- Basic Instruments
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- Volatility Derivatives 1
- The world of Structured Products 4
- Library of Structured Products 0
- Table of Contents
- Vanilla Options
- Volatility, Skew and Term Stru
- Option Sensitivies: Greeks
- Option Strategies
- Dispersion Options
- Barrier Options
- Autocallable Structures
- The Cliquet Family
- Basic Models 0
- Local Volatility Models 5
- Stochastic Volatility Models 5
- Introduction 1
- Delta 2
- Gamma 4
- Theta 2
- Vega 3
- Rho 2
- Vanna 0
- Questions/Answers 2
- General Practical Example
- Flavours of Volatility 4
- Volatility Models 1
- The Volatility Smile 9
- Questions/Answers 1
- Bonds 1
- Equities 1
- Swaps 4
- Options 5
- Questions/Answers 2
- Brief Reminder on Basic Instru
- Introduction 0
- Mechanics 8
- The Market 9
- Uses of Variance Swaps 11
- Replication and Hedging 9
- Future Developments 0
- 3rd Generation Products
- Derivatives on Variance
- Monte Carlo Simulation 1
- Partial Differential Equation Approach 1
- Risk-Neutral Valuation 1
- Mathematical concepts 8
- Questions/Answers 2
- Cliquet Options 3
- Barrier Options 5
- Mountain Range Options 0
- Autocall 6
Brief Reminder on Basic Instruments
2. Brief Reminder on Basic Financial Instruments
In this part,we will just briefly reviewed some of the basic instruments that are essential to understand and price structured products.
2.1. Interest Rates
Interest rates represent the amount charged by a lender to a borrower for the use of assets. This amount of money depends on the credit risk, which is the risk of loss due to the non-payment of the borrower's duty.
Interest rates are involved to a large extent in the pricing of all derivatives. For any given currency, there are many types of rates that are quoted and traded in the market. It is therefore essential to understand the differences between these rates and the implications of each on the valuation of financial instruments.
2.1.1. LIBOR and Treasury rates
Treasury rates are the rates earned on debt instruments issued by governments.
A number of regulatory issues can impact the value of Treasury rates and cause them to be consistently low. For this reason, LIBOR is considered by derivatives traders to be a better measurement of ST risk-free rates.
The London Interbank Offered Rate (LIBOR) is the interest rate at which a bank offers to lend funds to other banks in the interbank market. LIBOR rates can have different maturities corresponding to the length of deposits and are associated with all major currencies. Typically, a bank must have an AA credit rating to be able to accept deposits at the LIBOR rate.
The TED Spread is the difference between 3m Treasury Bills and 3m LIBOR and can be used as a measure of liquidity in interbank lending. LIBOR rates involve credit risk whereas Treasury rates do not. Therefore the TED spread serves as a measure of credit risk in the interbank market.
2.1.2. Yield Curves
For any major currency, the interest rates paid on bonds, swaps or futures are closely watched by traders and plotted on a graph against their maturities. The points on the curve are only known with certainty for specific maturity dates; the rest of the curve is built by interpolating these points. They are typically expressed as an annual rate. This allows interest rates to be compared easily.
In order to price a financial instrument, a trader will choose the yield curve that corresponds to the type of debt associated with this instrument.
Yield curves are typically upwards sloping, with longer term rates higher than shorter term rates. However, under different market scenarios the yield curve can take several different shapes, being humped or possibly downward sloping.
A bond is a debt security used by governments and companies to raise capital. In exchange for lending funds, the holder of the bond is entitled to receive coupons paid periodically as well as the return of the initial investment at the maturity date of the bond. Usually, the coupon rate is constant throughout the life of the bond. The coupons can also be linked to an index; we then talk about floating rate notes. Bonds can have a range of maturities classified as: short (less than 1 year), medium (1 to 10 years) and long term (greater than 10 years).
The market price of a bond is then equal to the sum of the present values of the expected cashflows.
The market price of a bond may include the interest that has accrued since the last coupon date. The price, including accrued interest, is known as the dirty price and corresponds to the fair value of a bond. It is important to note that the dirty price is the price effectively paid for the bond. However, many bond markets add accrued interest on explicitly after trading. Quoted bonds, such as those whose prices appear in the Financial Times are the clean prices of these bonds.
Bonds are generally considered to be a safer investment than stocks due to many reasons, one being that bonds are senior to stocks in the capital structure of corporations, and in the event of default bondholders receive money first. Also, bonds generally suffer from less liquidity issues than stocks. In times of high volatility in the stock market, the bond can serve as a diversification instrument to lower volatility.
Nonetheless, bonds are not free of risk, because bond prices are a direct function of interest rates. In fact, fixed rate bonds are attractive as long as the coupons paid are high compared to the market rates, which vary during the life of the product. Consequently, bonds are subject to interest rate risk, since a rise in the market’s interest rates decreases the value of bonds and vice versa. We can also understand this effect by looking at the bond price formula: if the interest rate used to discount the coupons goes up, their present value goes down and the price of the bond decreases. Alternatively, if interest rates go down, bond prices increase.
Moreover, bond prices depend on the credit rating of the issuer. If credit rating agencies decide to downgrade the credit rating of an issuer, this causes the relevant bonds to be considered a riskier investment, therefore a bondholder would require a higher interest for bearing greater credit risk. Since the coupons are constant, the price of the bond decreases.
