highly rated instruments like pension funds. The lowest rated instruments will be retained by the CDO . This gives banks an option to monitor the loan. These entire process of aggregation of assets and selling it to appropriate investors is called Securitization.

b) Explaining why the American Call Options should never be exercised before the maturity date :

The main reason for not exercising the American Call Option before maturity is that it forfeits the extrinsic value of option. For example , if the spot is trading for 100, the 99 strike call will be worth 1 and if exercised that will be considered as profit. Usually for an american call early exercising is not optimal. because the exercise requires payment of the strike price. By holding till the expiration date the option holder can save its interest. Then the option holder gains more by exercising rather than waiting .

c) Creating Box Spread and its showoff at maturity :

Box Spread is an options arbitage strategy that combines buying a bull call spread with a matching bear put spread.the box spread payoff will always be going to be the difference between the two strike prices. the cost to implement box spread like commissions charged can be a significant factor in its potential profitability. The box Spread also called as long spread is used optimally when the spreads themselves are underpriced with respect to expiration values.

If the cost of the spread after commissions is less than the difference between the two strike prices then the the trader locks in a riskless profit making it a delta neautral strategy. Usually the option will be having three elemnts like underlying asset,exercise price and the expiration date. The profit at expiration is the payoff minus the cost of setting up the strategy.

d) By holding all other factors constant , the effect of change in "time to maturity " in the price of european options :

Options will be having limited life span thus their value is affected by the passing of time . As the time to expiration increases, the value of the option also increases , because the time to expiration gets closer the value of option begins to decrease .If the call option expires in the moneym you end up paying a higher price to purchase the stock than that we would have paid if we bought the syock outright.Since the call optins are derivative instruments the prices are derived from the underlying security such as stock . The buyer has the way to sell the options contract to another option buyer at any time before the expiration date, at the prevailing market price of the contract.

e) From the Binomial option pricing model , we can compute the price of the option as f=e-rT[p fu + (1-p) fd ] , where by 'p' is the price at node B .

p = ert-d / u-d

In finance , the binomial pricing model option provides a generalizable numerical method for the value of options. This model uses a descrete time model of the varying price over time of the underlying financial instrument, which addresses cases where the closed form Black Scholes formula is wanting.

This model values options using an iterative approach utilizing multiple periods to value american options. The two possibke outcomes with each iteration is move up and move down followed by binomial tree. This model is used frequently in the Black Scholes model.