Financial derivatives: concepts, pricing, and applications

Financial Derivative

The aim of this report is to help us take a decision about the use of Black-Scholes valuation formula for the use of our organization. In the beginning itself, let us understand that Black Scholes formula looks to be very mathematical and thus frightening to many people who are not so conversant with mathematics and statistics. The prices as calculated through different models are available for earlier years, and even for all Fortune 500 companies to enable us take a decision regarding the use of this formula. At the same time, the difference in Call and Put options from using stochastic volatility models that we have been using till now, and the use of regular Black Scholes model is not likely to be more than 10% according to mathematical experts. (Stochastic Volatility Model) Thus the entire question of using Black Scholes model need not be looked at with great concern.

Black Scholes method is a very famous method for the valuation of an equity share and other variables related to the value of an equity share in the future months. At the outset we should remember that the future value of an equity share is unknown and all future estimation is at best estimation, and there is no guarantee that the estimation will be accurate. We are a stock broking firm and our business is in the purchase and sales of shares and our earnings come from the commissions that we earn on the same sale and purchase. We make certain recommendations but never state that we shall compensate clients for investments made on the basis of our recommendations. The clients have to take their own decisions regarding investment along with the concerned risks, and if we try to proceed in any other manner, then it will be a violation of our rules for being a stock broker. Now let us try to understand how the famous valuation method of Black Scholes operates. (FAS 123(R): Lattice vs. Black-Scholes)

The method used is a differential equation which has the basic assumptions seeded in it. Let us again not go into mathematical details, but once the key characteristics are plugged into the Black Scholes formula, the price and price volatility of the underlying stock, coupled with the available rate of return on a risk free stock the formula devised by Black Scholes provides the value for an option. The original Black Scholes formula and others derived on them have been used for many years by investors dealing in options which are traded on the exchange. The general view that is taken of the options produced by these formulae is considered to be theoretically and empirically sound. (FAS 123(R): Lattice vs. Black-Scholes) At the same time, there is no opinion that there cannot be any other method for calculation of options values, or that the calculations based on Black Scholes are likely to be wrong. As stock brokers, we have been dealing in the trading of options based on our own devised formula and this formula has been reasonable accurate till date. There is no specific reason for us to abandon our method and get our activities changed and modified to start using Black Scholes methods.

Now let us delve a little further into the theories of calls and options. The basis of all decisions regarding an organization is based on three elements. The first of these elements is the published financial statements which are assumed to be accurate; the second are the market prices regarding the firm's debt and equity, and the third is an appraisal of the firm's prospects and risks. Of these, the first two are made available in the market by different forces, and as stock brokers we have no special role to play - we can only inform the investors of the same, should we choose to. The investors have no role to play in those two also, and our information will not be of much service in the interests of our firm. Another element is the price of all concerned items and it is known that all prices are forward looking. For determining the future prospects of a firm, the investor will have to use the subjective appraisal of the firm's prospects and risks, financial statements and the prices of competition. (Black Scholes Model)

We also use the same and then get into an analysis and combinations of different factors to decide whether we should advise our clients to buy or sell the equity shares of the firm. Thus the prices reflected in the market are a combination of all these forces acting on all the investors and their advisors. The genesis for understanding the link between the market value of a firm's assets and the market value of its equity led to the general derivative pricing model by Merton. The option pricing model of Black Scholes is a special case of this model by Merton. (Black Scholes Model) Thus one can say that the theoretical basis of Black Scholes is sound and there should be no objection to the use of that model if it is thought to be required.

The situation of equity is relatively simple as it has a residual claim on assets of a company after all the obligations of the company have been met, and yet the liability of a shareholder is limited. One of the call options now available has an option on the assets after the strike price of the option is met. The general value of this strike option is dependent on the book value of the liabilities that the firm has. In short, there is an option to pay out the creditors of the organization and take over the assets. This option is useful for the holders of the options only if there is an expected surplus after meeting the liabilities to the creditors, and only then will they use the option to pay the money and take over the assets. Otherwise no option will be exercised and the firm will be left to the creditors. (Black Scholes Model) This sort of options are not related directly to analysis of the nature discussed earlier, and may have to be treated differently, as their valuation depends more on the pricing of the assets of the company. So far as we are concerned, we get a commission on brokerage, and it does not really matter to us what type of option we deal in. Generally however, we have not dealt with options of this type earlier.

The new interest in Black Scholes has come due to decision by the financial Accounting Standards Board in December which said that a new standard will have to be accepted by about this time. This will require the expensing of all stock options. The rules permit only footnote disclosure and full expensing is now required from the companies if they have met some specified criteria. These are concerned with the options for the employees who are probably the largest holders of options. For the purpose of being treated as only a footnote treatment and not mention of full details, the options have to be traded at full market value of the stocks and that there should be no other condition on the exercise of the option than a standard number of years completion of service. This is the general method of equity-based compensation of firms as the firms prefer to provide incentives in a manner that does not have to be shown as expenses. (Lattice vs. Black-Scholes)

This is now reaching a position where valuation of stock is becoming important for them, and of the important methods for valuation of stock has been Black Scholes. The difficulty is that there are some differences in the assumptions of Black Scholes and these options. For Black Scholes the assumption is that trading in the concerned stock along with the ability for exercise of the option is continuous and unrestricted, but employee options are subject to conditions in terms of vesting periods, direct blackouts and security trading laws for insider trading. The interest rate in the theory is also assumed to be constant and that may be valid for a 3-month period but the same assumption cannot be held to be valid for a ten-year period for which these options are issued. There are similar assumptions for constant volatility and again that is difficult to expect for 10 years. Again there are assumptions of risk neutral environment which may not be accepted for a 10-year period. (Lattice vs. Black-Scholes)

Well these are considerations for the financial officers in the client company and are not important considerations for us, as we are not dealing in these options. So there is also little reason for us to consider changing our practices or interest in Black Scholes method for this reason. As an organization we have been successful with our present methods for many years and it is better if we continue with what we know to be useful.

