Short-term interest rate options

In a later section we will examine why investors and others might want to use these exchange-traded bond options. Before this, however, we will turn our attention towards the other major exchange-traded interest rate product, short-term interest rate options. 

Euronext-LIFFE s 3-month EURIBOR futures option, traded on the Chicago Mercantile Exchange, is an actively traded short-term interest rate option that enjoys high trading volume. If these options are exercised, the buyer and the seller of the option take positions in an underlying 3-month EURIBOR futures contract. The futures contract is cash-settled and the final price at delivery is equal to 100 minus the 3-month LIBOR. 

Range accrual notes can be based on almost any qnoted market rate. In this example, the return on a dollar-denominated instrnment is linked to European short-term interest rates, but it could also be linked to exchange rates, stock or commodity prices. In most cases they are structured using strips of digital options. 

When valuing an option written on say, an equity the price of the underlying asset is the current price of the equity. When pricing an interest-rate option the underlying is obtained via a random process that described the instantaneous risk-free zero-coupon rate, which is generally termed the short rate. 

This chapter explores interest rate options—a vitat part of the European fixed income securities market. The first section tooks at exchange-traded options, where 20 bittion worth of bond options and over 250 billion of options on short-term rates change hands every day. Next, we ll look at the flexible OTC markets for interest rate options, including caps, collars, swaptions, and structured products. Finally, having explained the products themselves, we ll move on to explore how they can be used to hedge interest rate risk. 

BDT, HW, and BK models extended the Ho-Lee model to match a term structure volatility curve (for example the cap prices) in addition to the term structure. The BK model is a generalization of the BDT model and it overcomes the problem of negative interest rates assuming that the short rate r is the exponential of an Ornstein-Uhlenbeck process having time-dependent coefficients. It is popular with practitioners because it fits the swaption volatility surface well. Nevertheless, it does not have closed formulae for bonds or options on bonds. 

Calculate the price of a call option written with strike price 21 and a maturity of three months written on a non-dividend-paying stock whose current share price is 25 and whose implied volatility is 23 percent, given a short-term risk-free interest rate of 5 percent. 

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