Interest Rate Options - Essay Example

INTEREST RATE OPTIONS Interest rate options are those types of options whose payoffs are calculated based on the level of interest charged. There are a number of ways to price such options. The models used most popularly are based on Black Scholes model. The extended version of Black Scholes model, uses the rate of interest to calculate the payoffs of the options, and this model is called popularly, the Black’s Model. Among the products that are most popular in the market are, (i) exchange interest rate options, (ii) embedded bond options, (iii) European bond options, (iv) interest rate caps, and (v) European swap options. Exchange interest rate options: A common example of this bond is, the Treasury Bond Futures Option. Others are Treasury Notes Futures Options and Eurodollar Futures Options. The Treasury Bond Future Options is priced at 1/64th of 1% of the Treasury Bond face value; the Eurodollar Futures Bond is calculated at 0.01 basis point value being equivalent to $25. It is to be noted here that the interest rate futures prices are indirectly proportional to the bond price increases or decrease. The best way to valuate the American futures options (i.e. bond future options and Eurodollar futures options) is by the use of the binominal tree where the volatility parameter is dictated by the price of the bond futures options. Embedded bond options: These types of bonds are called thus because they have call and put options as a part of the option. In other words, this bond can be sold back at a pre-arranged time, after an initial lock in period of 2-3 years. Call options means permission to sell at a pre-determined time, and put options means demand to sell option at a pre-determined price, by holder and issuer respectively. Other examples of such bond options are, fixed rate loans (put option bonds), fixed rate interest deposits with pre-maturity redemption clauses, etc. Black’s Model and its use: Black’s model is a mutation from the Black Scholes Model, which uses the rate of interest as the base for pricing the options. The most important factor is that it functions on the assumptions that “a key market variable will be lognormally distributed at a future time”. When Blacks model is used to value the price of European interest rate options, the worth of future price of V(variable) for a contract maturing at time T, is usually set equal to the forward price of V rather than its futures price. However, this is more theoretical than practical since in this case you will have to assume that the rates of interest also remain constant while discounting over the same period of future, which is definitely not the case. European Bond Options: This is an option which has pre-determined selling price and time. This value is determined based on the Black’s Model assumptions, that the price is lognormal at the pre-fixed time in the future (cash price or dirty price is equal to the quoted price or clean price plus the interest accrued). The value (c) of the bond option can be worked out with the following equations using the Black’s model which sets Fo equal to the forward bond price: where, T = time to maturity of the options, F = futures price of V (variable) for a contract maturing at time T, Fo = Value of F at time zero, FT = Value of F at time T, K = strike price of the option, r = interest rate for maturity T, σ= volatility of F, VT = Value of V at time T. The bond’s forward price is also dependent on the yield volatility, though it is believed that the bond volatilities are based on price volatility. Volatility measures the standard deviation of percentage changes of the market variable (as per Black’s Model). Interest Rate Caps: This type of options have an in-built protection against the interest rates rising above a certain level. This is called cap rate. The exact value of the cap is calculated keeping in view a repetitive fixed period of time when the rate of interest is reset (called tenor) equal to the LIBOR. In this way, the option is insures that the interest rate does not rise above a certain ceiling. Another variant to this bond option is the interest rate collar, which fixes the rate of interest between two price points. This is also called a floor-ceiling agreement. What is a caplet: A caplet is an n number of call options which constitute a cap portfolio, when equation c = e-rT[F0N(d1) – KN(d2)] is calculated with the LIBOR rate taken at time t with maturity at time t What are floorlets: By interest rate floors we have the same meaning as caps. This instrument ensures that payoff when the interest rate dips below a certain level. It can be said within the equation above that, the floor gives the payoff at time tk+1 (k = 1, 2..... n) of Lmax(R-R,0). This way there will be a number of options to make a floor. Each such individual option is called a floorlet. What is a collar: An interest rate collar or a floor-ceiling agreement is an option which has the guarantee of payoff not to exceed certain levels (collars) both at the high and low ends of the interest rates. European Swap Options: These options are open-ended options that give the owner the freedom to “swap” interest rates at a certain time in the future, without imposing any obligations. With this type of option the holder will be able to take advantage of any or all favorable interest rate fluctuations in the market, with no risk. All the above models are priced on the assumptions that the bond price, the interest rate and the swap rate is lognormally distributed in the future. Logically speaking, all the three assumptions cannot be correct. This is why Black’s Model applications has limitations in applications to market reality. Another constraint of the Black Model is that it cannot be interchanged between different type of options (i.e. European and American options). Hence, a more accurate picture can be obtained by using term structure models because they do not base themselves on a market variable as the Black’s Model does, but on the fluctuations of the stock market prices. This also takes into consideration that the rates of interest do not raise or fall at a constant rate, but are influenced dynamically by the yield curve. References: 1. Chapter19 Interest Rate Options 2. Read More