Report: 2

The developments of credit derivatives began in 1980s as a new financial innovation after the swap market started. Swap market provided derivative organizations with profit due to their intermediary position while the credit margins for borrowers were reduced. As the swap market developed there was the development of new interest derivatives so that there were additions to the list of products. Credit derivatives are relatively recent introductions and these are mechanisms for the credit institutions to separate the credit risk from their loans and treat market risk as a separate category so that their pricing efficiency could be more competitive and the concerned organizations could be more competitive in the market. (Credit Derivatives Move Beyond Plain Vanilla)

Thus one can say that credit derivatives are a recent form that can be used by bankers to reduce risk, or increase risks and thus meet their corporate objectives. The general form of credit derivatives is a bilateral contract and the aim of that contract is to reduce their exposure to credit risk. For a bank like ours, the feeling may be that one particular customer is in difficulty and may not be in a position to repay the loan that has been given to him, or has been renewed for him. The bank can seek protection through selling the concerned credit risk to another party, though the risk will still remain on its books. It is not only for loans that the procedure may be used, but for any debt instrument or a group of instruments. While going through the procedure, one of the side results is the establishment of a default price for the loan or instrument. Apart from the reduction of risk, other organizations which have not made the loan can gain benefits from the loan that they have not made directly. (Credit Derivatives Move Beyond Plain Vanilla)

In a way the instrument offers a flexible method of managing risks of credit and also to improve yields from credits synthetically. This is due to the ability that it gives methods to purchase synthetic credit. At the same time, it cannot remove all risks in giving credits as though it may not have given direct credit to a company which is in a little difficult position, it may have got into a derivative for that company. There are also other instruments like Special Purpose Corporations/Vehicles that can be created to avoid the risks of getting into derivatives of companies with a little risky situation. This leads to different forms of credit derivatives - Credit Linked Notes, Total return Swaps, Credit Default Puts, Credit Spread Options and other forms. The concerned definition of credit risk in all these discussions is the likelihood of the borrower failing to service or repay a debt in time. The market notes this deficiency through the user of the credit rating for the party, and this is what defines the premium that it pays over the market price for its debts.

Thus the risk involved in giving a loan to a party has two elements - market risk and firm-specific risk. The benefit of credit derivatives is that it is allowing the lender to separate the risks that are involved and then insuring itself by selling those risks to others who are in the best position to evaluate and manage those risks. Earlier the methods of controlling them were through refusals to make loans, taking out insurances, through guarantees and letters of credit, etc. These were useful in normal situations, but when the market itself moved into a difficult situation due to economic downturns, and then all parties were likely to default at the same time. Thus financial institutions felt that they needed more security and came out with this scheme. (Credit Derivatives Move Beyond Plain Vanilla)

Now the credit derivatives market has grown and is expected to be near the $1 trillion mark, and this is causing demands for the systems to be calculated easily. This is leading to requirement of technology and other support for the trade and management of credit instruments. Leading organizations dealing in this area have already asked their software suppliers to develop applications which will support their business. (Designed for dealing) Earlier the use of these instruments were limited to banks, but now among the users are a large number of insurance companies, hedge funds, mutual funds, pension funds, corporate treasuries and even direct investors who are trying to get their yields increased or transfer the credit risks which they are now incurring. Earlier the credit derivatives were only for the use of financial institutions to manage their concentration of credit instruments and liabilities and now they are finding even to use credit exposure through support from others.

There are now many types of credit derivatives that are being used, but for our purpose we shall concentrate on four major varieties that make up the biggest volumes in them. These are Total return swaps, Credit default swaps, Credit spread options and Credit linked notes. They are often also named slightly differently and this makes it very difficult to have constant terminology for this market. Credit default swaps are also called credit swaps by some users. This is what makes the traders and marketing personnel use the complete descriptions of profile of transactions that each deal contains. The first item being discussed is a total return swap and that permits the investor to receive the total returns from the concerned asset, but the investor does not buy the asset. The return means the income from the asset less or increased by any changes in capital value that occurs during the period the deal is for. Thus one of the parties to the deal pays the total economic return for a notional amount of principal that the deal is for. In return, the other party pays the regular fixed or floating rate of interest and some difference. The reference rates of interest can be any other financial asset, or basket of assets or even an index. The changes on using this derivative can be in using one asset, or even a single credit made by the party. The reference levels have minimum and maximum levels fixed on some reference credit that is fixed earlier. The life or these agreements is for periods from one year to three years. This method is used by banks to transfer the risks of credit that they have given out to another party. (Credit Derivatives Move Beyond Plain Vanilla)