2.1.4. Zero Coupon Bonds
Zero coupon bonds are debt instruments where the lender receives back a principal amount plus interest, only at maturity. No coupons are paid during the life of the product. In fact the interest is deducted up front and is reflected in the price of the zero coupon bond since it is sold at a discount, which means that its price is lower than 100% of the notional.
The price of a ZC is equal to the present value of the par value, which is the only cashflow of this instrument and paid at maturity T. ZC bonds are tradeable securities that can be exchanged in the secondary market.
Using continuous compounding to discount CFs, B(t,T) = e−r(t,T)×(T−t)
Companies need cash to operate or finance new projects. They can choose to raise capital by issuing equity. To compensate stockholders for not receiving interest that they might have received with other investments, companies usually pay them dividends. Dividends can vary over time depending on the company’s performance. Dividends can be expressed as discrete dividends or as a continuous equivalent dividend yield q.
If an investor believes a stock price is going to decrease over time. He would then be interested in having a short position in this stock. If he doesn’t hold the stock, he can enter into a repurchase agreement or repo.
A repo is a transaction in which the investor borrows the stock from a counterparty that holds the stock and agrees to give it back at a specific date in the future. Repos allow the investor to hold the stock and sell it short immediately in the belief that he can buy it back later in the market at a cheaper price and return it to the lending counterparty. Repos play a large role as speculative instruments. It is interesting to note that stock lenders are people who are just not planning to trade in it. They could be investors that own the stock in order to take control of the company, and repos offer them the advantage to earn an added income paid by the borrowers. The rate of interest used is called the repo rate or borrowing cost.
When trading stock, an investor should also be cautious with liquidity that can be quantified by looking at the average daily traded volume. For a stock to be considered liquid, one should be able to buy or sell it without moving its price in the market. Take the scenario where an investor wants to sell a large position in stocks. If the stock is not liquid enough, it is possible that the investor wouldn’t find a buyer at the right time and would not be able to make a profit from his investment. Liquidity is correlated to the stock price. If the latter is too high or too low, the liquidity of the stock suffers.
Let us now analyse the forward price of a stock, which is defined as the fair value of the stock at a specific point of time in the future. The forward price of a stock can be viewed as equal to the spot price plus the cost of carrying it.
Interest rate increases the cost of carry since the interest that might be received by the stockholder if he had immediately sold his shares and invested his money in a risk-free investment.
--> IR increases the forward
If a stock provides an additional income to the stockholder, this causes the cost of carry to decrease, since the stock also becomes a source of profit. Dividends and stock loans (repos) constitute a source of income when carrying a stock.
--> Dividend yield and repo decrease the forward
F0(T ) = S0 × e(r−q−b)×T
2.3.1. Interest Rate Swaps
IRSs are OTC agreements between two counterparties to exchange or swap CFs in the future.
A plain vanilla IRS is one in which two parties swap a fixed rate of interest and a floating rate. In an IRS, the notional is the principal amount that is used to compute interest percentages, but this sum will not actually change hands. Payments are netted, because all CFs are in the same currency.
The payer on the swap is the person who agrees to pay the fixed rate and expects the IR to rise. He is long the swap. The receiver is the person who agrees to receive the fixed rate. The receiver expects interest rates to fall and is short the swap.
A basis swap is an IRS where a floating rate is swapped for a different floating rate.
To compute the value of a swap, one should calculate the NPV of all future CFs, which is equal to the PV from the receiving leg minus the PV from the paying leg. Initially, the terms of a swap contract are defined in such a way that its value is null.
2.3.2. Cross-currency Swaps
A CCS is a swap in which CFs are based on different currencies. Unlike an IRS, in a currency swap the notional actually changes hands at the beginning and at the termination of the swap. Interest payments are also made without netting.
In reality, market participants have different levels of access to funds in different currencies and therefore their funding costs are not always equal to LIBOR.
An approach to work around this is to select one currency as the funding currency, and select one curve in this currency as the discount curve. CFs in the funding currency are discounted on this curve. CFs in any other currency are first swapped into the funding currency via a cross currency swap and then discounted.
2.3.3. Total Return Swaps
A TRS is a swap agreement in which a party pays fixed or floating interest and receives the total return of an asset. The total return is defined as the capital gain /loss from the asset in addition to any interest/dividends received during the life of the swap. The party that pays fixed/floating rates believes the asset will appreciate. A total return swap enables both parties to gain exposure to a specific asset without having to pay additional costs for holding it.
An equity swap is a particular type of total return swap where the asset can be an individual stock, a stock index or a basket of stocks. Compared to holding the stock, she does not have to pay anything up front. Instead, she would deposit an amount of money, equal to the spot price of the stock (a different amount in the case of a margin), and would receive interest on it.
Thus, the investor creates a synthetic equity fund by making a deposit and being long the equity swap. Typically, equity swaps are entered into to gain exposure to an equity without paying additional transaction costs, locally based dividend taxes. It also enables investors to avoid limitations on leverage and to get around the restrictions concerning the types of investment an institution can hold.
2.3.4. Dividend Swaps
A dividend swap is an OTC derivative on an index or a stock and involves two counterparties who exchange CFs based on the dividends paid by the index/stock/basket of stocks. In the first of the two legs a fixed payment is made (long the swap), and in the second leg the actual dividends of the index or the stock are paid (short the swap). The dividend swap is a simple and price effective tool for investors to speculate on future dividends directly, and it can also serve as a vehicle for traders holding portfolios of stocks to hedge dividend risk. The liquidity of such swaps has increased in recent years for both these reasons.